From 09686ac207da684a6589dec61d60ae0074133312 Mon Sep 17 00:00:00 2001
From: Juan Escobar <juan.escobar@aero.obs-mip.fr>
Date: Fri, 25 Sep 2015 12:25:40 +0000
Subject: [PATCH] Juan 25/09/2015: forgotten routine for WENO5 & JPHEXT <> 1
---
src/MNH/advec_weno_k_3_aux.f90 | 4707 +++++++++++++++++---------------
1 file changed, 2444 insertions(+), 2263 deletions(-)
diff --git a/src/MNH/advec_weno_k_3_aux.f90 b/src/MNH/advec_weno_k_3_aux.f90
index bc2170c49..13c324b4a 100644
--- a/src/MNH/advec_weno_k_3_aux.f90
+++ b/src/MNH/advec_weno_k_3_aux.f90
@@ -8,12 +8,11 @@
!
INTERFACE
!
- SUBROUTINE ADVEC_WENO_K_3_UX(HLBCX,PSRC, PRUCT, PR, TPHALO2)
+ SUBROUTINE ADVEC_WENO_K_3_UX(HLBCX,PSRC, PRUCT, PR)
!
USE MODE_ll
USE MODD_LUNIT
USE MODD_CONF
-USE MODD_ARGSLIST_ll, ONLY : HALO2LIST_ll
!
CHARACTER (LEN=4), DIMENSION(2), INTENT(IN) :: HLBCX ! X direction LBC type
!
@@ -22,18 +21,16 @@ REAL, DIMENSION(:,:,:), INTENT(IN) :: PRUCT ! contrav. comp. on MASS GRID
!
! output source term
REAL, DIMENSION(:,:,:), INTENT(INOUT) :: PR
-TYPE(HALO2_ll), OPTIONAL, POINTER :: TPHALO2 ! halo2 for the field at t
!
END SUBROUTINE ADVEC_WENO_K_3_UX
!
-! ----------------------------
+!---------------------------------------------------------------------------------
!
- SUBROUTINE ADVEC_WENO_K_3_MX(HLBCX,PSRC, PRUCT, PR, TPHALO2)
+ SUBROUTINE ADVEC_WENO_K_3_MX(HLBCX,PSRC, PRUCT, PR)
!
USE MODE_ll
USE MODD_LUNIT
USE MODD_CONF
-USE MODD_ARGSLIST_ll, ONLY : HALO2LIST_ll
!
CHARACTER (LEN=4), DIMENSION(2), INTENT(IN) :: HLBCX ! X direction LBC type
!
@@ -42,18 +39,16 @@ REAL, DIMENSION(:,:,:), INTENT(IN) :: PRUCT ! contrav. comp. on MASS GRID
!
! output source term
REAL, DIMENSION(:,:,:), INTENT(INOUT) :: PR
-TYPE(HALO2_ll), OPTIONAL, POINTER :: TPHALO2 ! halo2 for the field at t
!
END SUBROUTINE ADVEC_WENO_K_3_MX
!
-! ---------------------------
+!---------------------------------------------------------------------------------
!
- SUBROUTINE ADVEC_WENO_K_3_VY(HLBCY,PSRC, PRVCT, PR, TPHALO2)
+ SUBROUTINE ADVEC_WENO_K_3_VY(HLBCY,PSRC, PRVCT, PR)
!
USE MODE_ll
USE MODD_LUNIT
USE MODD_CONF
-USE MODD_ARGSLIST_ll, ONLY : HALO2LIST_ll
!
CHARACTER (LEN=4), DIMENSION(2), INTENT(IN) :: HLBCY ! Y direction LBC type
!
@@ -63,18 +58,16 @@ REAL, DIMENSION(:,:,:), INTENT(IN) :: PRVCT ! contrav. comp. on MASS GRID
!
! output source term
REAL, DIMENSION(:,:,:), INTENT(INOUT) :: PR
-TYPE(HALO2_ll), OPTIONAL, POINTER :: TPHALO2 ! halo2 for the field at t
!
END SUBROUTINE ADVEC_WENO_K_3_VY
!
-! ------------------------------
+!---------------------------------------------------------------------------------
!
- SUBROUTINE ADVEC_WENO_K_3_MY(HLBCY,PSRC, PRVCT, PR, TPHALO2)
+ SUBROUTINE ADVEC_WENO_K_3_MY(HLBCY,PSRC, PRVCT, PR)
!
USE MODE_ll
USE MODD_LUNIT
USE MODD_CONF
-USE MODD_ARGSLIST_ll, ONLY : HALO2LIST_ll
!
CHARACTER (LEN=4), DIMENSION(2), INTENT(IN) :: HLBCY ! Y direction LBC type
!
@@ -83,11 +76,10 @@ REAL, DIMENSION(:,:,:), INTENT(IN) :: PRVCT ! contrav. comp. on MASS GRID
!
! output source term
REAL, DIMENSION(:,:,:), INTENT(INOUT) :: PR
-TYPE(HALO2_ll), OPTIONAL, POINTER :: TPHALO2 ! halo2 for the field at t
!
END SUBROUTINE ADVEC_WENO_K_3_MY
!
-! -------------------------------
+!---------------------------------------------------------------------------------
!
FUNCTION WENO_K_3_WZ(PSRC, PRWCT) RESULT(PR)
!
@@ -99,7 +91,7 @@ REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)) :: PR
!
END FUNCTION WENO_K_3_WZ
!
-! ------------------------------
+!---------------------------------------------------------------------------------
!
FUNCTION WENO_K_3_MZ(PSRC, PRWCT) RESULT(PR)
!
@@ -118,7 +110,7 @@ END MODULE MODI_ADVEC_WENO_K_3_AUX
!-----------------------------------------------------------------------------
!
! ############################################################
- SUBROUTINE ADVEC_WENO_K_3_UX(HLBCX,PSRC, PRUCT, PR, TPHALO2)
+ SUBROUTINE ADVEC_WENO_K_3_UX(HLBCX,PSRC, PRUCT, PR)
! ############################################################
!!
!!**** Computes PRUCT * PUT. Upstream fluxes of U in X direction.
@@ -131,13 +123,17 @@ END MODULE MODI_ADVEC_WENO_K_3_AUX
!!
!! MODIFICATIONS
!! -------------
+!! T. Lunet 02/10/2014: Correction of periodic boudary conditions
+!! Change of structure in order to adapt WENO to NHALOK
+!! Suppression of second layer HALO pointers
+!! Complete code documentation
+!! J.Escobar : 25/09/2015 : WENO5 & JPHEXT <> 1
!!
!-------------------------------------------------------------------------------
!
USE MODE_ll
USE MODD_LUNIT
USE MODD_CONF
-USE MODD_ARGSLIST_ll, ONLY : HALO2LIST_ll
!
IMPLICIT NONE
!
@@ -150,13 +146,12 @@ REAL, DIMENSION(:,:,:), INTENT(IN) :: PRUCT ! contrav. comp. on MASS GRID
!
! output source term
REAL, DIMENSION(:,:,:), INTENT(INOUT) :: PR
-TYPE(HALO2_ll), OPTIONAL, POINTER :: TPHALO2 ! halo2 for the field at t
!
!* 0.2 Declarations of local variables :
!
INTEGER :: IIB,IJB ! Begining useful area in x,y,z directions
INTEGER :: IIE,IJE ! End useful area in x,y,z directions
-INTEGER:: IW,IE,IWF,IEF ! Coordinate of third order diffusion area
+INTEGER :: IW,IE ! Physical boundary index
!
INTEGER:: ILUOUT,IRESP ! for prints
!
@@ -165,7 +160,6 @@ INTEGER:: ILUOUT,IRESP ! for prints
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZFPOS1, ZFPOS2, ZFPOS3
!
! intermediate reconstruction fluxes for negative wind case
-! we need only one since ZFNEG2 = ZFPOS2
!
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZFNEG1, ZFNEG2, ZFNEG3
!
@@ -174,19 +168,13 @@ REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZFNEG1, ZFNEG2, ZFNEG3
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZBPOS1, ZBPOS2, ZBPOS3
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZBNEG1, ZBNEG2, ZBNEG3
!
-! WENO weights
+! WENO non-normalized weights
!
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)) :: ZOMP1, ZOMP2, ZOMP3
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)) :: ZOMN1, ZOMN2, ZOMN3
!
-! standard weights
-!
-REAL, PARAMETER :: ZGAMMA1 = 1./10.
-REAL, PARAMETER :: ZGAMMA2 = 3./5.
-REAL, PARAMETER :: ZGAMMA3 = 3./10.
-REAL, PARAMETER :: ZGAMMA1_PRIM = 1./3.
-REAL, PARAMETER :: ZGAMMA2_PRIM = 2./3.
-!
+! EPSILON for weno weights calculation
+!
REAL, PARAMETER :: ZEPS = 1.0E-15
!
!-----------------------------------------------------------------------------
@@ -196,7 +184,6 @@ REAL, PARAMETER :: ZEPS = 1.0E-15
CALL GET_INDICE_ll(IIB,IJB,IIE,IJE)
!
!-------------------------------------------------------------------------------
-!
!* 0.4. INITIALIZE THE FIELD
! ---------------------
!
@@ -222,536 +209,560 @@ ZOMN2 = 0.0
ZOMN3 = 0.0
!
!-------------------------------------------------------------------------------
+!* 1.1. Interior Fluxes
+! ---------------------
+IW=IIB
+IE=IIE
!
-SELECT CASE ( HLBCX(1) ) ! X direction LBC type: (1) for left side
-!
-!* 1.1 CYCLIC CASE IN THE X DIRECTION:
-!
-CASE ('CYCL') ! In that case one must have HLBCX(1) == HLBCX(2)
-!
- IF(NHALO == 1) THEN
- IW=IIB
- IE=IIE
- ELSE
- CALL FMLOOK_ll(CLUOUT0,CLUOUT0,ILUOUT,IRESP)
- WRITE(ILUOUT,*) 'ERROR : 3rd order advection in CYCLic case '
- WRITE(ILUOUT,*) 'cannot be used with NHALO=2'
- CALL ABORT
- STOP
- END IF
-!
-! r: many left cells in regard to 'i' cell for each stencil
-!
-! intermediate fluxes at the mass point on Ugrid u(i+1/2,j,k) for positive wind
-! case (left to the right)
-! (r=2 for the first stencil ZFPOS1, r=1 for the second ZFPOS2 and
-! r=0 for the last ZFPOS3)
-!
- ZFPOS1(IW+1:IE-1,:,:) = 1./6 * (2.0*PSRC(IW-1:IE-3,:,:) - &
- 7.0*PSRC(IW:IE-2,:,:) + 11.0*PSRC(IW+1:IE-1,:,:))
- ZFPOS1(IW, :,:) = 1./6 * (2.0*TPHALO2%WEST(:,:) - &
- 7.0*PSRC(IW-1, :,:) + 11.0*PSRC(IW, :,:))
- ZFPOS1(IW-1, :,:) = 0.5 * (3.0*PSRC(IW-1 ,:,:) - TPHALO2%WEST(:,:))
- ZFPOS1(IE, :,:) = 0.5 * (3.0*PSRC(IE ,:,:) - PSRC(IE-1, :,:))
- ZFPOS1(IE+1, :,:) = 0.5 * (3.0*PSRC(IE+1 ,:,:) - PSRC(IE, :,:))
-!
-!
- ZFPOS2(IW:IE-1,:,:) = 1./6 * (-1.0*PSRC(IW-1:IE-2,:,:) + 5.0*PSRC(IW:IE-1,:,:) + 2.0*PSRC(IW+1:IE,:,:))
- ZFPOS2(IW-1, :,:) = 0.5 * (PSRC(IW-1 ,:,:) + PSRC(IW, :,:))
- ZFPOS2(IE, :,:) = 0.5 * (PSRC(IE ,:,:) + PSRC(IE+1, :,:))
- ZFPOS2(IE+1, :,:) = 0.5 * (PSRC(IE+1 ,:,:) + TPHALO2%EAST(:,:))
+!-------------------------------------------------------------------------------
+! Flux calculation in the physical domain far enough from the boundary
+! WENO scheme order 5, IW+1 -> IE-2
+! Computation at the mass point on Ugrid u(i+1/2,j,k)
+!-------------------------------------------------------------------------------
!
- ZFPOS3(IW:IE-1,:,:) = 1./6 * (2.0*PSRC(IW:IE-1,:,:) + 5.0*PSRC(IW+1:IE,:,:) &
- - PSRC(IW+2:IE+1,:,:))
+! ----- Positive fluxes -----
+!
+! First positive stencil, needs indices i-2, i-1, i
+ZFPOS1(IW+1:IE-2,:,:) = 1./6. * (2.0*PSRC(IW-1:IE-4,:,:) - 7.0*PSRC(IW:IE-3,:,:) + 11.0*PSRC(IW+1:IE-2,:,:)) ! Flux
+ZBPOS1(IW+1:IE-2,:,:) = 13./12. * ( PSRC(IW-1:IE-4,:,:) - 2.0*PSRC(IW:IE-3,:,:) + PSRC(IW+1:IE-2,:,:))**2 &
+ + 1./4 * ( PSRC(IW-1:IE-4,:,:) - 4.0*PSRC(IW:IE-3,:,:) + 3.0* PSRC(IW+1:IE-2,:,:))**2 ! Smoothness indicator
+ZOMP1(IW+1:IE-2,:,:) = 1./10. / (ZEPS + ZBPOS1(IW+1:IE-2,:,:))**2
+!
+! Second positive stencil, needs indices i-1, i, i+1
+ZFPOS2(IW+1:IE-2,:,:) = 1./6. * (-1.0*PSRC(IW:IE-3,:,:) + 5.0*PSRC(IW+1:IE-2,:,:) + 2.0*PSRC(IW+2:IE-1,:,:))! Flux
+ZBPOS2(IW+1:IE-2,:,:) = 13./12 * ( PSRC(IW:IE-3,:,:) - 2.0*PSRC(IW+1:IE-2,:,:) + PSRC(IW+2:IE-1,:,:))**2 &
+ + 1./4 * ( PSRC(IW:IE-3,:,:) - PSRC(IW+2:IE-1,:,:))**2! Smoothness indicator
+ZOMP2(IW+1:IE-2,:,:) = 3./5. / (ZEPS + ZBPOS2(IW+1:IE-2,:,:))**2
+!
+! Third positive stencil, needs indices i, i+1, i+2
+ZFPOS3(IW+1:IE-2,:,:) = 1./6 * (2.0*PSRC(IW+1:IE-2,:,:) + 5.0*PSRC(IW+2:IE-1,:,:) - PSRC(IW+3:IE,:,:))! Flux
+ZBPOS3(IW+1:IE-2,:,:) = 13./12 * (PSRC(IW+1:IE-2,:,:) - 2.0*PSRC(IW+2:IE-1,:,:) + PSRC(IW+3:IE,:,:))**2 &
++ 1./4 * (3.0*PSRC(IW+1:IE-2,:,:) - 4.0*PSRC(IW+2:IE-1,:,:) + PSRC(IW+3:IE,:,:))**2! Smoothness indicator
+ZOMP3(IW+1:IE-2,:,:) = 3./10. / (ZEPS + ZBPOS3(IW+1:IE-2,:,:))**2
+!
+! ----- Negative fluxes -----
+!
+! First negative stencil, needs indices i+1, i+2, i+3
+ZFNEG1(IW+1:IE-2,:,:) = 1./6. * (11.0*PSRC(IW+2:IE-1,:,:) - 7.0*PSRC(IW+3:IE,:,:) + 2.0*PSRC(IW+4:IE+1,:,:)) ! Flux
+ZBNEG1(IW+1:IE-2,:,:) = 13./12. * ( PSRC(IW+2:IE-1,:,:) - 2.0*PSRC(IW+3:IE,:,:) + PSRC(IW+4:IE+1,:,:))**2 &
+ + 1./4 * (3.0* PSRC(IW+2:IE-1,:,:) - 4.0*PSRC(IW+3:IE,:,:) + PSRC(IW+4:IE+1,:,:))**2 ! Smoothness indicator
+ZOMN1(IW+1:IE-2,:,:) = 1./10. / (ZEPS + ZBNEG1(IW+1:IE-2,:,:))**2
+!
+! Second negative stencil, needs indices i, i+1, i+2
+ZFNEG2(IW+1:IE-2,:,:) = 1./6. * (2.0*PSRC(IW+1:IE-2,:,:) + 5.0*PSRC(IW+2:IE-1,:,:) - 1.0*PSRC(IW+3:IE,:,:))! Flux
+ZBNEG2(IW+1:IE-2,:,:) = 13./12 * ( PSRC(IW+1:IE-2,:,:) - 2.0*PSRC(IW+2:IE-1,:,:) + PSRC(IW+3:IE,:,:))**2 &
+ + 1./4 * ( PSRC(IW+1:IE-2,:,:) - PSRC(IW+3:IE,:,:))**2! Smoothness indicator
+ZOMN2(IW+1:IE-2,:,:) = 3./5. / (ZEPS + ZBNEG2(IW+1:IE-2,:,:))**2! Non-normalized weight
+!
+! Third negative stencil, needs indices i-1, i, i+1
+ZFNEG3(IW+1:IE-2,:,:) = 1./6 * (-1.0*PSRC(IW:IE-3,:,:) + 5.0*PSRC(IW+1:IE-2,:,:) + 2.0*PSRC(IW+2:IE-1,:,:))! Flux
+ZBNEG3(IW+1:IE-2,:,:) = 13./12 * ( PSRC(IW:IE-3,:,:) - 2.0*PSRC(IW+1:IE-2,:,:) + PSRC(IW+2:IE-1,:,:))**2 &
+ + 1./4 * ( PSRC(IW:IE-3,:,:) - 4.0*PSRC(IW+1:IE-2,:,:) + 3.0*PSRC(IW+2:IE-1,:,:))**2! Smoothness indicator
+ZOMN3(IW+1:IE-2,:,:) = 3./10. / (ZEPS + ZBNEG3(IW+1:IE-2,:,:))**2! Non-normalized weight
+!
+!
+! ----- Total flux -----
+!
+PR(IW+1:IE-2,:,:) = (ZOMP1(IW+1:IE-2,:,:)/(ZOMP1(IW+1:IE-2,:,:)+ZOMP2(IW+1:IE-2,:,:)+ZOMP3(IW+1:IE-2,:,:)) &
+ * ZFPOS1(IW+1:IE-2,:,:) + &
+ ZOMP2(IW+1:IE-2,:,:)/(ZOMP1(IW+1:IE-2,:,:)+ZOMP2(IW+1:IE-2,:,:)+ZOMP3(IW+1:IE-2,:,:)) &
+ * ZFPOS2(IW+1:IE-2,:,:) + &
+ ZOMP3(IW+1:IE-2,:,:)/(ZOMP1(IW+1:IE-2,:,:)+ZOMP2(IW+1:IE-2,:,:)+ZOMP3(IW+1:IE-2,:,:)) &
+ * ZFPOS3(IW+1:IE-2,:,:)) &
+ * (0.5+SIGN(0.5,PRUCT(IW+1:IE-2,:,:))) &
+ + (ZOMN1(IW+1:IE-2,:,:)/(ZOMN1(IW+1:IE-2,:,:)+ZOMN2(IW+1:IE-2,:,:)+ZOMN3(IW+1:IE-2,:,:)) &
+ * ZFNEG1(IW+1:IE-2,:,:) &
+ + ZOMN2(IW+1:IE-2,:,:)/(ZOMN1(IW+1:IE-2,:,:)+ZOMN2(IW+1:IE-2,:,:)+ZOMN3(IW+1:IE-2,:,:)) &
+ * ZFNEG2(IW+1:IE-2,:,:) &
+ + ZOMN3(IW+1:IE-2,:,:)/(ZOMN1(IW+1:IE-2,:,:)+ZOMN2(IW+1:IE-2,:,:)+ZOMN3(IW+1:IE-2,:,:)) &
+ * ZFNEG3(IW+1:IE-2,:,:)) &
+ * (0.5-SIGN(0.5,PRUCT(IW+1:IE-2,:,:)))
!
+!-------------------------------------------------------------------------------
+!* 1.2. West border
+! ---------------------
!
-! r: many left cells in regard to 'i+1' cell for each stencil
+IF( LWEST_ll() .AND. .FALSE. ) THEN
+!-----------------------------------------------------------------------------
+! West border is physical -- IW,IW-1
+!-----------------------------------------------------------------------------
+SELECT CASE (HLBCX(1)) ! X direction LBC type on left side
!
-! intermediate flux at the mass point on Ugrid (i+1/2,j,k)=((i+1)-1/2,j,k) for
-! negative wind case (right to the left)
-! (r=2 for the last stencil ZFNEG3=ZFPOS2, r=1 for the second ZFNEG2=ZFPOS3
-! and r=0 for the first ZFNEG1)
-!
- ZFNEG1(IW:IE-2,:,:) = 1./6 * (11.0*PSRC(IW+1:IE-1,:,:) - &
- 7.0*PSRC(IW+2:IE,:,:) + 2.0*PSRC(IW+3:IE+1,:,:))
- ZFNEG1(IE-1, :,:) = 1./6 * (11.0*PSRC(IE, :,:) - &
- 7.0*PSRC(IE+1, :,:) + 2.0*TPHALO2%EAST(:,:))
- ZFNEG1(IE, :,:) = 0.5 * (3.0*PSRC(IE+1,:,:) - TPHALO2%EAST(:,:))
- ZFNEG1(IE+1,:,:) = - 999.
- ZFNEG1(IW-1,:,:) = 0.5 * (3.0*PSRC(IW, :,:) - PSRC(IW+1, :,:))
+CASE ('CYCL')
+!---------------------------------------------------------------------------
+! Periodic boundary condition
+!---------------------------------------------------------------------------
!
+IF( LEAST_ll() .AND. .FALSE. ) THEN! East boundary is physical (monoproc)
+!
+! First positive stencil, needs indices i-2, i-1, i
+ZFPOS1(IW,:,:) = 1./6. * (2.0*PSRC(IE,:,:) - 7.0*PSRC(IW-1,:,:) + 11.0*PSRC(IW,:,:))! Flux IW
+ZFPOS1(IW-1,:,:) = 1./6. * (2.0*PSRC(IE-1,:,:) - 7.0*PSRC(IE,:,:) + 11.0*PSRC(IW-1,:,:))! Flux IW-1
+ZBPOS1(IW,:,:) = 13./12. * (PSRC(IE,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IE,:,:) - 4.0*PSRC(IW-1,:,:) + 3.0*PSRC(IW,:,:))**2 ! Smoothness indicator IW
+ZBPOS1(IW-1,:,:) = 13./12. * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IW-1,:,:))**2 &
+ + 1./4 * (PSRC(IE-1,:,:) - 4.0*PSRC(IE,:,:) + 3.0*PSRC(IW-1,:,:))**2 ! Smoothness indicator IW-1
+ZOMP1(IW-1:IW,:,:) = 1./10. / (ZEPS + ZBPOS1(IW-1:IW,:,:))**2! Non-normalized weight IW,IW-1
+!
+! Second positive stencil, needs indices i-1, i, i+1
+ZFPOS2(IW,:,:) = 1./6.* (-1.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) + 2.0*PSRC(IW+1,:,:))! Flux IW
+ZFPOS2(IW-1,:,:) = 1./6.* (-1.0*PSRC(IE,:,:) + 5.0*PSRC(IW-1,:,:) + 2.0*PSRC(IW,:,:)) ! Flux IW-1
+ZBPOS2(IW,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (PSRC(IW-1,:,:) - PSRC(IW+1,:,:))**2! Smoothness indicator IW
+ZBPOS2(IW-1,:,:) = 13./12 * (PSRC(IE,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IE,:,:) - PSRC(IW,:,:))**2! Smoothness indicator IW-1
+ZOMP2(IW-1:IW,:,:) = 3./5. / (ZEPS + ZBPOS2(IW-1:IW,:,:))**2! Non-normalized weight IW,IW-1
+!
+! Third negative stencil, needs indices i-1, i, i+1
+ZFNEG3(IW,:,:) = 1./6 * (-1.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) + 2.0*PSRC(IW+1,:,:))! Flux IW
+ZFNEG3(IW-1,:,:) = 1./6 * (-1.0*PSRC(IE,:,:) + 5.0*PSRC(IW-1,:,:) + 2.0*PSRC(IW,:,:))! Flux IW-1
+ZBNEG3(IW,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (PSRC(IW-1,:,:) - 4.0*PSRC(IW,:,:) + 3.0*PSRC(IW+1,:,:))**2! Smoothness indicator IW
+ZBNEG3(IW-1,:,:) = 13./12 * (PSRC(IE,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IE,:,:) - 4.0*PSRC(IW-1,:,:) + 3.0*PSRC(IW,:,:))**2! Smoothness indicator IW-1
+ZOMN3(IW-1:IW,:,:) = 3./10. / (ZEPS + ZBNEG3(IW-1:IW,:,:))**2! Non-normalized weight IW,IW-1
!
- ZFNEG2(IW:IE-1,:,:) = 1./6 * (2.0*PSRC(IW:IE-1,:,:) + &
- 5.0*PSRC(IW+1:IE,:,:) - PSRC(IW+2:IE+1,:,:))
- ZFNEG2(IE, :,:) = 0.5 * (PSRC(IE, :,:) + PSRC(IE+1,:,:))
- ZFNEG2(IE+1,:,:) = 0.5 * (PSRC(IE+1, :,:) + TPHALO2%EAST(:,:))
- ZFNEG2(IW-1,:,:) = 0.5 * (PSRC(IW-1, :,:) + PSRC(IW,:,:))
-!
-!
- ZFNEG3(IW:IE-1,:,:) = 1./6 * (-1.0*PSRC(IW-1:IE-2,:,:) + &
- 5.0*PSRC(IW:IE-1,:,:) + 2.0*PSRC(IW+1:IE,:,:))
-!
-! smoothness indicators for positive wind case
-!
- ZBPOS1(IW+1:IE-1,:,:) = 13./12 * (PSRC(IW-1:IE-3,:,:) - 2.0*PSRC(IW:IE-2,:,:)&
- + PSRC(IW+1:IE-1,:,:))**2 + 1./4 * (PSRC(IW-1:IE-3,:,:) &
- - 4.0*PSRC(IW:IE-2,:,:) + 3.0*PSRC(IW+1:IE-1,:,:))**2
- ZBPOS1(IW, :,:) = 13./12 * (TPHALO2%WEST(:,:) - 2.0*PSRC(IW-1,:,:) + &
- PSRC(IW,:,:))**2 + 1./4 * (TPHALO2%WEST(:,:) - &
- 4.0*PSRC(IW-1,:,:) + 3.0*PSRC(IW,:,:))**2
- ZBPOS1(IW-1, :,:) = (PSRC(IW-1,:,:) - TPHALO2%WEST(:,:))**2
- ZBPOS1(IE, :,:) = (PSRC(IE ,:,:) - PSRC(IE-1, :,:))**2
- ZBPOS1(IE+1, :,:) = (PSRC(IE+1,:,:) - PSRC(IE, :,:))**2
-!
-!
- ZBPOS2(IW:IE-1,:,:) = 13./12 * (PSRC(IW-1:IE-2,:,:) - 2.0*PSRC(IW:IE-1,:,:) +&
- PSRC(IW+1:IE,:,:))**2 + 1./4 * (PSRC(IW-1:IE-2,:,:) - PSRC(IW+1:IE,:,:))**2
- ZBPOS2(IW-1,:,:) = (PSRC(IW, :,:) - PSRC(IW-1,:,:))**2
- ZBPOS2(IE, :,:) = (PSRC(IE+1,:,:) - PSRC(IE, :,:))**2
- ZBPOS2(IE+1,:,:) = (TPHALO2%EAST(:,:) - PSRC(IE+1,:,:))**2
-!
-!
- ZBPOS3(IW:IE-1,:,:) = 13./12 * (PSRC(IW:IE-1,:,:) - 2.0*PSRC(IW+1:IE,:,:) + &
- PSRC(IW+2:IE+1,:,:))**2 + 1./4 * ( 3.0*PSRC(IW:IE-1,:,:) - &
- 4.0*PSRC(IW+1:IE,:,:) + PSRC(IW+2:IE+1,:,:))**2
-!
-! smoothness indicators for negative wind case
-!
- ZBNEG1(IW:IE-2,:,:) = 13./12 * (PSRC(IW+1:IE-1,:,:) - 2.0*PSRC(IW+2:IE,:,:) +&
- PSRC(IW+3:IE+1,:,:))**2 + 1./4 * ( 3.0*PSRC(IW+1:IE-1,:,:) - &
- 4.0*PSRC(IW+2:IE,:,:) + PSRC(IW+3:IE+1,:,:))**2
- ZBNEG1(IE-1, :,:) = 13./12 * (PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + &
- TPHALO2%EAST(:,:))**2 + 1./4 * ( 3.0*PSRC(IE,:,:) - &
- 4.0*PSRC(IE+1,:,:) + TPHALO2%EAST(:,:))**2
- ZBNEG1(IE, :,:) = (PSRC(IE+1, :,:) - TPHALO2%EAST(:,:))**2
- ZBNEG1(IE+1, :,:) = - 999.
- ZBNEG1(IW-1, :,:) = (PSRC(IW, :,:) - PSRC(IW+1, :,:))**2
-!
-!
- ZBNEG2(IW:IE-1,:,:) = 13./12 * (PSRC(IW:IE-1,:,:) - 2.0*PSRC(IW+1:IE,:,:) + &
- PSRC(IW+2:IE+1,:,:))**2 + 1./4 * (PSRC(IW:IE-1,:,:) - PSRC(IW+2:IE+1,:,:))**2
- ZBNEG2(IW-1,:,:) = (PSRC(IW-1,:,:) - PSRC(IW, :,:))**2
- ZBNEG2(IE ,:,:) = (PSRC(IE, :,:) - PSRC(IE+1,:,:))**2
- ZBNEG2(IE+1,:,:) = (PSRC(IE+1,:,:) - TPHALO2%EAST(:,:))**2
-!
+ELSEIF(IW>3) THEN! East boundary is proc border, with minimum 3 HALO points on west side
+!
+! First positive stencil, needs indices i-2, i-1, i
+ZFPOS1(IW,:,:) = 1./6. * (2.0*PSRC(IW-2,:,:) - 7.0*PSRC(IW-1,:,:) + 11.0*PSRC(IW,:,:))! Flux IW
+ZFPOS1(IW-1,:,:) = 1./6. * (2.0*PSRC(IW-3,:,:) - 7.0*PSRC(IW-2,:,:) + 11.0*PSRC(IW-1,:,:))! Flux IW-1
+ZBPOS1(IW,:,:) = 13./12. * (PSRC(IW-1,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IW-1,:,:) - 4.0*PSRC(IW-1,:,:) + 3.0*PSRC(IW,:,:))**2 ! Smoothness indicator IW
+ZBPOS1(IW-1,:,:) = 13./12. * (PSRC(IW-3,:,:) - 2.0*PSRC(IW-2,:,:) + PSRC(IW-1,:,:))**2 &
+ + 1./4 * (PSRC(IW-3,:,:) - 4.0*PSRC(IW-2,:,:) + 3.0*PSRC(IW-1,:,:))**2 ! Smoothness indicator IW-1
+ZOMP1(IW-1:IW,:,:) = 1./10. / (ZEPS + ZBPOS1(IW-1:IW,:,:))**2! Non-normalized weight IW,IW-1
+!
+! Second positive stencil, needs indices i-1, i, i+1
+ZFPOS2(IW,:,:) = 1./6.* (-1.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) + 2.0*PSRC(IW+1,:,:))! Flux IW
+ZFPOS2(IW-1,:,:) = 1./6.* (-1.0*PSRC(IW-2,:,:) + 5.0*PSRC(IW-1,:,:) + 2.0*PSRC(IW,:,:))! Flux IW-1
+ZBPOS2(IW,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (PSRC(IW-1,:,:) - PSRC(IW+1,:,:))**2! Smoothness indicator IW
+ZBPOS2(IW-1,:,:) = 13./12 * (PSRC(IW-2,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IW-2,:,:) - PSRC(IW,:,:))**2! Smoothness indicator IW-1
+ZOMP2(IW-1:IW,:,:) = 3./5. / (ZEPS + ZBPOS2(IW-1:IW,:,:))**2! Non-normalized weight IW,IW-1
+!
+! Third negative stencil, needs indices i-1, i, i+1
+ZFNEG3(IW,:,:) = 1./6 * (-1.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) + 2.0*PSRC(IW+1,:,:))! Flux IW
+ ZFNEG3(IW-1,:,:) = 1./6 * (-1.0*PSRC(IW-2,:,:) + 5.0*PSRC(IW-1,:,:) + 2.0*PSRC(IW,:,:)) ! Flux IW-1
+ ZBNEG3(IW,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (PSRC(IW-1,:,:) - 4.0*PSRC(IW,:,:) + 3.0*PSRC(IW+1,:,:))**2 ! Smoothness indicator IW
+ ZBNEG3(IW-1,:,:) = 13./12 * (PSRC(IW-2,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IW-2,:,:) - 4.0*PSRC(IW-1,:,:) + 3.0*PSRC(IW,:,:))**2 ! Smoothness indicator IW-1
+ ZOMN3(IW-1:IW,:,:) = 3./10. / (ZEPS + ZBNEG3(IW-1:IW,:,:))**2 ! Non-normalized weight IW,IW-1
+!
+ ELSE ! East boundary is proc border, with NHALO < 3 on west side
+ PRINT *,'WARNING : WENO5 fluxes calculation needs NHALO >= 3 on west side'
+ CALL ABORT
+ ENDIF
+!
+ ! Third positive stencil, needs indices i, i+1, i+2
+ ZFPOS3(IW,:,:) = 1./6 * (2.0*PSRC(IW,:,:) + 5.0*PSRC(IW+1,:,:) - PSRC(IW+2,:,:)) ! Flux IW
+ ZFPOS3(IW-1,:,:) = 1./6 * (2.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) - PSRC(IW+1,:,:)) ! Flux IW-1
+ ZBPOS3(IW,:,:) = 13./12 * ( PSRC(IW,:,:) - 2.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IW,:,:) - 4.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 ! Smoothness indicator IW
+ ZBPOS3(IW-1,:,:) = 13./12 * ( PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IW-1,:,:) - 4.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 ! Smoothness indicator IW-1
+ ZOMP3(IW-1:IW,:,:) = 3./10. / (ZEPS + ZBPOS3(IW-1:IW,:,:))**2 ! Non-normalized weight IW,IW-1
+!
+ ! First negative stencil, needs indices i+1, i+2, i+3
+ ZFNEG1(IW,:,:) = 1./6. * (11.0*PSRC(IW+1,:,:) - 7.0*PSRC(IW+2,:,:) + 2.0*PSRC(IW+3,:,:)) ! Flux IW
+ ZFNEG1(IW-1,:,:) = 1./6. * (11.0*PSRC(IW,:,:) - 7.0*PSRC(IW+1,:,:) + 2.0*PSRC(IW+2,:,:)) ! Flux IW-1
+ ZBNEG1(IW,:,:) = 13./12. * ( PSRC(IW+1,:,:) - 2.0*PSRC(IW+2,:,:) + PSRC(IW+3,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IW+1,:,:) - 4.0*PSRC(IW+2,:,:) + PSRC(IW+3,:,:))**2 ! Smoothness indicator IW
+ ZBNEG1(IW-1,:,:) = 13./12. * ( PSRC(IW,:,:) - 2.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IW,:,:) - 4.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 ! Smoothness indicator IW-1
+ ZOMN1(IW-1:IW,:,:) = 1./10. / (ZEPS + ZBNEG1(IW-1:IW,:,:))**2 ! Non-normalized weight IW,IW-1
+!
+ ! Second negative stencil, needs indices i, i+1, i+2
+ ZFNEG2(IW,:,:) = 1./6. * (2.0*PSRC(IW,:,:) + 5.0*PSRC(IW+1,:,:) - 1.0*PSRC(IW+2,:,:)) ! Flux IW
+ ZFNEG2(IW-1,:,:) = 1./6. * (2.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) - 1.0*PSRC(IW+1,:,:)) ! Flux IW-1
+ ZBNEG2(IW,:,:) = 13./12 * (PSRC(IW,:,:) - 2.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 &
+ + 1./4 * (PSRC(IW,:,:) - PSRC(IW+2,:,:))**2 ! Smoothness indicator IW
+ ZBNEG2(IW-1,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (PSRC(IW-1,:,:) - PSRC(IW+1,:,:))**2 ! Smoothness indicator IW-1
+ ZOMN2(IW-1:IW,:,:) = 3./5. / (ZEPS + ZBNEG2(IW-1:IW,:,:))**2 ! Non-normalized weight IW,IW-1
+!
+ ! ----- Total flux -----
+!
+ PR(IW-1:IW,:,:) = ( ZOMP1(IW-1:IW,:,:)/(ZOMP1(IW-1:IW,:,:)+ZOMP2(IW-1:IW,:,:)+ZOMP3(IW-1:IW,:,:)) * ZFPOS1(IW-1:IW,:,:) &
+ + ZOMP2(IW-1:IW,:,:)/(ZOMP1(IW-1:IW,:,:)+ZOMP2(IW-1:IW,:,:)+ZOMP3(IW-1:IW,:,:)) * ZFPOS2(IW-1:IW,:,:) &
+ + ZOMP3(IW-1:IW,:,:)/(ZOMP1(IW-1:IW,:,:)+ZOMP2(IW-1:IW,:,:)+ZOMP3(IW-1:IW,:,:)) * ZFPOS3(IW-1:IW,:,:)) &
+ * (0.5+SIGN(0.5,PRUCT(IW-1:IW,:,:))) &
+ + ( ZOMN1(IW-1:IW,:,:)/(ZOMN1(IW-1:IW,:,:)+ZOMN2(IW-1:IW,:,:)+ZOMN3(IW-1:IW,:,:)) * ZFNEG1(IW-1:IW,:,:) &
+ + ZOMN2(IW-1:IW,:,:)/(ZOMN1(IW-1:IW,:,:)+ZOMN2(IW-1:IW,:,:)+ZOMN3(IW-1:IW,:,:)) * ZFNEG2(IW-1:IW,:,:) &
+ + ZOMN3(IW-1:IW,:,:)/(ZOMN1(IW-1:IW,:,:)+ZOMN2(IW-1:IW,:,:)+ZOMN3(IW-1:IW,:,:)) * ZFNEG3(IW-1:IW,:,:)) &
+ * (0.5-SIGN(0.5,PRUCT(IW-1:IW,:,:)))
+!
+!
+ CASE ('OPEN','WALL','NEST')
+ !---------------------------------------------------------------------------
+ ! Open, or Wall, or Nest boundary condition => WENO order reduction
+ !---------------------------------------------------------------------------
+!
+ ! WENO scheme order 1, IW-1
+ PR(IW-1,:,:) = PSRC(IW-1,:,:) * (0.5+SIGN(0.5,PRUCT(IW-1,:,:))) + &
+ PSRC(IW,:,:) * &
+ (0.5-SIGN(0.5,PRUCT(IW-1,:,:)))
!
- ZBNEG3(IW:IE-1,:,:) = 13./12 * (PSRC(IW-1:IE-2,:,:) - 2.0*PSRC(IW:IE-1,:,:) +&
- PSRC(IW+1:IE,:,:))**2 + 1./4 * ( PSRC(IW-1:IE-2,:,:) - &
- 4.0*PSRC(IW:IE-1,:,:) + 3.0*PSRC(IW+1:IE,:,:))**2
+! ! WENO scheme order 3, IW
+ ZFPOS1(IW,:,:) = 0.5 * (3.0*PSRC(IW,:,:) - PSRC(IW-1,:,:)) ! First positive flux
+ ZFPOS2(IW,:,:) = 0.5 * ( PSRC(IW,:,:) + PSRC(IW+1,:,:)) ! Second positive flux
+ ZBPOS1(IW,:,:) = (PSRC(IW,:,:) - PSRC(IW-1,:,:))**2 ! First positive smoothness indicator
+ ZBPOS2(IW,:,:) = (PSRC(IW+1,:,:) - PSRC(IW,:,:))**2 ! Second positive smoothness indicator
+!
+ ZFNEG1(IW,:,:) = 0.5 * (3.0*PSRC(IW+1,:,:) - PSRC(IW+2,:,:)) ! First negative flux
+ ZFNEG2(IW,:,:) = 0.5 * ( PSRC(IW,:,:) + PSRC(IW+1,:,:)) ! Second negative flux
+ ZBNEG1(IW,:,:) = (PSRC(IW+1,:,:) - PSRC(IW+2,:,:))**2 ! First negative smoothness indicator
+ ZBNEG2(IW,:,:) = (PSRC(IW,:,:) - PSRC(IW+1,:,:))**2 ! Second negative smoothness indicator
+!
+ ZOMP1(IW,:,:) = 1./3. / (ZEPS + ZBPOS1(IW,:,:))**2 ! First positive non-normalized weight
+ ZOMP2(IW,:,:) = 2./3. / (ZEPS + ZBPOS2(IW,:,:))**2 ! Second positive non-normalized weight
+ ZOMN1(IW,:,:) = 1./3. / (ZEPS + ZBNEG1(IW,:,:))**2 ! First negative non-normalized weight
+ ZOMN2(IW,:,:) = 2./3. / (ZEPS + ZBNEG2(IW,:,:))**2 ! Second negative non-normalized weight
+!
+ PR(IW,:,:) = (ZOMN2(IW,:,:)/(ZOMN1(IW,:,:)+ZOMN2(IW,:,:)) * ZFNEG2(IW,:,:) + &
+ (ZOMN1(IW,:,:)/(ZOMN1(IW,:,:)+ZOMN2(IW,:,:)) * ZFNEG1(IW,:,:))) &
+ *(0.5-SIGN(0.5,PRUCT(IW,:,:))) + &
+ (ZOMP2(IW,:,:)/(ZOMP1(IW,:,:)+ZOMP2(IW,:,:)) * ZFPOS2(IW,:,:) + &
+ (ZOMP1(IW,:,:)/(ZOMP1(IW,:,:)+ZOMP2(IW,:,:)) * ZFPOS1(IW,:,:))) &
+ *(0.5+SIGN(0.5,PRUCT(IW,:,:))) ! Total flux
+!
+ END SELECT ! SELECT CASE (HLBCX(1)) ! X direction LBC type on left side
+!
+ELSE
+ !-----------------------------------------------------------------------------
+ ! West border is proc border -- IW,IW-1
+ !-----------------------------------------------------------------------------
+!
+ IF (NHALO<3) THEN
+ PRINT *,'WARNING : WENO5 not parallelisable with NHALO < 3'
+ CALL ABORT
+ ELSEIF (NHALO>=3) THEN
+ !---------------------------------------------------------------------------
+ ! NHALO >3 => WENO5 for all boundary points
+ !---------------------------------------------------------------------------
+!
+ ! ----- Positive fluxes -----
+!
+ ! First positive stencil, needs indices i-2, i-1, i
+ ZFPOS1(IW,:,:) = 1./6. * (2.0*PSRC(IW-2,:,:) - 7.0*PSRC(IW-1,:,:) + 11.0*PSRC(IW,:,:)) ! Flux IW
+ ZFPOS1(IW-1,:,:) = 1./6. * (2.0*PSRC(IW-3,:,:) - 7.0*PSRC(IW-2,:,:) + 11.0*PSRC(IW-1,:,:)) ! Flux IW-1
+ ZBPOS1(IW,:,:) = 13./12. * (PSRC(IW-2,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IW-2,:,:) - 4.0*PSRC(IW-1,:,:) + 3.0*PSRC(IW,:,:))**2 ! Smoothness indicator IW
+ ZBPOS1(IW-1,:,:) = 13./12. * (PSRC(IW-3,:,:) - 2.0*PSRC(IW-2,:,:) + PSRC(IW-1,:,:))**2 &
+ + 1./4 * (PSRC(IW-3,:,:) - 4.0*PSRC(IW-2,:,:) + 3.0*PSRC(IW-1,:,:))**2 ! Smoothness indicator IW-1
+ ZOMP1(IW-1:IW,:,:) = 1./10. / (ZEPS + ZBPOS1(IW-1:IW,:,:))**2 ! Non-normalized weight IW,IW-1
+!
+ ! Second positive stencil, needs indices i-1, i, i+1
+ ZFPOS2(IW,:,:) = 1./6.* (-1.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) + 2.0*PSRC(IW+1,:,:)) ! Flux IW
+ ZFPOS2(IW-1,:,:) = 1./6.* (-1.0*PSRC(IW-2,:,:) + 5.0*PSRC(IW-1,:,:) + 2.0*PSRC(IW,:,:)) ! Flux IW-1
+ ZBPOS2(IW,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (PSRC(IW-1,:,:) - PSRC(IW+1,:,:))**2 ! Smoothness indicator IW
+ ZBPOS2(IW-1,:,:) = 13./12 * (PSRC(IW-2,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IW-2,:,:) - PSRC(IW,:,:))**2 ! Smoothness indicator IW-1
+ ZOMP2(IW-1:IW,:,:) = 3./5. / (ZEPS + ZBPOS2(IW-1:IW,:,:))**2 ! Non-normalized weight IW,IW-1
+!
+ ! Third positive stencil, needs indices i, i+1, i+2
+ ZFPOS3(IW,:,:) = 1./6 * (2.0*PSRC(IW,:,:) + 5.0*PSRC(IW+1,:,:) - PSRC(IW+2,:,:)) ! Flux IW
+ ZFPOS3(IW-1,:,:) = 1./6 * (2.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) - PSRC(IW+1,:,:)) ! Flux IW-1
+ ZBPOS3(IW,:,:) = 13./12 * ( PSRC(IW,:,:) - 2.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IW,:,:) - 4.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 ! Smoothness indicator IW
+ ZBPOS3(IW-1,:,:) = 13./12 * ( PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IW-1,:,:) - 4.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 ! Smoothness indicator IW-1
+ ZOMP3(IW-1:IW,:,:) = 3./10. / (ZEPS + ZBPOS3(IW-1:IW,:,:))**2 ! Non-normalized weight IW,IW-1
+!
+ ! ----- Negative fluxes -----
+!
+ ! First negative stencil, needs indices i+1, i+2, i+3
+ ZFNEG1(IW,:,:) = 1./6. * (11.0*PSRC(IW+1,:,:) - 7.0*PSRC(IW+2,:,:) + 2.0*PSRC(IW+3,:,:)) ! Flux IW
+ ZFNEG1(IW-1,:,:) = 1./6. * (11.0*PSRC(IW,:,:) - 7.0*PSRC(IW+1,:,:) + 2.0*PSRC(IW+2,:,:)) ! Flux IW-1
+ ZBNEG1(IW,:,:) = 13./12. * ( PSRC(IW+1,:,:) - 2.0*PSRC(IW+2,:,:) + PSRC(IW+3,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IW+1,:,:) - 4.0*PSRC(IW+2,:,:) + PSRC(IW+3,:,:))**2 ! Smoothness indicator IW
+ ZBNEG1(IW-1,:,:) = 13./12. * ( PSRC(IW,:,:) - 2.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IW,:,:) - 4.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 ! Smoothness indicator IW-1
+ ZOMN1(IW-1:IW,:,:) = 1./10. / (ZEPS + ZBNEG1(IW-1:IW,:,:))**2 ! Non-normalized weight IW,IW-1
+!
+ ! Second negative stencil, needs indices i, i+1, i+2
+ ZFNEG2(IW,:,:) = 1./6. * (2.0*PSRC(IW,:,:) + 5.0*PSRC(IW+1,:,:) - 1.0*PSRC(IW+2,:,:)) ! Flux IW
+ ZFNEG2(IW-1,:,:) = 1./6. * (2.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) - 1.0*PSRC(IW+1,:,:)) ! Flux IW-1
+ ZBNEG2(IW,:,:) = 13./12 * (PSRC(IW,:,:) - 2.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 &
+ + 1./4 * (PSRC(IW,:,:) - PSRC(IW+2,:,:))**2 ! Smoothness indicator IW
+ ZBNEG2(IW-1,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (PSRC(IW-1,:,:) - PSRC(IW+1,:,:))**2 ! Smoothness indicator IW-1
+ ZOMN2(IW-1:IW,:,:) = 3./5. / (ZEPS + ZBNEG2(IW-1:IW,:,:))**2 ! Non-normalized weight IW,IW-1
+!
+ ! Third negative stencil, needs indices i-1, i, i+1
+ ZFNEG3(IW,:,:) = 1./6 * (-1.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) + 2.0*PSRC(IW+1,:,:)) ! Flux IW
+ ZFNEG3(IW-1,:,:) = 1./6 * (-1.0*PSRC(IW-2,:,:) + 5.0*PSRC(IW-1,:,:) + 2.0*PSRC(IW,:,:)) ! Flux IW-1
+ ZBNEG3(IW,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (PSRC(IW-1,:,:) - 4.0*PSRC(IW,:,:) + 3.0*PSRC(IW+1,:,:))**2 ! Smoothness indicator IW
+ ZBNEG3(IW-1,:,:) = 13./12 * (PSRC(IW-2,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IW-2,:,:) - 4.0*PSRC(IW-1,:,:) + 3.0*PSRC(IW,:,:))**2 ! Smoothness indicator IW-1
+ ZOMN3(IW-1:IW,:,:) = 3./10. / (ZEPS + ZBNEG3(IW-1:IW,:,:))**2 ! Non-normalized weight IW,IW-1
+!
+ ! ----- Total flux -----
+!
+ PR(IW-1:IW,:,:) = ( ZOMP1(IW-1:IW,:,:)/(ZOMP1(IW-1:IW,:,:)+ZOMP2(IW-1:IW,:,:)+ZOMP3(IW-1:IW,:,:)) * ZFPOS1(IW-1:IW,:,:) &
+ + ZOMP2(IW-1:IW,:,:)/(ZOMP1(IW-1:IW,:,:)+ZOMP2(IW-1:IW,:,:)+ZOMP3(IW-1:IW,:,:)) * ZFPOS2(IW-1:IW,:,:) &
+ + ZOMP3(IW-1:IW,:,:)/(ZOMP1(IW-1:IW,:,:)+ZOMP2(IW-1:IW,:,:)+ZOMP3(IW-1:IW,:,:)) * ZFPOS3(IW-1:IW,:,:)) &
+ * (0.5+SIGN(0.5,PRUCT(IW-1:IW,:,:))) &
+ + ( ZOMN1(IW-1:IW,:,:)/(ZOMN1(IW-1:IW,:,:)+ZOMN2(IW-1:IW,:,:)+ZOMN3(IW-1:IW,:,:)) * ZFNEG1(IW-1:IW,:,:) &
+ + ZOMN2(IW-1:IW,:,:)/(ZOMN1(IW-1:IW,:,:)+ZOMN2(IW-1:IW,:,:)+ZOMN3(IW-1:IW,:,:)) * ZFNEG2(IW-1:IW,:,:) &
+ + ZOMN3(IW-1:IW,:,:)/(ZOMN1(IW-1:IW,:,:)+ZOMN2(IW-1:IW,:,:)+ZOMN3(IW-1:IW,:,:)) * ZFNEG3(IW-1:IW,:,:)) &
+ * (0.5-SIGN(0.5,PRUCT(IW-1:IW,:,:)))
!
-! WENO weights
+ END IF ! NHALO
!
- ZOMP1(IW:IE-1,:,:) = ZGAMMA1 / (ZEPS + ZBPOS1(IW:IE-1,:,:))**2
- ZOMP2(IW:IE-1,:,:) = ZGAMMA2 / (ZEPS + ZBPOS2(IW:IE-1,:,:))**2
- ZOMP3(IW:IE-1,:,:) = ZGAMMA3 / (ZEPS + ZBPOS3(IW:IE-1,:,:))**2
- ZOMN1(IW:IE-1,:,:) = ZGAMMA1 / (ZEPS + ZBNEG1(IW:IE-1,:,:))**2
- ZOMN2(IW:IE-1,:,:) = ZGAMMA2 / (ZEPS + ZBNEG2(IW:IE-1,:,:))**2
- ZOMN3(IW:IE-1,:,:) = ZGAMMA3 / (ZEPS + ZBNEG3(IW:IE-1,:,:))**2
-!
- ZOMP1(IW-1,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(IW-1,:,:))**2
- ZOMP2(IW-1,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(IW-1,:,:))**2
- ZOMP1(IE, :,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(IE, :,:))**2
- ZOMP2(IE, :,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(IE, :,:))**2
- ZOMP1(IE+1,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(IE+1,:,:))**2
- ZOMP2(IE+1,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(IE+1,:,:))**2
- ZOMN1(IW-1,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(IW-1,:,:))**2
- ZOMN2(IW-1,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(IW-1,:,:))**2
- ZOMN1(IE, :,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(IE, :,:))**2
- ZOMN2(IE, :,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(IE, :,:))**2
- ZOMN1(IE+1,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(IE+1,:,:))**2
- ZOMN2(IE+1,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(IE+1,:,:))**2
-!
-! WENO fluxes (5th order)
-!
- PR(IW:IE-1,:,:) = (ZOMP2(IW:IE-1,:,:)/(ZOMP1(IW:IE-1,:,:)+ZOMP2(IW:IE-1,:,:)+&
- ZOMP3(IW:IE-1,:,:)) * ZFPOS2(IW:IE-1,:,:) &
- + ZOMP1(IW:IE-1,:,:)/(ZOMP1(IW:IE-1,:,:)+ZOMP2(IW:IE-1,:,:)+&
- ZOMP3(IW:IE-1,:,:)) * ZFPOS1(IW:IE-1,:,:) &
- + ZOMP3(IW:IE-1,:,:)/(ZOMP1(IW:IE-1,:,:)+ZOMP2(IW:IE-1,:,:)+&
- ZOMP3(IW:IE-1,:,:)) * ZFPOS3(IW:IE-1,:,:))&
- * (0.5+SIGN(0.5,PRUCT(IW:IE-1,:,:))) &
- + (ZOMN2(IW:IE-1,:,:)/(ZOMN1(IW:IE-1,:,:)+ZOMN2(IW:IE-1,:,:)+&
- ZOMN3(IW:IE-1,:,:)) * ZFNEG2(IW:IE-1,:,:) &
- + ZOMN1(IW:IE-1,:,:)/(ZOMN1(IW:IE-1,:,:)+ZOMN2(IW:IE-1,:,:)+&
- ZOMN3(IW:IE-1,:,:)) * ZFNEG1(IW:IE-1,:,:) &
- + ZOMN3(IW:IE-1,:,:)/(ZOMN1(IW:IE-1,:,:)+ZOMN2(IW:IE-1,:,:)+&
- ZOMN3(IW:IE-1,:,:)) * ZFNEG3(IW:IE-1,:,:))&
- * (0.5-SIGN(0.5,PRUCT(IW:IE-1,:,:)))
-!
-! WENO fluxes (3rd order)
-!
- PR(IW-1,:,:) = (ZOMN2(IW-1,:,:)/(ZOMN1(IW-1,:,:)+ZOMN2(IW-1,:,:)) * &
- ZFNEG2(IW-1,:,:) &
- + (ZOMN1(IW-1,:,:)/(ZOMN1(IW-1,:,:)+ZOMN2(IW-1,:,:)) * &
- ZFNEG1(IW-1,:,:))) * &
- (0.5-SIGN(0.5,PRUCT(IW-1,:,:))) &
- + (ZOMP2(IW-1,:,:)/(ZOMP1(IW-1,:,:)+ZOMP2(IW-1,:,:)) * &
- ZFPOS2(IW-1,:,:) &
- + (ZOMP1(IW-1,:,:)/(ZOMP1(IW-1,:,:)+ZOMP2(IW-1,:,:)) * &
- ZFPOS1(IW-1,:,:))) * &
- (0.5+SIGN(0.5,PRUCT(IW-1,:,:)))
-!
- PR(IE, :,:) = (ZOMN2(IE, :,:)/(ZOMN1(IE, :,:)+ZOMN2(IE, :,:)) * &
- ZFNEG2(IE, :,:) &
- + (ZOMN1(IE, :,:)/(ZOMN1(IE, :,:)+ZOMN2(IE, :,:)) * &
- ZFNEG1(IE, :,:))) * &
- (0.5-SIGN(0.5,PRUCT(IE, :,:))) &
- + (ZOMP2(IE, :,:)/(ZOMP1(IE, :,:)+ZOMP2(IE, :,:)) * &
- ZFPOS2(IE, :,:) &
- + (ZOMP1(IE, :,:)/(ZOMP1(IE, :,:)+ZOMP2(IE, :,:)) * &
- ZFPOS1(IE, :,:))) * &
- (0.5+SIGN(0.5,PRUCT(IE, :,:)))
-!
- PR(IE+1,:,:) = (ZOMN2(IE+1,:,:)/(ZOMN1(IE+1,:,:)+ZOMN2(IE+1,:,:)) * &
- ZFNEG2(IE+1,:,:) &
- + (ZOMN1(IE+1,:,:)/(ZOMN1(IE+1,:,:)+ZOMN2(IE+1,:,:)) * &
- ZFNEG1(IE+1,:,:))) * &
- (0.5-SIGN(0.5,PRUCT(IE+1,:,:))) &
- + (ZOMP2(IE+1,:,:)/(ZOMP1(IE+1,:,:)+ZOMP2(IE+1,:,:)) * &
- ZFPOS2(IE+1,:,:) &
- + (ZOMP1(IE+1,:,:)/(ZOMP1(IE+1,:,:)+ZOMP2(IE+1,:,:)) * &
- ZFPOS1(IE+1,:,:))) * &
- (0.5+SIGN(0.5,PRUCT(IE+1,:,:)))
-!
-!
-! OPEN, WALL, NEST CASE IN THE X DIRECTION
-!
-CASE ('OPEN','WALL','NEST')
-!
- IW=IIB
- IE=IIE
-!
-! LATERAL BOUNDARY CONDITIONS
-! AT THE PHYSICAL BORDER: USE A FIRST ORDER UPSTREAM WENO SCHEME AT THE POINTS: IW-1,
-! IE /AND/ A THIRD ORDER WENO SCHEME AT THE POINTS: IW, IE-1
-! AT THE PROC. BORDER: A THIRD ORDER UPSTREAM WENO SCHEME AT THE POINTS: IW-1, IE /AND/
-! A FIFTH ORDER WENO SCHEME AT THE POINTS: IW, IE-1
-!
-! PHYSICAL BORDER (WEST)
-!
- IF(LWEST_ll()) THEN
-!
-! FISRT ORDER WENO SCHEME
+END IF ! IF(LWEST_ll())
!
- PR(IW-1,:,:) = PSRC(IW-1,:,:) * (0.5+SIGN(0.5,PRUCT(IW-1,:,:))) + &
- PSRC(IW,:,:) * &
- (0.5-SIGN(0.5,PRUCT(IW-1,:,:)))
+!-------------------------------------------------------------------------------
+!* 1.3. East border
+! ---------------------
!
-! THIRD ORDER WENO SCHEME
-!
- ZFPOS1(IW,:,:) = 0.5 * (3.0*PSRC(IW,:,:) - PSRC(IW-1,:,:))
- ZFPOS2(IW,:,:) = 0.5 * (PSRC(IW ,:,:) + PSRC(IW+1,:,:))
- ZBPOS1(IW,:,:) = (PSRC(IW,:,:) - PSRC(IW-1,:,:))**2
- ZBPOS2(IW,:,:) = (PSRC(IW+1, :,:) - PSRC(IW,:,:))**2
-!
- ZFNEG1(IW,:,:) = 0.5 * (3.0*PSRC(IW+1,:,:) - PSRC(IW+2,:,:))
- ZFNEG2(IW,:,:) = 0.5 * (PSRC(IW, :,:) + PSRC(IW+1,:,:))
- ZBNEG1(IW,:,:) = (PSRC(IW+1,:,:) - PSRC(IW+2,:,:))**2
- ZBNEG2(IW,:,:) = (PSRC(IW, :,:) - PSRC(IW+1,:,:))**2
-!
- ZOMP1(IW,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(IW,:,:))**2
- ZOMP2(IW,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(IW,:,:))**2
- ZOMN1(IW,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(IW,:,:))**2
- ZOMN2(IW,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(IW,:,:))**2
-!
- PR(IW,:,:) = (ZOMN2(IW,:,:)/(ZOMN1(IW,:,:)+ZOMN2(IW,:,:)) * &
- ZFNEG2(IW,:,:) + &
- (ZOMN1(IW,:,:)/(ZOMN1(IW,:,:)+ZOMN2(IW,:,:)) * ZFNEG1(IW,:,:))) * &
- (0.5-SIGN(0.5,PRUCT(IW,:,:))) + &
- (ZOMP2(IW,:,:)/(ZOMP1(IW,:,:)+ZOMP2(IW,:,:)) * ZFPOS2(IW,:,:) + &
- (ZOMP1(IW,:,:)/(ZOMP1(IW,:,:)+ZOMP2(IW,:,:)) * ZFPOS1(IW,:,:))) * &
- (0.5+SIGN(0.5,PRUCT(IW,:,:)))
-!
-! PROC. BORDER (WEST)
-!
- ELSEIF(NHALO == 1) THEN
-!
-! THIRD ORDER WENO SCHEME
-!
- ZFPOS1(IW-1,:,:) = 0.5 * (3.0*PSRC(IW-1,:,:) - TPHALO2%WEST(:,:))
- ZFPOS2(IW-1,:,:) = 0.5 * (PSRC(IW-1, :,:) + PSRC(IW,:,:))
- ZBPOS1(IW-1,:,:) = (PSRC(IW-1,:,:) - TPHALO2%WEST(:,:))**2
- ZBPOS2(IW-1,:,:) = (PSRC(IW, :,:) - PSRC(IW-1,:,:))**2
-!
- ZFNEG1(IW-1,:,:) = 0.5 * (3.0*PSRC(IW,:,:) - PSRC(IW+1,:,:))
- ZFNEG2(IW-1,:,:) = 0.5 * (PSRC(IW-1, :,:) + PSRC(IW, :,:))
- ZBNEG1(IW-1,:,:) = (PSRC(IW, :,:) - PSRC(IW+1,:,:))**2
- ZBNEG2(IW-1,:,:) = (PSRC(IW-1,:,:) - PSRC(IW, :,:))**2
-!
- ZOMP1(IW-1,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(IW-1,:,:))**2
- ZOMP2(IW-1,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(IW-1,:,:))**2
- ZOMN1(IW-1,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(IW-1,:,:))**2
- ZOMN2(IW-1,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(IW-1,:,:))**2
-!
- PR(IW-1,:,:) = (ZOMN2(IW-1,:,:)/(ZOMN1(IW-1,:,:)+ZOMN2(IW-1,:,:)) &
- * ZFNEG2(IW-1,:,:) &
- + (ZOMN1(IW-1,:,:)/(ZOMN1(IW-1,:,:)+ZOMN2(IW-1,:,:)) * &
- ZFNEG1(IW-1,:,:))) *&
- (0.5-SIGN(0.5,PRUCT(IW-1,:,:))) &
- + (ZOMP2(IW-1,:,:)/(ZOMP1(IW-1,:,:)+ZOMP2(IW-1,:,:)) * &
- ZFPOS2(IW-1,:,:) &
- + (ZOMP1(IW-1,:,:)/(ZOMP1(IW-1,:,:)+ZOMP2(IW-1,:,:)) * &
- ZFPOS1(IW-1,:,:))) *&
- (0.5+SIGN(0.5,PRUCT(IW-1,:,:)))
-!
-! FIFTH ORDER WENO SCHEME
-!
- ZFPOS1(IW,:,:) = 1./6 * (2.0*TPHALO2%WEST(:,:) - 7.0*PSRC(IW-1,:,:) + &
- 11.0*PSRC(IW, :,:))
- ZFPOS2(IW,:,:) = 1./6 * (-1.0*PSRC(IW-1, :,:) + 5.0*PSRC(IW, :,:) + &
- 2.0*PSRC(IW+1,:,:))
- ZFPOS3(IW,:,:) = 1./6 * (2.0*PSRC(IW, :,:) + 5.0*PSRC(IW+1,:,:) - &
- PSRC(IW+2,:,:))
-!
- ZFNEG1(IW,:,:) = 1./6 * (11.0*PSRC(IW+1,:,:) - 7.0*PSRC(IW+2,:,:) + &
- 2.0*PSRC(IW+3,:,:))
- ZFNEG2(IW,:,:) = 1./6 * ( 2.0*PSRC(IW, :,:) + 5.0*PSRC(IW+1,:,:) - &
- PSRC(IW+2,:,:))
- ZFNEG3(IW,:,:) = 1./6 * (-1.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW, :,:) + &
- 2.0*PSRC(IW+1,:,:))
-!
- ZBPOS1(IW,:,:) = 13./12 * (TPHALO2%WEST(:,:) - 2.0*PSRC(IW-1,:,:) + &
- PSRC(IW,:,:))**2 + &
- 1./4 * (TPHALO2%WEST(:,:) - 4.0*PSRC(IW-1,:,:) + &
- 3.0*PSRC(IW,:,:))**2
- ZBPOS2(IW,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + &
- PSRC(IW+1,:,:))**2 + &
- 1./4 * (PSRC(IW-1,:,:) - PSRC(IW+1,:,:))**2
- ZBPOS3(IW,:,:) = 13./12 * (PSRC(IW,:,:) - 2.0*PSRC(IW+1,:,:) + &
- PSRC(IW+2,:,:))**2 + &
- 1./4 * ( 3.0*PSRC(IW,:,:) - 4.0*PSRC(IW+1,:,:) + &
- PSRC(IW+2,:,:))**2
-!
- ZBNEG1(IW,:,:) = 13./12 * (PSRC(IW+1,:,:) - 2.0*PSRC(IW+2,:,:) + &
- PSRC(IW+3,:,:))**2 + &
- 1./4 * ( 3.0*PSRC(IW+1,:,:) - 4.0*PSRC(IW+2,:,:) + &
- PSRC(IW+3,:,:))**2
- ZBNEG2(IW,:,:) = 13./12 * (PSRC(IW,:,:) - 2.0*PSRC(IW+1,:,:) + &
- PSRC(IW+2,:,:))**2 + &
- 1./4 * (PSRC(IW,:,:) - PSRC(IW+2,:,:))**2
- ZBNEG3(IW,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + &
- PSRC(IW+1,:,:))**2 + &
- 1./4 * ( PSRC(IW-1,:,:) - 4.0*PSRC(IW,:,:) + &
- 3.0*PSRC(IW+1,:,:))**2
-!
- ZOMP1(IW,:,:) = ZGAMMA1 / (ZEPS + ZBPOS1(IW,:,:))**2
- ZOMP2(IW,:,:) = ZGAMMA2 / (ZEPS + ZBPOS2(IW,:,:))**2
- ZOMP3(IW,:,:) = ZGAMMA3 / (ZEPS + ZBPOS3(IW,:,:))**2
- ZOMN1(IW,:,:) = ZGAMMA1 / (ZEPS + ZBNEG1(IW,:,:))**2
- ZOMN2(IW,:,:) = ZGAMMA2 / (ZEPS + ZBNEG2(IW,:,:))**2
- ZOMN3(IW,:,:) = ZGAMMA3 / (ZEPS + ZBNEG3(IW,:,:))**2
-!
- PR(IW,:,:) = (ZOMP2(IW,:,:)/(ZOMP1(IW,:,:)+ZOMP2(IW,:,:)+ &
- ZOMP3(IW,:,:)) * ZFPOS2(IW,:,:) &
- + ZOMP1(IW,:,:)/(ZOMP1(IW,:,:)+ZOMP2(IW,:,:)+ &
- ZOMP3(IW,:,:)) * ZFPOS1(IW,:,:) &
- + ZOMP3(IW,:,:)/(ZOMP1(IW,:,:)+ZOMP2(IW,:,:)+ &
- ZOMP3(IW,:,:)) * ZFPOS3(IW,:,:)) *&
- (0.5+SIGN(0.5,PRUCT(IW,:,:))) &
- + (ZOMN2(IW,:,:)/(ZOMN1(IW,:,:)+ZOMN2(IW,:,:)+&
- ZOMN3(IW,:,:)) * ZFNEG2(IW,:,:) &
- + ZOMN1(IW,:,:)/(ZOMN1(IW,:,:)+ZOMN2(IW,:,:)+ &
- ZOMN3(IW,:,:)) * ZFNEG1(IW,:,:) &
- + ZOMN3(IW,:,:)/(ZOMN1(IW,:,:)+ZOMN2(IW,:,:)+ &
- ZOMN3(IW,:,:)) * ZFNEG3(IW,:,:)) *&
- (0.5-SIGN(0.5,PRUCT(IW,:,:)))
-!
- ENDIF
-!
-! PHYSICAL BORDER (EAST)
-!
- IF(LEAST_ll()) THEN
+IF( LEAST_ll() .AND. .FALSE. ) THEN
+ !-----------------------------------------------------------------------------
+ ! East border is physical -- IE-1,IE
+ !-----------------------------------------------------------------------------
+ SELECT CASE (HLBCX(2)) ! X direction LBC type on right side
+!
+ CASE ('CYCL')
+ !---------------------------------------------------------------------------
+ ! Periodic boundary condition
+ !---------------------------------------------------------------------------
+!
+ IF (LWEST_ll() .AND. .FALSE. ) THEN ! West boundary is physical (monoproc)
+!
+ ! Third positive stencil, needs indices i, i+1, i+2
+ ZFPOS3(IE-1,:,:) = 1./6 * (2.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) - PSRC(IE+1,:,:)) ! Flux IE-1
+ ZFPOS3(IE,:,:) = 1./6 * (2.0*PSRC(IE,:,:) + 5.0*PSRC(IE+1,:,:) - PSRC(IW,:,:)) ! Flux IE
+ ZBPOS3(IE-1,:,:) = 13./12 * ( PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE-1,:,:) - 4.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 ! Smoothness indicator IE-1
+ ZBPOS3(IE,:,:) = 13./12 * ( PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE,:,:) - 4.0*PSRC(IE+1,:,:) + PSRC(IW,:,:))**2 ! Smoothness indicator IE
+ ZOMP3(IE-1:IE,:,:) = 3./10. / (ZEPS + ZBPOS3(IE-1:IE,:,:))**2 ! Non-normalized weight IE-1,IE
+!
+ ! First negative stencil, needs indices i+1, i+2, i+3
+ ZFNEG1(IE-1,:,:) = 1./6. * (11.0*PSRC(IE,:,:) - 7.0*PSRC(IE+1,:,:) + 2.0*PSRC(IW,:,:)) ! Flux IE-1
+ ZFNEG1(IE,:,:) = 1./6. * (11.0*PSRC(IE+1,:,:) - 7.0*PSRC(IW,:,:) + 2.0*PSRC(IW+1,:,:)) ! Flux IE
+ ZBNEG1(IE-1,:,:) = 13./12. * ( PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE,:,:) - 4.0*PSRC(IE+1,:,:) + PSRC(IW,:,:))**2 ! Smoothness indicator IE-1
+ ZBNEG1(IE,:,:) = 13./12. * ( PSRC(IE+1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE+1,:,:) - 4.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 ! Smoothness indicator IE
+ ZOMN1(IE-1:IE,:,:) = 1./10. / (ZEPS + ZBNEG1(IE-1:IE,:,:))**2 ! Non-normalized weight IE-1,IE
+!
+ ! Second negative stencil, needs indices i, i+1, i+2
+ ZFNEG2(IE-1,:,:) = 1./6. * (2.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) - 1.0*PSRC(IE+1,:,:)) ! Flux IE-1
+ ZFNEG2(IE,:,:) = 1./6. * (2.0*PSRC(IE,:,:) + 5.0*PSRC(IE+1,:,:) - 1.0*PSRC(IW,:,:)) ! Flux IE
+ ZBNEG2(IE-1,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (PSRC(IE-1,:,:) - PSRC(IE+1,:,:))**2 ! Smoothness indicator IE-1
+ ZBNEG2(IE,:,:) = 13./12 * (PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IE,:,:) - PSRC(IW,:,:))**2 ! Smoothness indicator IE
+ ZOMN2(IE-1:IE,:,:) = 3./5. / (ZEPS + ZBNEG2(IE-1:IE,:,:))**2 ! Non-normalized weight IE-1,IE
+!
+ ELSEIF(IE<=SIZE(PSRC,1)-3) THEN ! West boundary is proc border, with minimum 3 HALO points on east side
+!
+ ! Third positive stencil, needs indices i, i+1, i+2
+ ZFPOS3(IE-1,:,:) = 1./6 * (2.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) - PSRC(IE+1,:,:)) ! Flux IE-1
+ ZFPOS3(IE,:,:) = 1./6 * (2.0*PSRC(IE,:,:) + 5.0*PSRC(IE+1,:,:) - PSRC(IE+2,:,:)) ! Flux IE
+ ZBPOS3(IE-1,:,:) = 13./12 * ( PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE-1,:,:) - 4.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 ! Smoothness indicator IE-1
+ ZBPOS3(IE,:,:) = 13./12 * ( PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE,:,:) - 4.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 ! Smoothness indicator IE
+ ZOMP3(IE-1:IE,:,:) = 3./10. / (ZEPS + ZBPOS3(IE-1:IE,:,:))**2 ! Non-normalized weight IE-1,IE
+!
+ ! First negative stencil, needs indices i+1, i+2, i+3
+ ZFNEG1(IE-1,:,:) = 1./6. * (11.0*PSRC(IE,:,:) - 7.0*PSRC(IE+1,:,:) + 2.0*PSRC(IE+2,:,:)) ! Flux IE-1
+ ZFNEG1(IE,:,:) = 1./6. * (11.0*PSRC(IE+1,:,:) - 7.0*PSRC(IE+2,:,:) + 2.0*PSRC(IE+3,:,:)) ! Flux IE
+ ZBNEG1(IE-1,:,:) = 13./12. * ( PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE,:,:) - 4.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 ! Smoothness indicator IE-1
+ ZBNEG1(IE,:,:) = 13./12. * ( PSRC(IE+1,:,:) - 2.0*PSRC(IE+2,:,:) + PSRC(IE+3,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE+1,:,:) - 4.0*PSRC(IE+2,:,:) + PSRC(IE+3,:,:))**2 ! Smoothness indicator IE
+ ZOMN1(IE-1:IE,:,:) = 1./10. / (ZEPS + ZBNEG1(IE-1:IE,:,:))**2 ! Non-normalized weight IE-1,IE
+!
+ ! Second negative stencil, needs indices i, i+1, i+2
+ ZFNEG2(IE-1,:,:) = 1./6. * (2.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) - 1.0*PSRC(IE+1,:,:)) ! Flux IE-1
+ ZFNEG2(IE,:,:) = 1./6. * (2.0*PSRC(IE,:,:) + 5.0*PSRC(IE+1,:,:) - 1.0*PSRC(IE+2,:,:)) ! Flux IE
+ ZBNEG2(IE-1,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (PSRC(IE-1,:,:) - PSRC(IE+1,:,:))**2 ! Smoothness indicator IE-1
+ ZBNEG2(IE,:,:) = 13./12 * (PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 &
+ + 1./4 * (PSRC(IE,:,:) - PSRC(IE+2,:,:))**2 ! Smoothness indicator IE
+ ZOMN2(IE-1:IE,:,:) = 3./5. / (ZEPS + ZBNEG2(IE-1:IE,:,:))**2 ! Non-normalized weight IE-1,IE
+!
+ ELSE ! West boundary is proc border, with NHALO < 3 on east side
+ PRINT *,'WARNING : WENO5 fluxes calculation needs NHALO >= 3 on east side'
+ CALL ABORT
+ ENDIF
+!
+ ! First positive stencil, needs indices i-2, i-1, i
+ ZFPOS1(IE-1,:,:) = 1./6. * (2.0*PSRC(IE-3,:,:) - 7.0*PSRC(IE-2,:,:) + 11.0*PSRC(IE-1,:,:)) ! Flux IE-1
+ ZFPOS1(IE,:,:) = 1./6. * (2.0*PSRC(IE-2,:,:) - 7.0*PSRC(IE-1,:,:) + 11.0*PSRC(IE,:,:)) ! Flux IE
+ ZBPOS1(IE-1,:,:) = 13./12. * (PSRC(IE-3,:,:) - 2.0*PSRC(IE-2,:,:) + PSRC(IE-1,:,:))**2 &
+ + 1./4 * (PSRC(IE-3,:,:) - 4.0*PSRC(IE-2,:,:) + 3.0*PSRC(IE-1,:,:))**2 ! Smoothness indicator IE-1
+ ZBPOS1(IE,:,:) = 13./12. * (PSRC(IE-2,:,:) - 2.0*PSRC(IE-1,:,:) + PSRC(IE,:,:))**2 &
+ + 1./4 * (PSRC(IE-2,:,:) - 4.0*PSRC(IE-1,:,:) + 3.0*PSRC(IE,:,:))**2 ! Smoothness indicator IE
+ ZOMP1(IE-1:IE,:,:) = 1./10. / (ZEPS + ZBPOS1(IE-1:IE,:,:))**2 ! Non-normalized weight IE-1,IE
+!
+ ! Second positive stencil, needs indices i-1, i, i+1
+ ZFPOS2(IE-1,:,:) = 1./6. * (-1.0*PSRC(IE-2,:,:) + 5.0*PSRC(IE-1,:,:) + 2.0*PSRC(IE,:,:)) ! Flux IE-1
+ ZFPOS2(IE,:,:) = 1./6. * (-1.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) + 2.0*PSRC(IE+1,:,:)) ! Flux IE
+ ZBPOS2(IE-1,:,:) = 13./12 * (PSRC(IE-2,:,:) - 2.0*PSRC(IE-1,:,:) + PSRC(IE,:,:))**2 &
+ + 1./4 * (PSRC(IE-2,:,:) - PSRC(IE,:,:))**2 ! Smoothness indicator IE-1
+ ZBPOS2(IE,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (PSRC(IE-1,:,:) - PSRC(IE+1,:,:))**2 ! Smoothness indicator IE
+ ZOMP2(IE-1:IE,:,:) = 3./5. / (ZEPS + ZBPOS2(IE-1:IE,:,:))**2 ! Non-normalized weight IE-1,IE
+!
+ ! Third negative stencil, needs indices i-1, i, i+1
+ ZFNEG3(IE-1,:,:) = 1./6 * (-1.0*PSRC(IE-2,:,:) + 5.0*PSRC(IE-1,:,:) + 2.0*PSRC(IE,:,:)) ! Flux IE-1
+ ZFNEG3(IE,:,:) = 1./6 * (-1.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) + 2.0*PSRC(IE+1,:,:)) ! Flux IE
+ ZBNEG3(IE-1,:,:) = 13./12 * (PSRC(IE-2,:,:) - 2.0*PSRC(IE-1,:,:) + PSRC(IE,:,:))**2 &
+ + 1./4 * (PSRC(IE-2,:,:) - 4.0*PSRC(IE-1,:,:) + 3.0*PSRC(IE,:,:))**2 ! Smoothness indicator IE-1
+ ZBNEG3(IE,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (PSRC(IE-1,:,:) - 4.0*PSRC(IE,:,:) + 3.0*PSRC(IE+1,:,:))**2 ! Smoothness indicator IE
+ ZOMN3(IE-1:IE,:,:) = 3./10. / (ZEPS + ZBNEG3(IE-1:IE,:,:))**2 ! Non-normalized weight IE-1,IE
+!
+ ! ----- Total flux -----
+!
+ PR(IE-1:IE,:,:) = ( ZOMP1(IE-1:IE,:,:)/(ZOMP1(IE-1:IE,:,:)+ZOMP2(IE-1:IE,:,:)+ZOMP3(IE-1:IE,:,:)) * ZFPOS1(IE-1:IE,:,:) &
+ + ZOMP2(IE-1:IE,:,:)/(ZOMP1(IE-1:IE,:,:)+ZOMP2(IE-1:IE,:,:)+ZOMP3(IE-1:IE,:,:)) * ZFPOS2(IE-1:IE,:,:) &
+ + ZOMP3(IE-1:IE,:,:)/(ZOMP1(IE-1:IE,:,:)+ZOMP2(IE-1:IE,:,:)+ZOMP3(IE-1:IE,:,:)) * ZFPOS3(IE-1:IE,:,:)) &
+ * (0.5+SIGN(0.5,PRUCT(IE-1:IE,:,:))) &
+ + ( ZOMN1(IE-1:IE,:,:)/(ZOMN1(IE-1:IE,:,:)+ZOMN2(IE-1:IE,:,:)+ZOMN3(IE-1:IE,:,:)) * ZFNEG1(IE-1:IE,:,:) &
+ + ZOMN2(IE-1:IE,:,:)/(ZOMN1(IE-1:IE,:,:)+ZOMN2(IE-1:IE,:,:)+ZOMN3(IE-1:IE,:,:)) * ZFNEG2(IE-1:IE,:,:) &
+ + ZOMN3(IE-1:IE,:,:)/(ZOMN1(IE-1:IE,:,:)+ZOMN2(IE-1:IE,:,:)+ZOMN3(IE-1:IE,:,:)) * ZFNEG3(IE-1:IE,:,:)) &
+ * (0.5-SIGN(0.5,PRUCT(IE-1:IE,:,:)))
+!
+!
+ CASE ('OPEN','WALL','NEST')
+ !---------------------------------------------------------------------------
+ ! Open, or Wall, or Nest boundary condition => WENO order reduction
+ !---------------------------------------------------------------------------
+!
+ ! WENO scheme order 1, IE
PR(IE,:,:) = PSRC(IE,:,:) * (0.5+SIGN(0.5,PRUCT(IE,:,:))) + &
PSRC(IE+1,:,:) * &
(0.5-SIGN(0.5,PRUCT(IE,:,:)))
!
- ZFPOS1(IE-1,:,:) = 0.5 * (3.0*PSRC(IE-1,:,:) - PSRC(IE-2,:,:))
- ZFPOS2(IE-1,:,:) = 0.5 * (PSRC(IE-1, :,:) + PSRC(IE, :,:))
- ZBPOS1(IE-1,:,:) = (PSRC(IE-1,:,:) - PSRC(IE-2,:,:))**2
- ZBPOS2(IE-1,:,:) = (PSRC(IE, :,:) - PSRC(IE-1,:,:))**2
-!
- ZFNEG1(IE-1,:,:) = 0.5 * (3.0*PSRC(IE,:,:) - PSRC(IE+1,:,:))
- ZFNEG2(IE-1,:,:) = 0.5 * (PSRC(IE-1, :,:) + PSRC(IE, :,:))
- ZBNEG1(IE-1,:,:) = (PSRC(IE, :,:) - PSRC(IE+1,:,:))**2
- ZBNEG2(IE-1,:,:) = (PSRC(IE-1,:,:) - PSRC(IE, :,:))**2
-!
- ZOMP1(IE-1,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(IE-1,:,:))**2
- ZOMP2(IE-1,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(IE-1,:,:))**2
- ZOMN1(IE-1,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(IE-1,:,:))**2
- ZOMN2(IE-1,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(IE-1,:,:))**2
-!
- PR(IE-1,:,:) = (ZOMN2(IE-1,:,:)/(ZOMN1(IE-1,:,:)+ZOMN2(IE-1,:,:)) * &
- ZFNEG2(IE-1,:,:)&
- + (ZOMN1(IE-1,:,:)/(ZOMN1(IE-1,:,:)+ZOMN2(IE-1,:,:)) * &
- ZFNEG1(IE-1,:,:))) *&
- (0.5-SIGN(0.5,PRUCT(IE-1,:,:))) &
- + (ZOMP2(IE-1,:,:)/(ZOMP1(IE-1,:,:)+ZOMP2(IE-1,:,:)) * &
- ZFPOS2(IE-1,:,:) &
- + (ZOMP1(IE-1,:,:)/(ZOMP1(IE-1,:,:)+ZOMP2(IE-1,:,:)) * &
- ZFPOS1(IE-1,:,:))) *&
- (0.5+SIGN(0.5,PRUCT(IE-1,:,:)))
-!
-! PROC. BORDER (EAST)
-!
- ELSEIF(NHALO == 1) THEN
-!
- ZFPOS1(IE,:,:) = 0.5 * (3.0*PSRC(IE,:,:) - PSRC(IE-1,:,:))
- ZFPOS2(IE,:,:) = 0.5 * (PSRC(IE, :,:) + PSRC(IE+1,:,:))
- ZBPOS1(IE,:,:) = (PSRC(IE, :,:) - PSRC(IE-1,:,:))**2
- ZBPOS2(IE,:,:) = (PSRC(IE+1,:,:) - PSRC(IE, :,:))**2
-!
- ZFNEG1(IE,:,:) = 0.5 * (3.0*PSRC(IE+1,:,:) - TPHALO2%EAST(:,:))
- ZFNEG2(IE,:,:) = 0.5 * (PSRC(IE, :,:) + PSRC(IE+1,:,:))
- ZBNEG1(IE,:,:) = (PSRC(IE+1,:,:) - TPHALO2%EAST(:,:))**2
- ZBNEG2(IE,:,:) = (PSRC(IE, :,:) - PSRC(IE+1,:,:))**2
-!
- ZOMP1(IE,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(IE,:,:))**2
- ZOMP2(IE,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(IE,:,:))**2
- ZOMN1(IE,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(IE,:,:))**2
- ZOMN2(IE,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(IE,:,:))**2
-!
- PR(IE,:,:) = (ZOMN2(IE,:,:)/(ZOMN1(IE,:,:)+ZOMN2(IE,:,:)) * ZFNEG2(IE,:,:)&
- + (ZOMN1(IE,:,:)/(ZOMN1(IE,:,:)+ZOMN2(IE,:,:)) * ZFNEG1(IE,:,:))) *&
- (0.5-SIGN(0.5,PRUCT(IE,:,:))) &
- + (ZOMP2(IE,:,:)/(ZOMP1(IE,:,:)+ZOMP2(IE,:,:)) * ZFPOS2(IE,:,:) &
- + (ZOMP1(IE,:,:)/(ZOMP1(IE,:,:)+ZOMP2(IE,:,:)) * ZFPOS1(IE,:,:))) *&
- (0.5+SIGN(0.5,PRUCT(IE,:,:)))
-!
-!
- ZFPOS1(IE-1,:,:) = 1./6 * (2.0 *PSRC(IE-3,:,:) - 7.0*PSRC(IE-2,:,:) + &
- 11.0*PSRC(IE-1,:,:))
- ZFPOS2(IE-1,:,:) = 1./6 * (-1.0*PSRC(IE-2,:,:) + 5.0*PSRC(IE-1,:,:) + &
- 2.0*PSRC(IE,:,:))
- ZFPOS3(IE-1,:,:) = 1./6 * (2.0 *PSRC(IE-1,:,:) + 5.0*PSRC(IE, :,:) - &
- PSRC(IE+1, :,:))
-!
- ZFNEG1(IE-1,:,:) = 1./6 * (11.0*PSRC(IE,:,:) - 7.0*PSRC(IE+1,:,:) + &
- 2.0*TPHALO2%EAST(:,:))
- ZFNEG2(IE-1,:,:) = 1./6 * (2.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) - &
- PSRC(IE+1,:,:))
- ZFNEG3(IE-1,:,:) = 1./6 * (-1.0*PSRC(IE-2,:,:) + 5.0*PSRC(IE-1,:,:) + &
- 2.0*PSRC(IE,:,:))
-!
- ZBPOS1(IE-1,:,:) = 13./12 * (PSRC(IE-3,:,:) - 2.0*PSRC(IE-2,:,:) + &
- PSRC(IE-1,:,:))**2 + &
- 1./4 * (PSRC(IE-3,:,:) - 4.0*PSRC(IE-2,:,:) + &
- 3.0*PSRC(IE-1,:,:))**2
- ZBPOS2(IE-1,:,:) = 13./12 * (PSRC(IE-2,:,:) - 2.0*PSRC(IE-1,:,:) + &
- PSRC(IE,:,:))**2 + &
- 1./4 * (PSRC(IE-2,:,:) - PSRC(IE,:,:))**2
- ZBPOS3(IE-1,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + &
- PSRC(IE+1,:,:))**2 + &
- 1./4 * ( 3.0*PSRC(IE-1,:,:) - 4.0*PSRC(IE,:,:) + &
- PSRC(IE+1,:,:))**2!
- ZBNEG1(IE-1,:,:) = 13./12 * (PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + &
- TPHALO2%EAST(:,:))**2 + &
- 1./4 * ( 3.0*PSRC(IE,:,:) - 4.0*PSRC(IE+1,:,:) + &
- TPHALO2%EAST(:,:))**2
- ZBNEG2(IE-1,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + &
- PSRC(IE+1,:,:))**2 + &
- 1./4 * (PSRC(IE-1,:,:) - PSRC(IE+1,:,:))**2
- ZBNEG3(IE-1,:,:) = 13./12 * (PSRC(IE-2,:,:) - 2.0*PSRC(IE-1,:,:) + &
- PSRC(IE,:,:))**2 + &
- 1./4 * ( PSRC(IE-2,:,:) - 4.0*PSRC(IE-1,:,:) + &
- 3.0*PSRC(IE,:,:))**2
-!
- ZOMP1(IE-1,:,:) = ZGAMMA1 / (ZEPS + ZBPOS1(IE-1,:,:))**2
- ZOMP2(IE-1,:,:) = ZGAMMA2 / (ZEPS + ZBPOS2(IE-1,:,:))**2
- ZOMP3(IE-1,:,:) = ZGAMMA3 / (ZEPS + ZBPOS3(IE-1,:,:))**2
- ZOMN1(IE-1,:,:) = ZGAMMA1 / (ZEPS + ZBNEG1(IE-1,:,:))**2
- ZOMN2(IE-1,:,:) = ZGAMMA2 / (ZEPS + ZBNEG2(IE-1,:,:))**2
- ZOMN3(IE-1,:,:) = ZGAMMA3 / (ZEPS + ZBNEG3(IE-1,:,:))**2
-!
- PR(IE-1,:,:) = (ZOMP2(IE-1,:,:)/(ZOMP1(IE-1,:,:)+ZOMP2(IE-1,:,:)+ &
- ZOMP3(IE-1,:,:)) * ZFPOS2(IE-1,:,:) &
- + ZOMP1(IE-1,:,:)/(ZOMP1(IE-1,:,:)+ZOMP2(IE-1,:,:)+ &
- ZOMP3(IE-1,:,:)) * ZFPOS1(IE-1,:,:) &
- + ZOMP3(IE-1,:,:)/(ZOMP1(IE-1,:,:)+ZOMP2(IE-1,:,:)+ &
- ZOMP3(IE-1,:,:)) * ZFPOS3(IE-1,:,:)) * &
- (0.5+SIGN(0.5,PRUCT(IE-1,:,:))) &
- + (ZOMN2(IE-1,:,:)/(ZOMN1(IE-1,:,:)+ZOMN2(IE-1,:,:)+ &
- ZOMN3(IE-1,:,:)) * ZFNEG2(IE-1,:,:) &
- + ZOMN1(IE-1,:,:)/(ZOMN1(IE-1,:,:)+ZOMN2(IE-1,:,:)+ &
- ZOMN3(IE-1,:,:)) * ZFNEG1(IE-1,:,:) &
- + ZOMN3(IE-1,:,:)/(ZOMN1(IE-1,:,:)+ZOMN2(IE-1,:,:)+ &
- ZOMN3(IE-1,:,:)) * ZFNEG3(IE-1,:,:)) * &
- (0.5-SIGN(0.5,PRUCT(IE-1,:,:)))
-!
- ENDIF
-!
-! USE A FIFTH ORDER UPSTREAM WENO SCHEME ELSEWHERE (IW+1 --> IE-2)
-!
- ZFPOS1(IW+1:IE-2,:,:) = 1./6 * (2.0*PSRC(IW-1:IE-4,:,:) - &
- 7.0*PSRC(IW:IE-3,:,:) + 11.0*PSRC(IW+1:IE-2,:,:))
- ZFPOS2(IW+1:IE-2,:,:) = 1./6 * (-1.0*PSRC(IW:IE-3,:,:) + &
- 5.0*PSRC(IW+1:IE-2,:,:) + 2.0*PSRC(IW+2:IE-1,:,:))
- ZFPOS3(IW+1:IE-2,:,:) = 1./6 * (2.0*PSRC(IW+1:IE-2,:,:) + &
- 5.0*PSRC(IW+2:IE-1,:,:) - PSRC(IW+3:IE,:,:))
-!
- ZFNEG1(IW+1:IE-2,:,:) = 1./6 * (11.0*PSRC(IW+2:IE-1,:,:) - &
- 7.0*PSRC(IW+3:IE,:,:) + 2.0*PSRC(IW+4:IE+1,:,:))
- ZFNEG2(IW+1:IE-2,:,:) = 1./6 * (2.0*PSRC(IW+1:IE-2,:,:) + &
- 5.0*PSRC(IW+2:IE-1,:,:) - PSRC(IW+3:IE,:,:))
- ZFNEG3(IW+1:IE-2,:,:) = 1./6 * (-1.0*PSRC(IW:IE-3,:,:) + &
- 5.0*PSRC(IW+1:IE-2,:,:) + 2.0*PSRC(IW+2:IE-1,:,:))
-!
- ZBPOS1(IW+1:IE-2,:,:) = 13./12 * (PSRC(IW-1:IE-4,:,:) - &
- 2.0*PSRC(IW:IE-3,:,:) + PSRC(IW+1:IE-2,:,:))**2 + &
- 1./4 * (PSRC(IW-1:IE-4,:,:) - 4.0*PSRC(IW:IE-3,:,:) + &
- 3.0*PSRC(IW+1:IE-2,:,:))**2
- ZBPOS2(IW+1:IE-2,:,:) = 13./12 * (PSRC(IW:IE-3,:,:) - &
- 2.0*PSRC(IW+1:IE-2,:,:) + PSRC(IW+2:IE-1,:,:))**2 + &
- 1./4 * (PSRC(IW:IE-3,:,:) - PSRC(IW+2:IE-1,:,:))**2
- ZBPOS3(IW+1:IE-2,:,:) = 13./12 * (PSRC(IW+1:IE-2,:,:) - &
- 2.0*PSRC(IW+2:IE-1,:,:) + PSRC(IW+3:IE,:,:))**2 + &
- 1./4 * ( 3.0*PSRC(IW+1:IE-2,:,:) - 4.0*PSRC(IW+2:IE-1,:,:) &
- + PSRC(IW+3:IE,:,:))**2
-!
- ZBNEG1(IW+1:IE-2,:,:) = 13./12 * (PSRC(IW+2:IE-1,:,:) - &
- 2.0*PSRC(IW+3:IE,:,:) + PSRC(IW+4:IE+1,:,:))**2 + &
- 1./4 * ( 3.0*PSRC(IW+2:IE-1,:,:) - 4.0*PSRC(IW+3:IE,:,:) + &
- PSRC(IW+4:IE+1,:,:))**2
- ZBNEG2(IW+1:IE-2,:,:) = 13./12 * (PSRC(IW+1:IE-2,:,:) - &
- 2.0*PSRC(IW+2:IE-1,:,:) + PSRC(IW+3:IE,:,:))**2 + &
- 1./4 * (PSRC(IW+1:IE-2,:,:) - PSRC(IW+3:IE,:,:))**2
- ZBNEG3(IW+1:IE-2,:,:) = 13./12 * (PSRC(IW:IE-3,:,:) - &
- 2.0*PSRC(IW+1:IE-2,:,:) + PSRC(IW+2:IE-1,:,:))**2 + &
- 1./4 * ( PSRC(IW:IE-3,:,:) - 4.0*PSRC(IW+1:IE-2,:,:) + &
- 3.0*PSRC(IW+2:IE-1,:,:))**2
-!
- ZOMP1(IW+1:IE-2,:,:) = ZGAMMA1 / (ZEPS + ZBPOS1(IW+1:IE-2,:,:))**2
- ZOMP2(IW+1:IE-2,:,:) = ZGAMMA2 / (ZEPS + ZBPOS2(IW+1:IE-2,:,:))**2
- ZOMP3(IW+1:IE-2,:,:) = ZGAMMA3 / (ZEPS + ZBPOS3(IW+1:IE-2,:,:))**2
- ZOMN1(IW+1:IE-2,:,:) = ZGAMMA1 / (ZEPS + ZBNEG1(IW+1:IE-2,:,:))**2
- ZOMN2(IW+1:IE-2,:,:) = ZGAMMA2 / (ZEPS + ZBNEG2(IW+1:IE-2,:,:))**2
- ZOMN3(IW+1:IE-2,:,:) = ZGAMMA3 / (ZEPS + ZBNEG3(IW+1:IE-2,:,:))**2
-!
- PR(IW+1:IE-2,:,:) = (ZOMP2(IW+1:IE-2,:,:)/(ZOMP1(IW+1:IE-2,:,:)+ &
- ZOMP2(IW+1:IE-2,:,:)+ &
- ZOMP3(IW+1:IE-2,:,:)) * ZFPOS2(IW+1:IE-2,:,:) + &
- ZOMP1(IW+1:IE-2,:,:)/(ZOMP1(IW+1:IE-2,:,:)+ZOMP2(IW+1:IE-2,:,:)+ &
- ZOMP3(IW+1:IE-2,:,:)) * ZFPOS1(IW+1:IE-2,:,:) + &
- ZOMP3(IW+1:IE-2,:,:)/(ZOMP1(IW+1:IE-2,:,:)+ZOMP2(IW+1:IE-2,:,:)+ &
- ZOMP3(IW+1:IE-2,:,:)) * ZFPOS3(IW+1:IE-2,:,:)) * &
- (0.5+SIGN(0.5,PRUCT(IW+1:IE-2,:,:))) + &
- (ZOMN2(IW+1:IE-2,:,:)/(ZOMN1(IW+1:IE-2,:,:)+ZOMN2(IW+1:IE-2,:,:)+&
- ZOMN3(IW+1:IE-2,:,:)) * ZFNEG2(IW+1:IE-2,:,:) + &
- ZOMN1(IW+1:IE-2,:,:)/(ZOMN1(IW+1:IE-2,:,:)+ZOMN2(IW+1:IE-2,:,:)+ &
- ZOMN3(IW+1:IE-2,:,:)) * ZFNEG1(IW+1:IE-2,:,:) + &
- ZOMN3(IW+1:IE-2,:,:)/(ZOMN1(IW+1:IE-2,:,:)+ZOMN2(IW+1:IE-2,:,:)+ &
- ZOMN3(IW+1:IE-2,:,:)) * ZFNEG3(IW+1:IE-2,:,:)) * &
- (0.5-SIGN(0.5,PRUCT(IW+1:IE-2,:,:)))
-!
-END SELECT
-!
-PR = PR * PRUCT
+! ! WENO scheme order 3, IE-1
+ ZFPOS1(IE-1,:,:) = 0.5 * (3.0*PSRC(IE-1,:,:) - PSRC(IE-2,:,:)) ! First positive flux
+ ZFPOS2(IE-1,:,:) = 0.5 * ( PSRC(IE-1,:,:) + PSRC(IE,:,:)) ! Second positive flux
+ ZBPOS1(IE-1,:,:) = (PSRC(IE-1,:,:) - PSRC(IE-2,:,:))**2 ! First positive smoothness indicator
+ ZBPOS2(IE-1,:,:) = (PSRC(IE,:,:) - PSRC(IE-1,:,:))**2 ! Second positive smoothness indicator
+!
+ ZFNEG1(IE-1,:,:) = 0.5 * (3.0*PSRC(IE,:,:) - PSRC(IE+1,:,:)) ! First negative flux
+ ZFNEG2(IE-1,:,:) = 0.5 * ( PSRC(IE-1,:,:) + PSRC(IE,:,:)) ! Second negative flux
+ ZBNEG1(IE-1,:,:) = (PSRC(IE,:,:) - PSRC(IE+1,:,:))**2 ! First negative smoothness indicator
+ ZBNEG2(IE-1,:,:) = (PSRC(IE-1,:,:) - PSRC(IE,:,:))**2 ! Second negative smoothness indicator
+!
+ ZOMP1(IE-1,:,:) = 1./3. / (ZEPS + ZBPOS1(IE-1,:,:))**2 ! First positive non-normalized weight
+ ZOMP2(IE-1,:,:) = 2./3. / (ZEPS + ZBPOS2(IE-1,:,:))**2 ! Second positive non-normalized weight
+ ZOMN1(IE-1,:,:) = 1./3. / (ZEPS + ZBNEG1(IE-1,:,:))**2 ! First negative non-normalized weight
+ ZOMN2(IE-1,:,:) = 2./3. / (ZEPS + ZBNEG2(IE-1,:,:))**2 ! Second negative non-normalized weight
+!
+ PR(IE-1,:,:) = (ZOMN2(IE-1,:,:)/(ZOMN1(IE-1,:,:)+ZOMN2(IE-1,:,:))*ZFNEG2(IE-1,:,:) + &
+ (ZOMN1(IE-1,:,:)/(ZOMN1(IE-1,:,:)+ZOMN2(IE-1,:,:))*ZFNEG1(IE-1,:,:))) &
+ *(0.5-SIGN(0.5,PRUCT(IE-1,:,:))) + &
+ (ZOMP2(IE-1,:,:)/(ZOMP1(IE-1,:,:)+ZOMP2(IE-1,:,:))*ZFPOS2(IE-1,:,:) + &
+ (ZOMP1(IE-1,:,:)/(ZOMP1(IE-1,:,:)+ZOMP2(IE-1,:,:))*ZFPOS1(IE-1,:,:))) &
+ * (0.5+SIGN(0.5,PRUCT(IE-1,:,:))) ! Total flux
+!
+ END SELECT ! SELECT CASE (HLBCX(2)) ! X direction LBC type on right side
+!
+ELSE
+ !-----------------------------------------------------------------------------
+ ! East border is proc border -- IE-1,IE
+ !-----------------------------------------------------------------------------
+!
+ IF (NHALO<3) THEN
+ PRINT *,'WARNING : WENO5 not parallelisable with NHALO < 3'
+ CALL ABORT
+ ELSEIF (NHALO>=3) THEN
+ !---------------------------------------------------------------------------
+ ! NHALO >= 3 => WENO5 for all boundary points
+ !---------------------------------------------------------------------------
+!
+ ! ----- Positive fluxes -----
+!
+ ! First positive stencil, needs indices i-2, i-1, i
+ ZFPOS1(IE-1,:,:) = 1./6. * (2.0*PSRC(IE-3,:,:) - 7.0*PSRC(IE-2,:,:) + 11.0*PSRC(IE-1,:,:)) ! Flux IE-1
+ ZFPOS1(IE,:,:) = 1./6. * (2.0*PSRC(IE-2,:,:) - 7.0*PSRC(IE-1,:,:) + 11.0*PSRC(IE,:,:)) ! Flux IE
+ ZBPOS1(IE-1,:,:) = 13./12. * (PSRC(IE-3,:,:) - 2.0*PSRC(IE-2,:,:) + PSRC(IE-1,:,:))**2 &
+ + 1./4 * (PSRC(IE-3,:,:) - 4.0*PSRC(IE-2,:,:) + 3.0*PSRC(IE-1,:,:))**2 ! Smoothness indicator IE-1
+ ZBPOS1(IE,:,:) = 13./12. * (PSRC(IE-2,:,:) - 2.0*PSRC(IE-1,:,:) + PSRC(IE,:,:))**2 &
+ + 1./4 * (PSRC(IE-2,:,:) - 4.0*PSRC(IE-1,:,:) + 3.0*PSRC(IE,:,:))**2 ! Smoothness indicator IE
+ ZOMP1(IE-1:IE,:,:) = 1./10. / (ZEPS + ZBPOS1(IE-1:IE,:,:))**2 ! Non-normalized weight IE-1,IE
+!
+ ! Second positive stencil, needs indices i-1, i, i+1
+ ZFPOS2(IE-1,:,:) = 1./6. * (-1.0*PSRC(IE-2,:,:) + 5.0*PSRC(IE-1,:,:) + 2.0*PSRC(IE,:,:)) ! Flux IE-1
+ ZFPOS2(IE,:,:) = 1./6. * (-1.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) + 2.0*PSRC(IE+1,:,:)) ! Flux IE
+ ZBPOS2(IE-1,:,:) = 13./12 * (PSRC(IE-2,:,:) - 2.0*PSRC(IE-1,:,:) + PSRC(IE,:,:))**2 &
+ + 1./4 * (PSRC(IE-2,:,:) - PSRC(IE,:,:))**2 ! Smoothness indicator IE-1
+ ZBPOS2(IE,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (PSRC(IE-1,:,:) - PSRC(IE+1,:,:))**2 ! Smoothness indicator IE
+ ZOMP2(IE-1:IE,:,:) = 3./5. / (ZEPS + ZBPOS2(IE-1:IE,:,:))**2 ! Non-normalized weight IE-1,IE
+!
+ ! Third positive stencil, needs indices i, i+1, i+2
+ ZFPOS3(IE-1,:,:) = 1./6 * (2.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) - PSRC(IE+1,:,:)) ! Flux IE-1
+ ZFPOS3(IE,:,:) = 1./6 * (2.0*PSRC(IE,:,:) + 5.0*PSRC(IE+1,:,:) - PSRC(IE+2,:,:)) ! Flux IE
+ ZBPOS3(IE-1,:,:) = 13./12 * ( PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE-1,:,:) - 4.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 ! Smoothness indicator IE-1
+ ZBPOS3(IE,:,:) = 13./12 * ( PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE,:,:) - 4.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 ! Smoothness indicator IE
+ ZOMP3(IE-1:IE,:,:) = 3./10. / (ZEPS + ZBPOS3(IE-1:IE,:,:))**2 ! Non-normalized weight IE-1,IE
+!
+ ! ----- Negative fluxes -----
+!
+ ! First negative stencil, needs indices i+1, i+2, i+3
+ ZFNEG1(IE-1,:,:) = 1./6. * (11.0*PSRC(IE,:,:) - 7.0*PSRC(IE+1,:,:) + 2.0*PSRC(IE+2,:,:)) ! Flux IE-1
+ ZFNEG1(IE,:,:) = 1./6. * (11.0*PSRC(IE+1,:,:) - 7.0*PSRC(IE+2,:,:) + 2.0*PSRC(IE+3,:,:)) ! Flux IE
+ ZBNEG1(IE-1,:,:) = 13./12. * ( PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE,:,:) - 4.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 ! Smoothness indicator IE-1
+ ZBNEG1(IE,:,:) = 13./12. * ( PSRC(IE+1,:,:) - 2.0*PSRC(IE+2,:,:) + PSRC(IE+3,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE+1,:,:) - 4.0*PSRC(IE+2,:,:) + PSRC(IE+3,:,:))**2 ! Smoothness indicator IE
+ ZOMN1(IE-1:IE,:,:) = 1./10. / (ZEPS + ZBNEG1(IE-1:IE,:,:))**2 ! Non-normalized weight IE-1,IE
+!
+ ! Second negative stencil, needs indices i, i+1, i+2
+ ZFNEG2(IE-1,:,:) = 1./6. * (2.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) - 1.0*PSRC(IE+1,:,:)) ! Flux IE-1
+ ZFNEG2(IE,:,:) = 1./6. * (2.0*PSRC(IE,:,:) + 5.0*PSRC(IE+1,:,:) - 1.0*PSRC(IE+2,:,:)) ! Flux IE
+ ZBNEG2(IE-1,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (PSRC(IE-1,:,:) - PSRC(IE+1,:,:))**2 ! Smoothness indicator IE-1
+ ZBNEG2(IE,:,:) = 13./12 * (PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 &
+ + 1./4 * (PSRC(IE,:,:) - PSRC(IE+2,:,:))**2 ! Smoothness indicator IE
+ ZOMN2(IE-1:IE,:,:) = 3./5. / (ZEPS + ZBNEG2(IE-1:IE,:,:))**2 ! Non-normalized weight IE-1,IE
+!
+ ! Third negative stencil, needs indices i-1, i, i+1
+ ZFNEG3(IE-1,:,:) = 1./6 * (-1.0*PSRC(IE-2,:,:) + 5.0*PSRC(IE-1,:,:) + 2.0*PSRC(IE,:,:)) ! Flux IE-1
+ ZFNEG3(IE,:,:) = 1./6 * (-1.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) + 2.0*PSRC(IE+1,:,:)) ! Flux IE
+ ZBNEG3(IE-1,:,:) = 13./12 * (PSRC(IE-2,:,:) - 2.0*PSRC(IE-1,:,:) + PSRC(IE,:,:))**2 &
+ + 1./4 * (PSRC(IE-2,:,:) - 4.0*PSRC(IE-1,:,:) + 3.0*PSRC(IE,:,:))**2 ! Smoothness indicator IE-1
+ ZBNEG3(IE,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (PSRC(IE-1,:,:) - 4.0*PSRC(IE,:,:) + 3.0*PSRC(IE+1,:,:))**2 ! Smoothness indicator IE
+ ZOMN3(IE-1:IE,:,:) = 3./10. / (ZEPS + ZBNEG3(IE-1:IE,:,:))**2 ! Non-normalized weight IE-1,IE
+!
+ ! ----- Total flux -----
+!
+ PR(IE-1:IE,:,:) = ( ZOMP1(IE-1:IE,:,:)/(ZOMP1(IE-1:IE,:,:)+ZOMP2(IE-1:IE,:,:)+ZOMP3(IE-1:IE,:,:)) * ZFPOS1(IE-1:IE,:,:) &
+ + ZOMP2(IE-1:IE,:,:)/(ZOMP1(IE-1:IE,:,:)+ZOMP2(IE-1:IE,:,:)+ZOMP3(IE-1:IE,:,:)) * ZFPOS2(IE-1:IE,:,:) &
+ + ZOMP3(IE-1:IE,:,:)/(ZOMP1(IE-1:IE,:,:)+ZOMP2(IE-1:IE,:,:)+ZOMP3(IE-1:IE,:,:)) * ZFPOS3(IE-1:IE,:,:)) &
+ * (0.5+SIGN(0.5,PRUCT(IE-1:IE,:,:))) &
+ + ( ZOMN1(IE-1:IE,:,:)/(ZOMN1(IE-1:IE,:,:)+ZOMN2(IE-1:IE,:,:)+ZOMN3(IE-1:IE,:,:)) * ZFNEG1(IE-1:IE,:,:) &
+ + ZOMN2(IE-1:IE,:,:)/(ZOMN1(IE-1:IE,:,:)+ZOMN2(IE-1:IE,:,:)+ZOMN3(IE-1:IE,:,:)) * ZFNEG2(IE-1:IE,:,:) &
+ + ZOMN3(IE-1:IE,:,:)/(ZOMN1(IE-1:IE,:,:)+ZOMN2(IE-1:IE,:,:)+ZOMN3(IE-1:IE,:,:)) * ZFNEG3(IE-1:IE,:,:)) &
+ * (0.5-SIGN(0.5,PRUCT(IE-1:IE,:,:)))
+!
+ END IF ! NHALO
+!
+END IF ! IF(LWEST_ll())
+!-------------------------------------------------------------------------------
+!
+PR = PR * PRUCT ! Add contravariant flux
!
END SUBROUTINE ADVEC_WENO_K_3_UX
!
!------------------------------------------------------------------------------
!
! ############################################################
- SUBROUTINE ADVEC_WENO_K_3_MX(HLBCX,PSRC, PRUCT, PR, TPHALO2)
+ SUBROUTINE ADVEC_WENO_K_3_MX(HLBCX,PSRC, PRUCT, PR)
! ############################################################
!!
!!**** Computes PRUCT * PWT (or PRUCT * PVT). Upstream fluxes of W (or V)
@@ -765,13 +776,16 @@ END SUBROUTINE ADVEC_WENO_K_3_UX
!!
!! MODIFICATIONS
!! -------------
+!! T. Lunet 02/10/2014: Correction of periodic boudary conditions
+!! Change of structure in order to adapt WENO to NHALOK
+!! Suppression of second layer HALO pointers
+!! Complete code documentation
!!
!------------------------------------------------------------------------------
!
USE MODE_ll
USE MODD_LUNIT
USE MODD_CONF
-USE MODD_ARGSLIST_ll, ONLY : HALO2LIST_ll
!
IMPLICIT NONE
!
@@ -785,7 +799,6 @@ REAL, DIMENSION(:,:,:), INTENT(IN) :: PRUCT ! contrav. comp. on MASS GRID
! output source term
!
REAL, DIMENSION(:,:,:), INTENT(INOUT) :: PR
-TYPE(HALO2_ll), OPTIONAL, POINTER :: TPHALO2 ! halo2 for the field at t
!
!* 0.2 Declarations of local variables :
!
@@ -795,12 +808,10 @@ INTEGER:: IW,IE ! Coordinate of third order diffusion area
!
INTEGER:: ILUOUT,IRESP ! for prints
!
-!
! intermediate reconstruction fluxes for positive wind case
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZFPOS1, ZFPOS2, ZFPOS3
!
! intermediate reconstruction fluxes for negative wind case
-! we need only one since ZFNEG2 = ZFPOS2
!
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZFNEG1, ZFNEG2, ZFNEG3
!
@@ -813,14 +824,8 @@ REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZBNEG1, ZBNEG2, ZBNEG3
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)) :: ZOMP1, ZOMP2, ZOMP3
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)) :: ZOMN1, ZOMN2, ZOMN3
!
-! standard weights
-!
-REAL, PARAMETER :: ZGAMMA1 = 1./10.
-REAL, PARAMETER :: ZGAMMA2 = 3./5.
-REAL, PARAMETER :: ZGAMMA3 = 3./10.
-REAL, PARAMETER :: ZGAMMA1_PRIM = 1./3.
-REAL, PARAMETER :: ZGAMMA2_PRIM = 2./3.
-!
+! EPSILON for weno weights calculation
+!
REAL, PARAMETER :: ZEPS = 1.0E-15
!
!-------------------------------------------------------------------------------
@@ -856,524 +861,560 @@ ZOMN1 = 0.0
ZOMN2 = 0.0
ZOMN3 = 0.0
!
-!------------------------------------------------------------------------------
-!
-SELECT CASE ( HLBCX(1) ) ! X direction LBC type: (1) for left side
+!-------------------------------------------------------------------------------
+!* 1.1. Interior Fluxes
+! ---------------------
+IW=IIB
+IE=IIE
!
-!* 1.1 CYCLIC CASE IN THE X DIRECTION:
+!-------------------------------------------------------------------------------
+! Flux calculation in the physical domain far enough from the boundary
+! WENO scheme order 5, IW+2 -> IE-1
+! Computation at the mass point on Ugrid u(i-1/2,j,k)
+!-------------------------------------------------------------------------------
!
-CASE ('CYCL') ! In that case one must have HLBCX(1) == HLBCX(2)
+! ----- Positive fluxes -----
+!
+! First positive stencil, needs indices i-3, i-2, i-1
+ZFPOS1(IW+2:IE-1,:,:) = 1./6. * (2.0*PSRC(IW-1:IE-4,:,:) - 7.0*PSRC(IW:IE-3,:,:) + 11.0*PSRC(IW+1:IE-2,:,:)) ! Flux
+ZBPOS1(IW+2:IE-1,:,:) = 13./12. * ( PSRC(IW-1:IE-4,:,:) - 2.0*PSRC(IW:IE-3,:,:) + PSRC(IW+1:IE-2,:,:))**2 &
+ + 1./4 * ( PSRC(IW-1:IE-4,:,:) - 4.0*PSRC(IW:IE-3,:,:) + 3.0* PSRC(IW+1:IE-2,:,:))**2 ! Smoothness indicator
+ZOMP1(IW+2:IE-1,:,:) = 1./10. / (ZEPS + ZBPOS1(IW+2:IE-1,:,:))**2 ! Non-normalized weight
+!
+! Second positive stencil, needs indices i-2, i-1, i
+ZFPOS2(IW+2:IE-1,:,:) = 1./6. * (-1.0*PSRC(IW:IE-3,:,:) + 5.0*PSRC(IW+1:IE-2,:,:) + 2.0*PSRC(IW+2:IE-1,:,:)) ! Flux
+ZBPOS2(IW+2:IE-1,:,:) = 13./12 * ( PSRC(IW:IE-3,:,:) - 2.0*PSRC(IW+1:IE-2,:,:) + PSRC(IW+2:IE-1,:,:))**2 &
+ + 1./4 * ( PSRC(IW:IE-3,:,:) - PSRC(IW+2:IE-1,:,:))**2 ! Smoothness indicator
+ZOMP2(IW+2:IE-1,:,:) = 3./5. / (ZEPS + ZBPOS2(IW+2:IE-1,:,:))**2 ! Non-normalized weight
+!
+! Third positive stencil, needs indices i-1, i, i+1
+ZFPOS3(IW+2:IE-1,:,:) = 1./6 * (2.0*PSRC(IW+1:IE-2,:,:) + 5.0*PSRC(IW+2:IE-1,:,:) - PSRC(IW+3:IE,:,:)) ! Flux
+ZBPOS3(IW+2:IE-1,:,:) = 13./12 * ( PSRC(IW+1:IE-2,:,:) - 2.0*PSRC(IW+2:IE-1,:,:) + PSRC(IW+3:IE,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IW+1:IE-2,:,:) - 4.0*PSRC(IW+2:IE-1,:,:) + PSRC(IW+3:IE,:,:))**2 ! Smoothness indicator
+ZOMP3(IW+2:IE-1,:,:) = 3./10. / (ZEPS + ZBPOS3(IW+2:IE-1,:,:))**2 ! Non-normalized weight
+!
+! ----- Negative fluxes -----
+!
+! First negative stencil, needs indices i, i+1, i+2
+ZFNEG1(IW+2:IE-1,:,:) = 1./6. * (11.0*PSRC(IW+2:IE-1,:,:) - 7.0*PSRC(IW+3:IE,:,:) + 2.0*PSRC(IW+4:IE+1,:,:)) ! Flux
+ZBNEG1(IW+2:IE-1,:,:) = 13./12. * ( PSRC(IW+2:IE-1,:,:) - 2.0*PSRC(IW+3:IE,:,:) + PSRC(IW+4:IE+1,:,:))**2 &
+ + 1./4 * (3.0* PSRC(IW+2:IE-1,:,:) - 4.0*PSRC(IW+3:IE,:,:) + PSRC(IW+4:IE+1,:,:))**2 ! Smoothness indicator
+ZOMN1(IW+2:IE-1,:,:) = 1./10. / (ZEPS + ZBNEG1(IW+2:IE-1,:,:))**2 ! Non-normalized weight
+!
+! Second negative stencil, needs indices i-1, i, i+1
+ZFNEG2(IW+2:IE-1,:,:) = 1./6. * (2.0*PSRC(IW+1:IE-2,:,:) + 5.0*PSRC(IW+2:IE-1,:,:) - 1.0*PSRC(IW+3:IE,:,:)) ! Flux
+ZBNEG2(IW+2:IE-1,:,:) = 13./12 * ( PSRC(IW+1:IE-2,:,:) - 2.0*PSRC(IW+2:IE-1,:,:) + PSRC(IW+3:IE,:,:))**2 &
+ + 1./4 * ( PSRC(IW+1:IE-2,:,:) - PSRC(IW+3:IE,:,:))**2 ! Smoothness indicator
+ZOMN2(IW+2:IE-1,:,:) = 3./5. / (ZEPS + ZBNEG2(IW+2:IE-1,:,:))**2 ! Non-normalized weight
+!
+! Third negative stencil, needs indices i-2, i-1, i
+ZFNEG3(IW+2:IE-1,:,:) = 1./6 * (-1.0*PSRC(IW:IE-3,:,:) + 5.0*PSRC(IW+1:IE-2,:,:) + 2.0*PSRC(IW+2:IE-1,:,:)) ! Flux
+ZBNEG3(IW+2:IE-1,:,:) = 13./12 * ( PSRC(IW:IE-3,:,:) - 2.0*PSRC(IW+1:IE-2,:,:) + PSRC(IW+2:IE-1,:,:))**2 &
+ + 1./4 * ( PSRC(IW:IE-3,:,:) - 4.0*PSRC(IW+1:IE-2,:,:) + 3.0*PSRC(IW+2:IE-1,:,:))**2 ! Smoothness indicator
+ZOMN3(IW+2:IE-1,:,:) = 3./10. / (ZEPS + ZBNEG3(IW+2:IE-1,:,:))**2 ! Non-normalized weight
+!
+!
+! ----- Total flux -----
+!
+PR(IW+2:IE-1,:,:) = (ZOMP1(IW+2:IE-1,:,:)/(ZOMP1(IW+2:IE-1,:,:)+ZOMP2(IW+2:IE-1,:,:)+ZOMP3(IW+2:IE-1,:,:)) &
+ * ZFPOS1(IW+2:IE-1,:,:) + &
+ ZOMP2(IW+2:IE-1,:,:)/(ZOMP1(IW+2:IE-1,:,:)+ZOMP2(IW+2:IE-1,:,:)+ZOMP3(IW+2:IE-1,:,:)) &
+ * ZFPOS2(IW+2:IE-1,:,:) + &
+ ZOMP3(IW+2:IE-1,:,:)/(ZOMP1(IW+2:IE-1,:,:)+ZOMP2(IW+2:IE-1,:,:)+ZOMP3(IW+2:IE-1,:,:)) &
+ * ZFPOS3(IW+2:IE-1,:,:)) &
+ * (0.5+SIGN(0.5,PRUCT(IW+2:IE-1,:,:))) &
+ + (ZOMN1(IW+2:IE-1,:,:)/(ZOMN1(IW+2:IE-1,:,:)+ZOMN2(IW+2:IE-1,:,:)+ZOMN3(IW+2:IE-1,:,:)) &
+ * ZFNEG1(IW+2:IE-1,:,:) &
+ + ZOMN2(IW+2:IE-1,:,:)/(ZOMN1(IW+2:IE-1,:,:)+ZOMN2(IW+2:IE-1,:,:)+ZOMN3(IW+2:IE-1,:,:)) &
+ * ZFNEG2(IW+2:IE-1,:,:) &
+ + ZOMN3(IW+2:IE-1,:,:)/(ZOMN1(IW+2:IE-1,:,:)+ZOMN2(IW+2:IE-1,:,:)+ZOMN3(IW+2:IE-1,:,:)) &
+ * ZFNEG3(IW+2:IE-1,:,:)) &
+ * (0.5-SIGN(0.5,PRUCT(IW+2:IE-1,:,:)))
!
- IF(NHALO == 1) THEN
- IW=IIB
- IE=IIE
- ELSE
- CALL FMLOOK_ll(CLUOUT0,CLUOUT0,ILUOUT,IRESP)
- WRITE(ILUOUT,*) 'ERROR : 3rd order advection in CYCLic case '
- WRITE(ILUOUT,*) 'cannot be used with NHALO=2'
- CALL ABORT
- STOP
- END IF
+!-------------------------------------------------------------------------------
+!* 1.2. West border
+! ---------------------
!
-! r: many left cells in regard to 'i-1' cell for each stencil
+IF( LWEST_ll() .AND. .FALSE. ) THEN
+ !-----------------------------------------------------------------------------
+ ! West border is physical -- IW+1,IW
+ !-----------------------------------------------------------------------------
+ SELECT CASE (HLBCX(1)) ! X direction LBC type on left side
!
-! intermediate fluxes at the mass point on Ugrid u(i-1/2,j,k)=((i-1)+1/2,j,k)
-! for positive wind case (left to the right)
-! (r=2 for the first stencil ZFPOS1, r=1 for the second ZFPOS2 and
-! r=0 for the last ZFPOS3)
-!
- ZFPOS1(IW+2:IE,:,:) = 1./6 * (2.0*PSRC(IW-1:IE-3,:,:) - 7.0*PSRC(IW:IE-2,:,:) + &
- 11.0*PSRC(IW+1:IE-1,:,:))
- ZFPOS1(IW+1, :,:) = 1./6 * (2.0*TPHALO2%WEST(:,:) - 7.0*PSRC(IW-1, :,:) + &
- 11.0*PSRC(IW, :,:))
- ZFPOS1(IE+1,:,:) = 0.5 * (3.0*PSRC(IE, :,:) - PSRC(IE-1,:,:))
- ZFPOS1(IW, :,:) = 0.5 * (3.0*PSRC(IW-1,:,:) - TPHALO2%WEST(:,:) )
- ZFPOS1(IW-1,:,:) = - 999.
-!
-!
- ZFPOS2(IW+1:IE,:,:) = 1./6 * (-1.0*PSRC(IW-1:IE-2,:,:) + 5.0*PSRC(IW:IE-1,:,:) + &
- 2.0*PSRC(IW+1:IE,:,:))
- ZFPOS2(IE+1,:,:) = 0.5 * (PSRC(IE+1,:,:) + PSRC(IE, :,:))
- ZFPOS2(IW, :,:) = 0.5 * (PSRC(IW-1,:,:) + PSRC(IW, :,:))
- ZFPOS2(IW-1,:,:) = 0.5 * (TPHALO2%WEST(:,:) + PSRC(IW-1,:,:))
-!
-!
- ZFPOS3(IW+1:IE,:,:) = 1./6 * (2.0*PSRC(IW:IE-1,:,:) + 5.0*PSRC(IW+1:IE,:,:) - &
- PSRC(IW+2:IE+1,:,:))
-!
-! r: many left cells in regard to 'i' cell for each stencil
-!
-! intermediate fluxes at the mass point on Ugrid u(i-1/2,j,k) for negative wind
-! case (R. to the L.)
-! (r=2 for the third stencil ZFNEG3=ZFPOS2, r=1 for the second ZFNEG2=ZFPOS3
-! and r=0 for the first ZFNEG1)
-!
- ZFNEG1(IW+1:IE-1,:,:) = 1./6 * (11.0*PSRC(IW+1:IE-1,:,:) - 7.0*PSRC(IW+2:IE,:,:)&
- + 2.0*PSRC(IW+3:IE+1,:,:))
- ZFNEG1(IE, :,:) = 1./6 * (11.0*PSRC(IE, :,:) - 7.0*PSRC(IE+1, :,:)&
- + 2.0*TPHALO2%EAST(:,:))
- ZFNEG1(IW, :,:) = 0.5 * (3.0*PSRC(IW, :,:) - PSRC(IW+1, :,:))
- ZFNEG1(IW-1,:,:) = 0.5 * (3.0*PSRC(IW-1,:,:) - PSRC(IW, :,:))
- ZFNEG1(IE+1,:,:) = 0.5 * (3.0*PSRC(IE+1,:,:) - TPHALO2%EAST(:,:))
-!
-!
- ZFNEG2(IW+1:IE,:,:) = 1./6 * (2.0*PSRC(IW:IE-1,:,:) + 5.0*PSRC(IW+1:IE,:,:) - &
- PSRC(IW+2:IE+1,:,:))
- ZFNEG2(IW, :,:) = 0.5 * (PSRC(IW, :,:) + PSRC(IW-1, :,:))
- ZFNEG2(IW-1,:,:) = 0.5 * (PSRC(IW-1,:,:) + TPHALO2%WEST(:,:))
- ZFNEG2(IE+1,:,:) = 0.5 * (PSRC(IE+1,:,:) + PSRC(IE, :,:))
+ CASE ('CYCL')
+ !---------------------------------------------------------------------------
+ ! Periodic boundary condition
+ !---------------------------------------------------------------------------
+!
+ IF(LEAST_ll() .AND. .FALSE. ) THEN ! East border is physical
+!
+ ! First positive stencil, needs indices i-3, i-2, i-1
+ ZFPOS1(IW+1,:,:) = 1./6. * (2.0*PSRC(IE,:,:) - 7.0*PSRC(IW-1,:,:) + 11.0*PSRC(IW,:,:)) ! Flux IW+1
+ ZFPOS1(IW,:,:) = 1./6. * (2.0*PSRC(IE-1,:,:) - 7.0*PSRC(IE,:,:) + 11.0*PSRC(IW-1,:,:)) ! Flux IW
+ ZBPOS1(IW+1,:,:) = 13./12. * (PSRC(IE,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IE,:,:) - 4.0*PSRC(IW-1,:,:) + 3.0*PSRC(IW,:,:))**2 ! Smoothness indicator IW+1
+ ZBPOS1(IW,:,:) = 13./12. * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IW-1,:,:))**2 &
+ + 1./4 * (PSRC(IE-1,:,:) - 4.0*PSRC(IE,:,:) + 3.0*PSRC(IW-1,:,:))**2 ! Smoothness indicator IW
+ ZOMP1(IW:IW+1,:,:) = 1./10. / (ZEPS + ZBPOS1(IW:IW+1,:,:))**2 ! Non-normalized weight IW+1,IW
+!
+ ! Second positive stencil, needs indices i-2, i-1, i
+ ZFPOS2(IW+1,:,:) = 1./6.* (-1.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) + 2.0*PSRC(IW+1,:,:)) ! Flux IW+1
+ ZFPOS2(IW,:,:) = 1./6.* (-1.0*PSRC(IE,:,:) + 5.0*PSRC(IW-1,:,:) + 2.0*PSRC(IW,:,:)) ! Flux IW
+ ZBPOS2(IW+1,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (PSRC(IW-1,:,:) - PSRC(IW+1,:,:))**2 ! Smoothness indicator IW+1
+ ZBPOS2(IW,:,:) = 13./12 * (PSRC(IE,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IE,:,:) - PSRC(IW,:,:))**2 ! Smoothness indicator IW
+ ZOMP2(IW:IW+1,:,:) = 3./5. / (ZEPS + ZBPOS2(IW:IW+1,:,:))**2 ! Non-normalized weight IW+1,IW
+!
+ ! Third negative stencil, needs indices i-2, i-1, i
+ ZFNEG3(IW+1,:,:) = 1./6 * (-1.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) + 2.0*PSRC(IW+1,:,:)) ! Flux IW+1
+ ZFNEG3(IW,:,:) = 1./6 * (-1.0*PSRC(IE,:,:) + 5.0*PSRC(IW-1,:,:) + 2.0*PSRC(IW,:,:)) ! Flux IW
+ ZBNEG3(IW+1,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (PSRC(IW-1,:,:) - 4.0*PSRC(IW,:,:) + 3.0*PSRC(IW+1,:,:))**2 ! Smoothness indicator IW+1
+ ZBNEG3(IW,:,:) = 13./12 * (PSRC(IE,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IE,:,:) - 4.0*PSRC(IW-1,:,:) + 3.0*PSRC(IW,:,:))**2 ! Smoothness indicator IW
+ ZOMN3(IW:IW+1,:,:) = 3./10. / (ZEPS + ZBNEG3(IW:IW+1,:,:))**2 ! Non-normalized weight IW+1,IW
+!
+ ELSEIF(IW>3) THEN ! East boundary is proc border, with minimum 3 HALO points on west side
+!
+ ! First positive stencil, needs indices i-3, i-2, i-1
+ ZFPOS1(IW+1,:,:) = 1./6. * (2.0*PSRC(IW-2,:,:) - 7.0*PSRC(IW-1,:,:) + 11.0*PSRC(IW,:,:)) ! Flux IW+1
+ ZFPOS1(IW,:,:) = 1./6. * (2.0*PSRC(IW-3,:,:) - 7.0*PSRC(IW-2,:,:) + 11.0*PSRC(IW-1,:,:)) ! Flux IW
+ ZBPOS1(IW+1,:,:) = 13./12. * (PSRC(IW-2,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IW-2,:,:) - 4.0*PSRC(IW-1,:,:) + 3.0*PSRC(IW,:,:))**2 ! Smoothness indicator IW+1
+ ZBPOS1(IW,:,:) = 13./12. * (PSRC(IW-3,:,:) - 2.0*PSRC(IW-2,:,:) + PSRC(IW-1,:,:))**2 &
+ + 1./4 * (PSRC(IW-3,:,:) - 4.0*PSRC(IW-2,:,:) + 3.0*PSRC(IW-1,:,:))**2 ! Smoothness indicator IW
+ ZOMP1(IW:IW+1,:,:) = 1./10. / (ZEPS + ZBPOS1(IW:IW+1,:,:))**2 ! Non-normalized weight IW+1,IW
+!
+ ! Second positive stencil, needs indices i-2, i-1, i
+ ZFPOS2(IW+1,:,:) = 1./6.* (-1.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) + 2.0*PSRC(IW+1,:,:)) ! Flux IW+1
+ ZFPOS2(IW,:,:) = 1./6.* (-1.0*PSRC(IW-2,:,:) + 5.0*PSRC(IW-1,:,:) + 2.0*PSRC(IW,:,:)) ! Flux IW
+ ZBPOS2(IW+1,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (PSRC(IW-1,:,:) - PSRC(IW+1,:,:))**2 ! Smoothness indicator IW+1
+ ZBPOS2(IW,:,:) = 13./12 * (PSRC(IW-2,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IW-2,:,:) - PSRC(IW,:,:))**2 ! Smoothness indicator IW
+ ZOMP2(IW:IW+1,:,:) = 3./5. / (ZEPS + ZBPOS2(IW:IW+1,:,:))**2 ! Non-normalized weight IW+1,IW
+!
+ ! Third negative stencil, needs indices i-2, i-1, i
+ ZFNEG3(IW+1,:,:) = 1./6 * (-1.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) + 2.0*PSRC(IW+1,:,:)) ! Flux IW+1
+ ZFNEG3(IW,:,:) = 1./6 * (-1.0*PSRC(IW-2,:,:) + 5.0*PSRC(IW-1,:,:) + 2.0*PSRC(IW,:,:)) ! Flux IW
+ ZBNEG3(IW+1,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (PSRC(IW-1,:,:) - 4.0*PSRC(IW,:,:) + 3.0*PSRC(IW+1,:,:))**2 ! Smoothness indicator IW+1
+ ZBNEG3(IW,:,:) = 13./12 * (PSRC(IW-2,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IW-2,:,:) - 4.0*PSRC(IW-1,:,:) + 3.0*PSRC(IW,:,:))**2 ! Smoothness indicator IW
+ ZOMN3(IW:IW+1,:,:) = 3./10. / (ZEPS + ZBNEG3(IW:IW+1,:,:))**2 ! Non-normalized weight IW+1,IW
+!
+ ELSE ! East boundary is proc border, with NHALO < 3 on west side
+ PRINT *,'WARNING : WENO5 fluxes calculation needs NHALO >= 3 on west side'
+ CALL ABORT
+ ENDIF
!
+ ! Third positive stencil, needs indices i-1, i, i+1
+ ZFPOS3(IW+1,:,:) = 1./6 * (2.0*PSRC(IW,:,:) + 5.0*PSRC(IW+1,:,:) - PSRC(IW+2,:,:)) ! Flux IW+1
+ ZFPOS3(IW,:,:) = 1./6 * (2.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) - PSRC(IW+1,:,:)) ! Flux IW
+ ZBPOS3(IW+1,:,:) = 13./12 * ( PSRC(IW,:,:) - 2.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IW,:,:) - 4.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 ! Smoothness indicator IW+1
+ ZBPOS3(IW,:,:) = 13./12 * ( PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IW-1,:,:) - 4.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 ! Smoothness indicator IW
+ ZOMP3(IW:IW+1,:,:) = 3./10. / (ZEPS + ZBPOS3(IW:IW+1,:,:))**2 ! Non-normalized weight IW+1,IW
+!
+ ! ----- Negative fluxes -----
+!
+ ! First negative stencil, needs indices i, i+1, i+2
+ ZFNEG1(IW+1,:,:) = 1./6. * (11.0*PSRC(IW+1,:,:) - 7.0*PSRC(IW+2,:,:) + 2.0*PSRC(IW+3,:,:)) ! Flux IW+1
+ ZFNEG1(IW,:,:) = 1./6. * (11.0*PSRC(IW,:,:) - 7.0*PSRC(IW+1,:,:) + 2.0*PSRC(IW+2,:,:)) ! Flux IW
+ ZBNEG1(IW+1,:,:) = 13./12. * ( PSRC(IW+1,:,:) - 2.0*PSRC(IW+2,:,:) + PSRC(IW+3,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IW+1,:,:) - 4.0*PSRC(IW+2,:,:) + PSRC(IW+3,:,:))**2 ! Smoothness indicator IW+1
+ ZBNEG1(IW,:,:) = 13./12. * ( PSRC(IW,:,:) - 2.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IW,:,:) - 4.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 ! Smoothness indicator IW
+ ZOMN1(IW:IW+1,:,:) = 1./10. / (ZEPS + ZBNEG1(IW:IW+1,:,:))**2 ! Non-normalized weight IW+1,IW
+!
+ ! Second negative stencil, needs indices i-1, i, i+1
+ ZFNEG2(IW+1,:,:) = 1./6. * (2.0*PSRC(IW,:,:) + 5.0*PSRC(IW+1,:,:) - 1.0*PSRC(IW+2,:,:)) ! Flux IW+1
+ ZFNEG2(IW,:,:) = 1./6. * (2.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) - 1.0*PSRC(IW+1,:,:)) ! Flux IW
+ ZBNEG2(IW+1,:,:) = 13./12 * (PSRC(IW,:,:) - 2.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 &
+ + 1./4 * (PSRC(IW,:,:) - PSRC(IW+2,:,:))**2 ! Smoothness indicator IW+1
+ ZBNEG2(IW,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (PSRC(IW-1,:,:) - PSRC(IW+1,:,:))**2 ! Smoothness indicator IW
+ ZOMN2(IW:IW+1,:,:) = 3./5. / (ZEPS + ZBNEG2(IW:IW+1,:,:))**2 ! Non-normalized weight IW+1,IW
+!
+ ! ----- Total flux -----
+!
+ PR(IW:IW+1,:,:) = ( ZOMP1(IW:IW+1,:,:)/(ZOMP1(IW:IW+1,:,:)+ZOMP2(IW:IW+1,:,:)+ZOMP3(IW:IW+1,:,:)) * ZFPOS1(IW:IW+1,:,:) &
+ + ZOMP2(IW:IW+1,:,:)/(ZOMP1(IW:IW+1,:,:)+ZOMP2(IW:IW+1,:,:)+ZOMP3(IW:IW+1,:,:)) * ZFPOS2(IW:IW+1,:,:) &
+ + ZOMP3(IW:IW+1,:,:)/(ZOMP1(IW:IW+1,:,:)+ZOMP2(IW:IW+1,:,:)+ZOMP3(IW:IW+1,:,:)) * ZFPOS3(IW:IW+1,:,:)) &
+ * (0.5+SIGN(0.5,PRUCT(IW:IW+1,:,:))) &
+ + ( ZOMN1(IW:IW+1,:,:)/(ZOMN1(IW:IW+1,:,:)+ZOMN2(IW:IW+1,:,:)+ZOMN3(IW:IW+1,:,:)) * ZFNEG1(IW:IW+1,:,:) &
+ + ZOMN2(IW:IW+1,:,:)/(ZOMN1(IW:IW+1,:,:)+ZOMN2(IW:IW+1,:,:)+ZOMN3(IW:IW+1,:,:)) * ZFNEG2(IW:IW+1,:,:) &
+ + ZOMN3(IW:IW+1,:,:)/(ZOMN1(IW:IW+1,:,:)+ZOMN2(IW:IW+1,:,:)+ZOMN3(IW:IW+1,:,:)) * ZFNEG3(IW:IW+1,:,:)) &
+ * (0.5-SIGN(0.5,PRUCT(IW:IW+1,:,:)))
+!
+ CASE ('OPEN','WALL','NEST')
+ !---------------------------------------------------------------------------
+ ! Open, or Wall, or Nest boundary condition => WENO order reduction
+ !---------------------------------------------------------------------------
+!
+ ! WENO scheme order 1, IW
+ PR(IW,:,:) = PSRC(IW-1,:,:) * (0.5+SIGN(0.5,PRUCT(IW,:,:))) + &
+ PSRC(IW,:,:) * (0.5-SIGN(0.5,PRUCT(IW,:,:)))
+!
+! ! WENO scheme order 3, IW+1
+ ZFPOS1(IW+1,:,:) = 0.5 * (3.0*PSRC(IW,:,:) - PSRC(IW-1,:,:)) ! First positive flux
+ ZFPOS2(IW+1,:,:) = 0.5 * ( PSRC(IW,:,:) + PSRC(IW+1,:,:)) ! Second positive flux
+ ZBPOS1(IW+1,:,:) = (PSRC(IW,:,:) - PSRC(IW-1,:,:))**2 ! First positive smoothness indicator
+ ZBPOS2(IW+1,:,:) = (PSRC(IW+1,:,:) - PSRC(IW,:,:))**2 ! Second positive smoothness indicator
+!
+ ZFNEG1(IW+1,:,:) = 0.5 * (3.0*PSRC(IW+1,:,:) - PSRC(IW+2,:,:)) ! First negative flux
+ ZFNEG2(IW+1,:,:) = 0.5 * ( PSRC(IW,:,:) + PSRC(IW+1,:,:)) ! Second negative flux
+ ZBNEG1(IW+1,:,:) = (PSRC(IW+1,:,:) - PSRC(IW+2,:,:))**2 ! First negative smoothness indicator
+ ZBNEG2(IW+1,:,:) = (PSRC(IW,:,:) - PSRC(IW+1,:,:))**2 ! Second negative smoothness indicator
+!
+ ZOMP1(IW+1,:,:) = 1./3. / (ZEPS + ZBPOS1(IW+1,:,:))**2 ! First positive non-normalized weight
+ ZOMP2(IW+1,:,:) = 2./3. / (ZEPS + ZBPOS2(IW+1,:,:))**2 ! Second positive non-normalized weight
+ ZOMN1(IW+1,:,:) = 1./3. / (ZEPS + ZBNEG1(IW+1,:,:))**2 ! First negative non-normalized weight
+ ZOMN2(IW+1,:,:) = 2./3. / (ZEPS + ZBNEG2(IW+1,:,:))**2 ! Second negative non-normalized weight
+!
+ PR(IW+1,:,:) = (ZOMN2(IW+1,:,:)/(ZOMN1(IW+1,:,:)+ZOMN2(IW+1,:,:)) * ZFNEG2(IW+1,:,:) + &
+ (ZOMN1(IW+1,:,:)/(ZOMN1(IW+1,:,:)+ZOMN2(IW+1,:,:)) * ZFNEG1(IW+1,:,:))) &
+ *(0.5-SIGN(0.5,PRUCT(IW+1,:,:))) + &
+ (ZOMP2(IW+1,:,:)/(ZOMP1(IW+1,:,:)+ZOMP2(IW+1,:,:)) * ZFPOS2(IW+1,:,:) + &
+ (ZOMP1(IW+1,:,:)/(ZOMP1(IW+1,:,:)+ZOMP2(IW+1,:,:)) * ZFPOS1(IW+1,:,:))) &
+ *(0.5+SIGN(0.5,PRUCT(IW+1,:,:))) ! Total flux
+!
+ END SELECT ! SELECT CASE (HLBCX(1)) ! X direction LBC type on left side
+!
+ELSE
+ !-----------------------------------------------------------------------------
+ ! West border is proc border -- IW,IW-1
+ !-----------------------------------------------------------------------------
+!
+ IF (NHALO<3) THEN
+ PRINT *,'WARNING : WENO5 not parallelisable with NHALO < 3'
+ CALL ABORT
+ ELSEIF (NHALO>=3) THEN
+ !---------------------------------------------------------------------------
+ ! NHALO >3 => WENO5 for all boundary points
+ !---------------------------------------------------------------------------
+!
+ ! ----- Positive fluxes -----
+!
+ ! First positive stencil, needs indices i-3, i-2, i-1
+ ZFPOS1(IW+1,:,:) = 1./6. * (2.0*PSRC(IW-2,:,:) - 7.0*PSRC(IW-1,:,:) + 11.0*PSRC(IW,:,:)) ! Flux IW+1
+ ZFPOS1(IW,:,:) = 1./6. * (2.0*PSRC(IW-3,:,:) - 7.0*PSRC(IW-2,:,:) + 11.0*PSRC(IW-1,:,:)) ! Flux IW
+ ZBPOS1(IW+1,:,:) = 13./12. * (PSRC(IW-2,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IW-2,:,:) - 4.0*PSRC(IW-1,:,:) + 3.0*PSRC(IW,:,:))**2 ! Smoothness indicator IW+1
+ ZBPOS1(IW,:,:) = 13./12. * (PSRC(IW-3,:,:) - 2.0*PSRC(IW-2,:,:) + PSRC(IW-1,:,:))**2 &
+ + 1./4 * (PSRC(IW-3,:,:) - 4.0*PSRC(IW-2,:,:) + 3.0*PSRC(IW-1,:,:))**2 ! Smoothness indicator IW
+ ZOMP1(IW:IW+1,:,:) = 1./10. / (ZEPS + ZBPOS1(IW:IW+1,:,:))**2 ! Non-normalized weight IW+1,IW
+!
+ ! Second positive stencil, needs indices i-2, i-1, i
+ ZFPOS2(IW+1,:,:) = 1./6.* (-1.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) + 2.0*PSRC(IW+1,:,:)) ! Flux IW+1
+ ZFPOS2(IW,:,:) = 1./6.* (-1.0*PSRC(IW-2,:,:) + 5.0*PSRC(IW-1,:,:) + 2.0*PSRC(IW,:,:)) ! Flux IW
+ ZBPOS2(IW+1,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (PSRC(IW-1,:,:) - PSRC(IW+1,:,:))**2 ! Smoothness indicator IW+1
+ ZBPOS2(IW,:,:) = 13./12 * (PSRC(IW-2,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IW-2,:,:) - PSRC(IW,:,:))**2 ! Smoothness indicator IW
+ ZOMP2(IW:IW+1,:,:) = 3./5. / (ZEPS + ZBPOS2(IW:IW+1,:,:))**2 ! Non-normalized weight IW+1,IW
+!
+ ! Third positive stencil, needs indices i-1, i, i+1
+ ZFPOS3(IW+1,:,:) = 1./6 * (2.0*PSRC(IW,:,:) + 5.0*PSRC(IW+1,:,:) - PSRC(IW+2,:,:)) ! Flux IW+1
+ ZFPOS3(IW,:,:) = 1./6 * (2.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) - PSRC(IW+1,:,:)) ! Flux IW
+ ZBPOS3(IW+1,:,:) = 13./12 * ( PSRC(IW,:,:) - 2.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IW,:,:) - 4.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 ! Smoothness indicator IW+1
+ ZBPOS3(IW,:,:) = 13./12 * ( PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IW-1,:,:) - 4.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 ! Smoothness indicator IW
+ ZOMP3(IW:IW+1,:,:) = 3./10. / (ZEPS + ZBPOS3(IW:IW+1,:,:))**2 ! Non-normalized weight IW+1,IW
+!
+ ! ----- Negative fluxes -----
+!
+ ! First negative stencil, needs indices i, i+1, i+2
+ ZFNEG1(IW+1,:,:) = 1./6. * (11.0*PSRC(IW+1,:,:) - 7.0*PSRC(IW+2,:,:) + 2.0*PSRC(IW+3,:,:)) ! Flux IW+1
+ ZFNEG1(IW,:,:) = 1./6. * (11.0*PSRC(IW,:,:) - 7.0*PSRC(IW+1,:,:) + 2.0*PSRC(IW+2,:,:)) ! Flux IW
+ ZBNEG1(IW+1,:,:) = 13./12. * ( PSRC(IW+1,:,:) - 2.0*PSRC(IW+2,:,:) + PSRC(IW+3,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IW+1,:,:) - 4.0*PSRC(IW+2,:,:) + PSRC(IW+3,:,:))**2 ! Smoothness indicator IW+1
+ ZBNEG1(IW,:,:) = 13./12. * ( PSRC(IW,:,:) - 2.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IW,:,:) - 4.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 ! Smoothness indicator IW
+ ZOMN1(IW:IW+1,:,:) = 1./10. / (ZEPS + ZBNEG1(IW:IW+1,:,:))**2 ! Non-normalized weight IW+1,IW
+!
+ ! Second negative stencil, needs indices i-1, i, i+1
+ ZFNEG2(IW+1,:,:) = 1./6. * (2.0*PSRC(IW,:,:) + 5.0*PSRC(IW+1,:,:) - 1.0*PSRC(IW+2,:,:)) ! Flux IW+1
+ ZFNEG2(IW,:,:) = 1./6. * (2.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) - 1.0*PSRC(IW+1,:,:)) ! Flux IW
+ ZBNEG2(IW+1,:,:) = 13./12 * (PSRC(IW,:,:) - 2.0*PSRC(IW+1,:,:) + PSRC(IW+2,:,:))**2 &
+ + 1./4 * (PSRC(IW,:,:) - PSRC(IW+2,:,:))**2 ! Smoothness indicator IW+1
+ ZBNEG2(IW,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (PSRC(IW-1,:,:) - PSRC(IW+1,:,:))**2 ! Smoothness indicator IW
+ ZOMN2(IW:IW+1,:,:) = 3./5. / (ZEPS + ZBNEG2(IW:IW+1,:,:))**2 ! Non-normalized weight IW+1,IW
+!
+ ! Third negative stencil, needs indices i-2, i-1, i
+ ZFNEG3(IW+1,:,:) = 1./6 * (-1.0*PSRC(IW-1,:,:) + 5.0*PSRC(IW,:,:) + 2.0*PSRC(IW+1,:,:)) ! Flux IW+1
+ ZFNEG3(IW,:,:) = 1./6 * (-1.0*PSRC(IW-2,:,:) + 5.0*PSRC(IW-1,:,:) + 2.0*PSRC(IW,:,:)) ! Flux IW
+ ZBNEG3(IW+1,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (PSRC(IW-1,:,:) - 4.0*PSRC(IW,:,:) + 3.0*PSRC(IW+1,:,:))**2 ! Smoothness indicator IW+1
+ ZBNEG3(IW,:,:) = 13./12 * (PSRC(IW-2,:,:) - 2.0*PSRC(IW-1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IW-2,:,:) - 4.0*PSRC(IW-1,:,:) + 3.0*PSRC(IW,:,:))**2 ! Smoothness indicator IW
+ ZOMN3(IW:IW+1,:,:) = 3./10. / (ZEPS + ZBNEG3(IW:IW+1,:,:))**2 ! Non-normalized weight IW+1,IW
+!
+ ! ----- Total flux -----
+!
+ PR(IW:IW+1,:,:) = ( ZOMP1(IW:IW+1,:,:)/(ZOMP1(IW:IW+1,:,:)+ZOMP2(IW:IW+1,:,:)+ZOMP3(IW:IW+1,:,:)) * ZFPOS1(IW:IW+1,:,:) &
+ + ZOMP2(IW:IW+1,:,:)/(ZOMP1(IW:IW+1,:,:)+ZOMP2(IW:IW+1,:,:)+ZOMP3(IW:IW+1,:,:)) * ZFPOS2(IW:IW+1,:,:) &
+ + ZOMP3(IW:IW+1,:,:)/(ZOMP1(IW:IW+1,:,:)+ZOMP2(IW:IW+1,:,:)+ZOMP3(IW:IW+1,:,:)) * ZFPOS3(IW:IW+1,:,:)) &
+ * (0.5+SIGN(0.5,PRUCT(IW:IW+1,:,:))) &
+ + ( ZOMN1(IW:IW+1,:,:)/(ZOMN1(IW:IW+1,:,:)+ZOMN2(IW:IW+1,:,:)+ZOMN3(IW:IW+1,:,:)) * ZFNEG1(IW:IW+1,:,:) &
+ + ZOMN2(IW:IW+1,:,:)/(ZOMN1(IW:IW+1,:,:)+ZOMN2(IW:IW+1,:,:)+ZOMN3(IW:IW+1,:,:)) * ZFNEG2(IW:IW+1,:,:) &
+ + ZOMN3(IW:IW+1,:,:)/(ZOMN1(IW:IW+1,:,:)+ZOMN2(IW:IW+1,:,:)+ZOMN3(IW:IW+1,:,:)) * ZFNEG3(IW:IW+1,:,:)) &
+ * (0.5-SIGN(0.5,PRUCT(IW:IW+1,:,:)))
!
- ZFNEG3(IW+1:IE,:,:) = 1./6 * (-1.0*PSRC(IW-1:IE-2,:,:) + 5.0*PSRC(IW:IE-1,:,:) + &
- 2.0*PSRC(IW+1:IE,:,:))
-!
-! smoothness indicators for positive wind case
+ END IF ! NHALO
!
- ZBPOS1(IW+2:IE,:,:) = 13./12 * (PSRC(IW-1:IE-3,:,:) - 2.0*PSRC(IW:IE-2,:,:) + &
- PSRC(IW+1:IE-1,:,:))**2 + &
- 1./4 * (PSRC(IW-1:IE-3,:,:) - 4.0*PSRC(IW:IE-2,:,:) + &
- 3.0*PSRC(IW+1:IE-1,:,:))**2
- ZBPOS1(IW+1, :,:) = 13./12 * (TPHALO2%WEST(:,:) - 2.0*PSRC(IW-1,:,:) + &
- PSRC(IW,:,:))**2 + &
- 1./4 * (TPHALO2%WEST(:,:) - 4.0*PSRC(IW-1,:,:) + &
- 3.0*PSRC(IW,:,:))**2
- ZBPOS1(IE+1,:,:) = (PSRC(IE, :,:) - PSRC(IE-1,:,:))**2
- ZBPOS1(IW, :,:) = (PSRC(IW-1,:,:) - TPHALO2%WEST(:,:))**2
- ZBPOS1(IW-1,:,:) = - 999.
-!
-!
- ZBPOS2(IW+1:IE,:,:) = 13./12 * (PSRC(IW-1:IE-2,:,:) - 2.0*PSRC(IW:IE-1,:,:) + &
- PSRC(IW+1:IE,:,:))**2 + &
- 1./4 * (PSRC(IW-1:IE-2,:,:) - PSRC(IW+1:IE,:,:))**2
- ZBPOS2(IE+1,:,:) = (PSRC(IE+1,:,:) - PSRC(IE,:,:))**2
- ZBPOS2(IW, :,:) = (PSRC(IW, :,:) - PSRC(IW-1,:,:))**2
- ZBPOS2(IW-1,:,:) = (PSRC(IW-1,:,:) - TPHALO2%WEST(:,:))**2
-!
-!
- ZBPOS3(IW+1:IE,:,:) = 13./12 * (PSRC(IW:IE-1,:,:) - 2.0*PSRC(IW+1:IE,:,:) + &
- PSRC(IW+2:IE+1,:,:))**2 + &
- 1./4 * ( 3.0*PSRC(IW:IE-1,:,:) - 4.0*PSRC(IW+1:IE,:,:) + &
- PSRC(IW+2:IE+1,:,:))**2
-!
-! smoothness indicators for negative wind case
-!
- ZBNEG1(IW+1:IE-1,:,:) = 13./12 * (PSRC(IW+1:IE-1,:,:) - 2.0*PSRC(IW+2:IE,:,:) + &
- PSRC(IW+3:IE+1,:,:))**2 + &
- 1./4 * ( 3.0*PSRC(IW+1:IE-1,:,:) - 4.0*PSRC(IW+2:IE,:,:)&
- + PSRC(IW+3:IE+1,:,:))**2
- ZBNEG1(IE, :,:) = 13./12 * (PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + &
- TPHALO2%EAST(:,:))**2 + &
- 1./4 * ( 3.0*PSRC(IE,:,:) - 4.0*PSRC(IE+1,:,:) + &
- TPHALO2%EAST(:,:))**2
- ZBNEG1(IW, :,:) = (PSRC(IW, :,:) - PSRC(IW+1,:,:))**2
- ZBNEG1(IW-1,:,:) = (PSRC(IW-1,:,:) - PSRC(IW, :,:))**2
- ZBNEG1(IE+1,:,:) = (PSRC(IE+1,:,:) - TPHALO2%EAST(:,:))**2
-!
-!
- ZBNEG2(IW+1:IE,:,:) = 13./12 * (PSRC(IW:IE-1,:,:) - 2.0*PSRC(IW+1:IE,:,:) + &
- PSRC(IW+2:IE+1,:,:))**2 + &
- 1./4 * (PSRC(IW:IE-1,:,:) - PSRC(IW+2:IE+1,:,:))**2
- ZBNEG2(IW, :,:) = (PSRC(IW-1,:,:) - PSRC(IW, :,:))**2
- ZBNEG2(IE+1,:,:) = (PSRC(IE, :,:) - PSRC(IE+1,:,:))**2
- ZBNEG2(IW-1,:,:) = (TPHALO2%WEST(:,:) - PSRC(IW-1,:,:))**2
-!
-!
- ZBNEG3(IW+1:IE,:,:) = 13./12 * (PSRC(IW-1:IE-2,:,:) - 2.0*PSRC(IW:IE-1,:,:) + &
- PSRC(IW+1:IE,:,:))**2 + &
- 1./4 * ( PSRC(IW-1:IE-2,:,:) - 4.0*PSRC(IW:IE-1,:,:) + &
- 3.0*PSRC(IW+1:IE,:,:))**2
+END IF ! IF(LWEST_ll())
!
-! WENO weights
+!-------------------------------------------------------------------------------
+!* 1.3. East border
+! ---------------------
!
- ZOMP1(IW+1:IE,:,:) = ZGAMMA1 / (ZEPS + ZBPOS1(IW+1:IE,:,:))**2
- ZOMP2(IW+1:IE,:,:) = ZGAMMA2 / (ZEPS + ZBPOS2(IW+1:IE,:,:))**2
- ZOMP3(IW+1:IE,:,:) = ZGAMMA3 / (ZEPS + ZBPOS3(IW+1:IE,:,:))**2
- ZOMN1(IW+1:IE,:,:) = ZGAMMA1 / (ZEPS + ZBNEG1(IW+1:IE,:,:))**2
- ZOMN2(IW+1:IE,:,:) = ZGAMMA2 / (ZEPS + ZBNEG2(IW+1:IE,:,:))**2
- ZOMN3(IW+1:IE,:,:) = ZGAMMA3 / (ZEPS + ZBNEG3(IW+1:IE,:,:))**2
-!
- ZOMP1(IW, :,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(IW, :,:))**2
- ZOMP2(IW, :,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(IW, :,:))**2
- ZOMN1(IW, :,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(IW, :,:))**2
- ZOMN2(IW, :,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(IW, :,:))**2
- ZOMP1(IW-1,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(IW-1,:,:))**2
- ZOMP2(IW-1,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(IW-1,:,:))**2
- ZOMN1(IW-1,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(IW-1,:,:))**2
- ZOMN2(IW-1,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(IW-1,:,:))**2
- ZOMP1(IE+1,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(IE+1,:,:))**2
- ZOMP2(IE+1,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(IE+1,:,:))**2
- ZOMN1(IE+1,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(IE+1,:,:))**2
- ZOMN2(IE+1,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(IE+1,:,:))**2
-!
-! WENO fluxes (5th order)
-!
- PR(IW+1:IE,:,:) = (ZOMP2(IW+1:IE,:,:)/(ZOMP1(IW+1:IE,:,:)+ZOMP2(IW+1:IE,:,:)+&
- ZOMP3(IW+1:IE,:,:)) * ZFPOS2(IW+1:IE,:,:) + &
- ZOMP1(IW+1:IE,:,:)/(ZOMP1(IW+1:IE,:,:)+ZOMP2(IW+1:IE,:,:) +&
- ZOMP3(IW+1:IE,:,:)) * ZFPOS1(IW+1:IE,:,:) + &
- ZOMP3(IW+1:IE,:,:)/(ZOMP1(IW+1:IE,:,:)+ZOMP2(IW+1:IE,:,:)+ &
- ZOMP3(IW+1:IE,:,:)) * &
- ZFPOS3(IW+1:IE,:,:)) * (0.5+SIGN(0.5,PRUCT(IW+1:IE,:,:))) &
- + (ZOMN2(IW+1:IE,:,:)/(ZOMN1(IW+1:IE,:,:)+ZOMN2(IW+1:IE,:,:)+&
- ZOMN3(IW+1:IE,:,:)) * &
- ZFNEG2(IW+1:IE,:,:) &
- + ZOMN1(IW+1:IE,:,:)/(ZOMN1(IW+1:IE,:,:)+ZOMN2(IW+1:IE,:,:)+&
- ZOMN3(IW+1:IE,:,:)) * ZFNEG1(IW+1:IE,:,:) &
- + ZOMN3(IW+1:IE,:,:)/(ZOMN1(IW+1:IE,:,:)+ZOMN2(IW+1:IE,:,:)+&
- ZOMN3(IW+1:IE,:,:)) * ZFNEG3(IW+1:IE,:,:)) &
- * (0.5-SIGN(0.5,PRUCT(IW+1:IE,:,:)))
-!
-! WENO fluxes (3rd order)
-!
- PR(IW,:,:) = (ZOMP2(IW,:,:)/(ZOMP1(IW,:,:)+ZOMP2(IW,:,:)) * ZFPOS2(IW,:,:) &
- + ZOMP1(IW,:,:)/(ZOMP1(IW,:,:)+ZOMP2(IW,:,:)) * ZFPOS1(IW,:,:)) * &
- (0.5+SIGN(0.5,PRUCT(IW,:,:))) &
- + (ZOMN2(IW,:,:)/(ZOMN1(IW,:,:)+ZOMN2(IW,:,:)) * ZFNEG2(IW,:,:) &
- + ZOMN1(IW,:,:)/(ZOMN1(IW,:,:)+ZOMN2(IW,:,:)) * ZFNEG1(IW,:,:)) * &
- (0.5-SIGN(0.5,PRUCT(IW,:,:)))
-!
- PR(IW-1,:,:) = (ZOMP2(IW-1,:,:)/(ZOMP1(IW-1,:,:)+ZOMP2(IW-1,:,:)) * &
- ZFPOS2(IW-1,:,:) &
- + ZOMP1(IW-1,:,:)/(ZOMP1(IW-1,:,:)+ZOMP2(IW-1,:,:)) * ZFPOS1(IW-1,:,:)) &
- * (0.5+SIGN(0.5,PRUCT(IW-1,:,:))) &
- + (ZOMN2(IW-1,:,:)/(ZOMN1(IW-1,:,:)+ZOMN2(IW-1,:,:)) * ZFNEG2(IW-1,:,:) &
- + ZOMN1(IW-1,:,:)/(ZOMN1(IW-1,:,:)+ZOMN2(IW-1,:,:)) * ZFNEG1(IW-1,:,:)) &
- * (0.5-SIGN(0.5,PRUCT(IW-1,:,:)))
-!
- PR(IE+1,:,:) = (ZOMP2(IE+1,:,:)/(ZOMP1(IE+1,:,:)+ZOMP2(IE+1,:,:)) * &
- ZFPOS2(IE+1,:,:) + &
- ZOMP1(IE+1,:,:)/(ZOMP1(IE+1,:,:)+ZOMP2(IE+1,:,:)) * ZFPOS1(IE+1,:,:)) &
- * (0.5+SIGN(0.5,PRUCT(IE+1,:,:))) &
- + (ZOMN2(IE+1,:,:)/(ZOMN1(IE+1,:,:)+ZOMN2(IE+1,:,:)) * ZFNEG2(IE+1,:,:)+&
- ZOMN1(IE+1,:,:)/(ZOMN1(IE+1,:,:)+ZOMN2(IE+1,:,:)) * ZFNEG1(IE+1,:,:)) &
- * (0.5-SIGN(0.5,PRUCT(IE+1,:,:)))
-!
-!
-! OPEN, WALL, NEST CASE IN THE X DIRECTION
-!
-CASE ('OPEN','WALL','NEST')
-!
- IW=IIB
- IE=IIE
-!
-! LATERAL BOUNDARY CONDITIONS
-! AT THE PHYSICAL BORDER: USE A FIRST ORDER UPSTREAM WENO SCHEME AT THE POINTS: IW, IE+1 /AND/ A THIRD ORDER WENO SCHEME AT THE POINTS: IW+1, IE
-! AT THE PROC. BORDER: A THIRD ORDER UPSTREAM WENO SCHEME AT THE POINTS: IW, IE+1 /AND/ A FIFTH ORDER WENO SCHEME AT THE POINTS: IW+1, IE
-!
-!
-! PHYSICAL BORDER (WEST)
-!
- IF(LWEST_ll()) THEN
-!
-! FIRST ORDER UPSTREAM WENO SCHEME
+IF(LEAST_ll() .AND. .FALSE. ) THEN
+ !-----------------------------------------------------------------------------
+ ! East border is physical -- IE,IE+1
+ !-----------------------------------------------------------------------------
+ SELECT CASE (HLBCX(2)) ! X direction LBC type on right side
+!
+ CASE ('CYCL')
+ !---------------------------------------------------------------------------
+ ! Periodic boundary condition
+ !---------------------------------------------------------------------------
!
- PR(IW,:,:) = PSRC(IW-1,:,:) * (0.5+SIGN(0.5,PRUCT(IW,:,:))) + &
- PSRC(IW,:,:) * (0.5-SIGN(0.5,PRUCT(IW,:,:)))
-!
-! THIRD ORDER UPSTREAM WENO SCHEME
-!
- ZFPOS1(IW+1,:,:) = 0.5 * (3.0*PSRC(IW,:,:) - PSRC(IW-1,:,:))
- ZFPOS2(IW+1,:,:) = 0.5 * (PSRC(IW, :,:) + PSRC(IW+1,:,:))
- ZBPOS1(IW+1,:,:) = (PSRC(IW, :,:) - PSRC(IW-1,:,:))**2
- ZBPOS2(IW+1,:,:) = (PSRC(IW+1,:,:) - PSRC(IW, :,:))**2
-!
- ZFNEG1(IW+1,:,:) = 0.5 * (3.0*PSRC(IW+1,:,:) - PSRC(IW+2,:,:))
- ZFNEG2(IW+1,:,:) = 0.5 * (PSRC(IW+1, :,:) + PSRC(IW, :,:))
- ZBNEG1(IW+1,:,:) = (PSRC(IW+1,:,:) - PSRC(IW+2,:,:))**2
- ZBNEG2(IW+1,:,:) = (PSRC(IW, :,:) - PSRC(IW+1,:,:))**2
-!
- ZOMP1(IW+1,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(IW+1,:,:))**2
- ZOMP2(IW+1,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(IW+1,:,:))**2
- ZOMN1(IW+1,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(IW+1,:,:))**2
- ZOMN2(IW+1,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(IW+1,:,:))**2
-!
- PR(IW+1,:,:) = (ZOMP2(IW+1,:,:)/(ZOMP1(IW+1,:,:)+ZOMP2(IW+1,:,:)) * &
- ZFPOS2(IW+1,:,:) &
- + ZOMP1(IW+1,:,:)/(ZOMP1(IW+1,:,:)+ZOMP2(IW+1,:,:)) * ZFPOS1(IW+1,:,:)) * &
- (0.5+SIGN(0.5,PRUCT(IW+1,:,:))) &
- + (ZOMN2(IW+1,:,:)/(ZOMN1(IW+1,:,:)+ZOMN2(IW+1,:,:)) * ZFNEG2(IW+1,:,:) &
- + ZOMN1(IW+1,:,:)/(ZOMN1(IW+1,:,:)+ZOMN2(IW+1,:,:)) * ZFNEG1(IW+1,:,:)) * &
- (0.5-SIGN(0.5,PRUCT(IW+1,:,:)))
-!
-! PROC. BORDER (WEST)
-!
- ELSEIF (NHALO == 1) THEN
-!
-! THIRD ORDER UPSTREAM WENO SCHEME
-!
- ZFPOS1(IW,:,:) = 0.5 * (3.0*PSRC(IW-1,:,:) - TPHALO2%WEST(:,:))
- ZFPOS2(IW,:,:) = 0.5 * (PSRC(IW-1, :,:) + PSRC(IW,:,:))
- ZBPOS1(IW,:,:) = (PSRC(IW-1,:,:) - TPHALO2%WEST(:,:))**2
- ZBPOS2(IW,:,:) = (PSRC(IW, :,:) - PSRC(IW-1,:,:))**2
-!
- ZFNEG1(IW,:,:) = 0.5 * (3.0*PSRC(IW,:,:) - PSRC(IW+1,:,:))
- ZFNEG2(IW,:,:) = 0.5 * (PSRC(IW, :,:) + PSRC(IW-1,:,:))
- ZBNEG1(IW,:,:) = (PSRC(IW, :,:) - PSRC(IW+1,:,:))**2
- ZBNEG2(IW,:,:) = (PSRC(IW-1,:,:) - PSRC(IW, :,:))**2
-!
- ZOMP1(IW,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(IW,:,:))**2
- ZOMP2(IW,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(IW,:,:))**2
- ZOMN1(IW,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(IW,:,:))**2
- ZOMN2(IW,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(IW,:,:))**2
-!
- PR(IW,:,:) = (ZOMP2(IW,:,:)/(ZOMP1(IW,:,:)+ZOMP2(IW,:,:)) * ZFPOS2(IW,:,:) &
- + ZOMP1(IW,:,:)/(ZOMP1(IW,:,:)+ZOMP2(IW,:,:)) * ZFPOS1(IW,:,:))&
- * (0.5+SIGN(0.5,PRUCT(IW,:,:))) &
- + (ZOMN2(IW,:,:)/(ZOMN1(IW,:,:)+ZOMN2(IW,:,:)) * ZFNEG2(IW,:,:) &
- + ZOMN1(IW,:,:)/(ZOMN1(IW,:,:)+ZOMN2(IW,:,:)) * ZFNEG1(IW,:,:))&
- * (0.5-SIGN(0.5,PRUCT(IW,:,:)))
-!
-! FIFTH ORDER UPSTREAM WENO SCHEME
-!
- ZFPOS1(IW+1,:,:) = 1./6. *(2.0*TPHALO2%WEST(:,:)-7.0*PSRC(IW-1,:,:)+ &
- 11.0*PSRC(IW, :,:))
- ZFPOS2(IW+1,:,:) = 1./6. *(-PSRC(IW-1, :,:)+ 5.0*PSRC(IW, :,:)+ &
- 2.0*PSRC(IW+1,:,:))
- ZFPOS3(IW+1,:,:) = 1./6. *(2.0*PSRC(IW, :,:)+5.0*PSRC(IW+1,:,:)- &
- PSRC(IW+2, :,:))
-!
- ZBPOS1(IW+1,:,:) = 13./12. *(TPHALO2%WEST(:,:)-2.0*PSRC(IW-1,:,:)+ &
- PSRC(IW,:,:))**2 &
- + 1./4. *(TPHALO2%WEST(:,:)-4.0*PSRC(IW-1,:,:)+ &
- 3.0*PSRC(IW,:,:))**2
- ZBPOS2(IW+1,:,:) = 13./12. *(PSRC(IW-1,:,:) -2.0*PSRC(IW,:,:)+ &
- PSRC(IW+1,:,:))**2 &
- + 1./4. *(PSRC(IW-1,:,:) - PSRC(IW+1,:,:))**2
- ZBPOS3(IW+1,:,:) = 13./12. *(PSRC(IW,:,:) - 2.0*PSRC(IW+1,:,:) + &
- PSRC(IW+2,:,:))**2 &
- + 1./4. *(3.0*PSRC(IW,:,:) - 4.0*PSRC(IW+1,:,:) + &
- PSRC(IW+2,:,:))**2
-!
- ZFNEG1(IW+1,:,:) = 1./6 * (11.0*PSRC(IW+1,:,:) - 7.0*PSRC(IW+2,:,:) + &
- 2.0*PSRC(IW+3,:,:))
- ZFNEG2(IW+1,:,:) = 1./6 * (2.0*PSRC(IW, :,:) + 5.0*PSRC(IW+1,:,:) - &
- PSRC(IW+2, :,:))
- ZFNEG3(IW+1,:,:) = 1./6 * (-PSRC(IW-1 ,:,:) + 5.0*PSRC(IW, :,:) + &
- 2.0*PSRC(IW+1,:,:))
-!
- ZBNEG1(IW+1,:,:) = 13./12 * (PSRC(IW+1,:,:) - 2.0*PSRC(IW+2,:,:) + &
- PSRC(IW+3,:,:))**2 &
- + 1./4 * (3.0*PSRC(IW+1,:,:) - 4.0*PSRC(IW+2,:,:) +&
- PSRC(IW+3,:,:))**2
- ZBNEG2(IW+1,:,:) = 13./12 * (PSRC(IW,:,:) - 2.0*PSRC(IW+1,:,:) + &
- PSRC(IW+2,:,:))**2 &
- + 1./4 * (PSRC(IW,:,:) - PSRC(IW+2,:,:))**2
- ZBNEG3(IW+1,:,:) = 13./12 * (PSRC(IW-1,:,:) - 2.0*PSRC(IW,:,:) + &
- PSRC(IW+1,:,:))**2 &
- + 1./4 * (PSRC(IW-1,:,:) - 4.0*PSRC(IW,:,:) + &
- 3.0*PSRC(IW+1,:,:))**2
-!
- ZOMP1(IW+1,:,:) = ZGAMMA1 / (ZEPS + ZBPOS1(IW+1,:,:))**2
- ZOMP2(IW+1,:,:) = ZGAMMA2 / (ZEPS + ZBPOS2(IW+1,:,:))**2
- ZOMP3(IW+1,:,:) = ZGAMMA3 / (ZEPS + ZBPOS3(IW+1,:,:))**2
- ZOMN1(IW+1,:,:) = ZGAMMA1 / (ZEPS + ZBNEG1(IW+1,:,:))**2
- ZOMN2(IW+1,:,:) = ZGAMMA2 / (ZEPS + ZBNEG2(IW+1,:,:))**2
- ZOMN3(IW+1,:,:) = ZGAMMA3 / (ZEPS + ZBNEG3(IW+1,:,:))**2
-!
- PR(IW+1,:,:) = (ZOMP2(IW+1,:,:)/(ZOMP1(IW+1,:,:)+ZOMP2(IW+1,:,:)+ &
- ZOMP3(IW+1,:,:)) * ZFPOS2(IW+1,:,:) &
- + ZOMP1(IW+1,:,:)/(ZOMP1(IW+1,:,:)+ZOMP2(IW+1,:,:)+ &
- ZOMP3(IW+1,:,:)) * ZFPOS1(IW+1,:,:) &
- + ZOMP3(IW+1,:,:)/(ZOMP1(IW+1,:,:)+ZOMP2(IW+1,:,:)+ &
- ZOMP3(IW+1,:,:)) * ZFPOS3(IW+1,:,:)) * &
- (0.5+SIGN(0.5,PRUCT(IW+1,:,:))) &
- + (ZOMN2(IW+1,:,:)/(ZOMN1(IW+1,:,:)+ZOMN2(IW+1,:,:)+ &
- ZOMN3(IW+1,:,:)) * ZFNEG2(IW+1,:,:) &
- + ZOMN1(IW+1,:,:)/(ZOMN1(IW+1,:,:)+ZOMN2(IW+1,:,:)+ &
- ZOMN3(IW+1,:,:)) * ZFNEG1(IW+1,:,:) &
- + ZOMN3(IW+1,:,:)/(ZOMN1(IW+1,:,:)+ZOMN2(IW+1,:,:)+ &
- ZOMN3(IW+1,:,:)) * ZFNEG3(IW+1,:,:)) * &
- (0.5-SIGN(0.5,PRUCT(IW+1,:,:)))
-!
- ENDIF
-!
-! PHYSICAL BORDER (EAST)
-!
- IF(LEAST_ll()) THEN
- PR(IE+1,:,:) = PSRC(IE,:,:) * (0.5+SIGN(0.5,PRUCT(IE+1,:,:))) + &
+ IF(LWEST_ll() .AND. .FALSE. ) THEN ! West border is physical
+!
+ ! Third positive stencil, needs indices i, i+1, i+2
+ ZFPOS3(IE,:,:) = 1./6 * (2.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) - PSRC(IE+1,:,:)) ! Flux IE
+ ZFPOS3(IE+1,:,:) = 1./6 * (2.0*PSRC(IE,:,:) + 5.0*PSRC(IE+1,:,:) - PSRC(IW,:,:)) ! Flux IE+1
+ ZBPOS3(IE,:,:) = 13./12 * ( PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE-1,:,:) - 4.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 ! Smoothness indicator IE
+ ZBPOS3(IE+1,:,:) = 13./12 * ( PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE,:,:) - 4.0*PSRC(IE+1,:,:) + PSRC(IW,:,:))**2 ! Smoothness indicator IE+1
+ ZOMP3(IE:IE+1,:,:) = 3./10. / (ZEPS + ZBPOS3(IE:IE+1,:,:))**2 ! Non-normalized weight IE,IE+1
+!
+ ! First negative stencil, needs indices i, i+1, i+2
+ ZFNEG1(IE,:,:) = 1./6. * (11.0*PSRC(IE,:,:) - 7.0*PSRC(IE+1,:,:) + 2.0*PSRC(IW,:,:)) ! Flux IE
+ ZFNEG1(IE+1,:,:) = 1./6. * (11.0*PSRC(IE+1,:,:) - 7.0*PSRC(IW,:,:) + 2.0*PSRC(IW+1,:,:)) ! Flux IE+1
+ ZBNEG1(IE,:,:) = 13./12. * ( PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE,:,:) - 4.0*PSRC(IE+1,:,:) + PSRC(IW,:,:))**2 ! Smoothness indicator IE
+ ZBNEG1(IE+1,:,:) = 13./12. * ( PSRC(IE+1,:,:) - 2.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE+1,:,:) - 4.0*PSRC(IW,:,:) + PSRC(IW+1,:,:))**2 ! Smoothness indicator IE+1
+ ZOMN1(IE:IE+1,:,:) = 1./10. / (ZEPS + ZBNEG1(IE:IE+1,:,:))**2 ! Non-normalized weight IE,IE+1
+!
+ ! Second negative stencil, needs indices i-1, i, i+1
+ ZFNEG2(IE,:,:) = 1./6. * (2.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) - 1.0*PSRC(IE+1,:,:)) ! Flux IE
+ ZFNEG2(IE+1,:,:) = 1./6. * (2.0*PSRC(IE,:,:) + 5.0*PSRC(IE+1,:,:) - 1.0*PSRC(IW,:,:)) ! Flux IE+1
+ ZBNEG2(IE,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (PSRC(IE-1,:,:) - PSRC(IE+1,:,:))**2 ! Smoothness indicator IE
+ ZBNEG2(IE+1,:,:) = 13./12 * (PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IW,:,:))**2 &
+ + 1./4 * (PSRC(IE,:,:) - PSRC(IW,:,:))**2 ! Smoothness indicator IE+1
+ ZOMN2(IE:IE+1,:,:) = 3./5. / (ZEPS + ZBNEG2(IE:IE+1,:,:))**2 ! Non-normalized weight IE,IE+1
+!
+ ELSEIF(IE<=SIZE(PSRC,1)-3) THEN ! West boundary is proc border, with minimum 3 HALO points on east side
+!
+ ! Third positive stencil, needs indices i, i+1, i+2
+ ZFPOS3(IE,:,:) = 1./6 * (2.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) - PSRC(IE+1,:,:)) ! Flux IE
+ ZFPOS3(IE+1,:,:) = 1./6 * (2.0*PSRC(IE,:,:) + 5.0*PSRC(IE+1,:,:) - PSRC(IE+2,:,:)) ! Flux IE+1
+ ZBPOS3(IE,:,:) = 13./12 * ( PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE-1,:,:) - 4.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 ! Smoothness indicator IE
+ ZBPOS3(IE+1,:,:) = 13./12 * ( PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE,:,:) - 4.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 ! Smoothness indicator IE+1
+ ZOMP3(IE:IE+1,:,:) = 3./10. / (ZEPS + ZBPOS3(IE:IE+1,:,:))**2 ! Non-normalized weight IE,IE+1
+!
+ ! First negative stencil, needs indices i, i+1, i+2
+ ZFNEG1(IE,:,:) = 1./6. * (11.0*PSRC(IE,:,:) - 7.0*PSRC(IE+1,:,:) + 2.0*PSRC(IE+2,:,:)) ! Flux IE
+ ZFNEG1(IE+1,:,:) = 1./6. * (11.0*PSRC(IE+1,:,:) - 7.0*PSRC(IE+2,:,:) + 2.0*PSRC(IE+3,:,:)) ! Flux IE+1
+ ZBNEG1(IE,:,:) = 13./12. * ( PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE,:,:) - 4.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 ! Smoothness indicator IE
+ ZBNEG1(IE+1,:,:) = 13./12. * ( PSRC(IE+1,:,:) - 2.0*PSRC(IE+2,:,:) + PSRC(IE+3,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE+1,:,:) - 4.0*PSRC(IE+2,:,:) + PSRC(IE+3,:,:))**2 ! Smoothness indicator IE+1
+ ZOMN1(IE:IE+1,:,:) = 1./10. / (ZEPS + ZBNEG1(IE:IE+1,:,:))**2 ! Non-normalized weight IE,IE+1
+!
+ ! Second negative stencil, needs indices i-1, i, i+1
+ ZFNEG2(IE,:,:) = 1./6. * (2.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) - 1.0*PSRC(IE+1,:,:)) ! Flux IE
+ ZFNEG2(IE+1,:,:) = 1./6. * (2.0*PSRC(IE,:,:) + 5.0*PSRC(IE+1,:,:) - 1.0*PSRC(IE+2,:,:)) ! Flux IE+1
+ ZBNEG2(IE,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (PSRC(IE-1,:,:) - PSRC(IE+1,:,:))**2 ! Smoothness indicator IE
+ ZBNEG2(IE+1,:,:) = 13./12 * (PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 &
+ + 1./4 * (PSRC(IE,:,:) - PSRC(IE+2,:,:))**2 ! Smoothness indicator IE+1
+ ZOMN2(IE:IE+1,:,:) = 3./5. / (ZEPS + ZBNEG2(IE:IE+1,:,:))**2 ! Non-normalized weight IE,IE+1
+!
+ ELSE ! West boundary is proc border, with NHALO < 3 on east side
+ PRINT *,'WARNING : WENO5 fluxes calculation needs NHALO >= 3 on east side'
+ CALL ABORT
+ ENDIF
+!
+ ! First positive stencil, needs indices i-3, i-2, i-1
+ ZFPOS1(IE,:,:) = 1./6. * (2.0*PSRC(IE-3,:,:) - 7.0*PSRC(IE-2,:,:) + 11.0*PSRC(IE-1,:,:)) ! Flux IE
+ ZFPOS1(IE+1,:,:) = 1./6. * (2.0*PSRC(IE-2,:,:) - 7.0*PSRC(IE-1,:,:) + 11.0*PSRC(IE,:,:)) ! Flux IE+1
+ ZBPOS1(IE,:,:) = 13./12. * (PSRC(IE-3,:,:) - 2.0*PSRC(IE-2,:,:) + PSRC(IE-1,:,:))**2 &
+ + 1./4 * (PSRC(IE-3,:,:) - 4.0*PSRC(IE-2,:,:) + 3.0*PSRC(IE-1,:,:))**2 ! Smoothness indicator IE
+ ZBPOS1(IE+1,:,:) = 13./12. * (PSRC(IE-2,:,:) - 2.0*PSRC(IE-1,:,:) + PSRC(IE,:,:))**2 &
+ + 1./4 * (PSRC(IE-2,:,:) - 4.0*PSRC(IE-1,:,:) + 3.0*PSRC(IE,:,:))**2 ! Smoothness indicator IE+1
+ ZOMP1(IE:IE+1,:,:) = 1./10. / (ZEPS + ZBPOS1(IE:IE+1,:,:))**2 ! Non-normalized weight IE,IE+1
+!
+ ! Second positive stencil, needs indices i-2, i-1, i
+ ZFPOS2(IE,:,:) = 1./6. * (-1.0*PSRC(IE-2,:,:) + 5.0*PSRC(IE-1,:,:) + 2.0*PSRC(IE,:,:)) ! Flux IE
+ ZFPOS2(IE+1,:,:) = 1./6. * (-1.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) + 2.0*PSRC(IE+1,:,:)) ! Flux IE+1
+ ZBPOS2(IE,:,:) = 13./12 * (PSRC(IE-2,:,:) - 2.0*PSRC(IE-1,:,:) + PSRC(IE,:,:))**2 &
+ + 1./4 * (PSRC(IE-2,:,:) - PSRC(IE,:,:))**2 ! Smoothness indicator IE
+ ZBPOS2(IE+1,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (PSRC(IE-1,:,:) - PSRC(IE+1,:,:))**2 ! Smoothness indicator IE+1
+ ZOMP2(IE:IE+1,:,:) = 3./5. / (ZEPS + ZBPOS2(IE:IE+1,:,:))**2 ! Non-normalized weight IE,IE+1
+!
+ ! Third negative stencil, needs indices i-2, i-1, i
+ ZFNEG3(IE,:,:) = 1./6 * (-1.0*PSRC(IE-2,:,:) + 5.0*PSRC(IE-1,:,:) + 2.0*PSRC(IE,:,:)) ! Flux IE
+ ZFNEG3(IE+1,:,:) = 1./6 * (-1.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) + 2.0*PSRC(IE+1,:,:)) ! Flux IE+1
+ ZBNEG3(IE,:,:) = 13./12 * (PSRC(IE-2,:,:) - 2.0*PSRC(IE-1,:,:) + PSRC(IE,:,:))**2 &
+ + 1./4 * (PSRC(IE-2,:,:) - 4.0*PSRC(IE-1,:,:) + 3.0*PSRC(IE,:,:))**2 ! Smoothness indicator IE
+ ZBNEG3(IE+1,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (PSRC(IE-1,:,:) - 4.0*PSRC(IE,:,:) + 3.0*PSRC(IE+1,:,:))**2 ! Smoothness indicator IE+1
+ ZOMN3(IE:IE+1,:,:) = 3./10. / (ZEPS + ZBNEG3(IE:IE+1,:,:))**2 ! Non-normalized weight IE,IE+1
+!
+ ! ----- Total flux -----
+!
+ PR(IE:IE+1,:,:) = ( ZOMP1(IE:IE+1,:,:)/(ZOMP1(IE:IE+1,:,:)+ZOMP2(IE:IE+1,:,:)+ZOMP3(IE:IE+1,:,:)) * ZFPOS1(IE:IE+1,:,:) &
+ + ZOMP2(IE:IE+1,:,:)/(ZOMP1(IE:IE+1,:,:)+ZOMP2(IE:IE+1,:,:)+ZOMP3(IE:IE+1,:,:)) * ZFPOS2(IE:IE+1,:,:) &
+ + ZOMP3(IE:IE+1,:,:)/(ZOMP1(IE:IE+1,:,:)+ZOMP2(IE:IE+1,:,:)+ZOMP3(IE:IE+1,:,:)) * ZFPOS3(IE:IE+1,:,:)) &
+ * (0.5+SIGN(0.5,PRUCT(IE:IE+1,:,:))) &
+ + ( ZOMN1(IE:IE+1,:,:)/(ZOMN1(IE:IE+1,:,:)+ZOMN2(IE:IE+1,:,:)+ZOMN3(IE:IE+1,:,:)) * ZFNEG1(IE:IE+1,:,:) &
+ + ZOMN2(IE:IE+1,:,:)/(ZOMN1(IE:IE+1,:,:)+ZOMN2(IE:IE+1,:,:)+ZOMN3(IE:IE+1,:,:)) * ZFNEG2(IE:IE+1,:,:) &
+ + ZOMN3(IE:IE+1,:,:)/(ZOMN1(IE:IE+1,:,:)+ZOMN2(IE:IE+1,:,:)+ZOMN3(IE:IE+1,:,:)) * ZFNEG3(IE:IE+1,:,:)) &
+ * (0.5-SIGN(0.5,PRUCT(IE:IE+1,:,:)))
+!
+!
+ CASE ('OPEN','WALL','NEST')
+ !---------------------------------------------------------------------------
+ ! Open, or Wall, or Nest boundary condition => WENO order reduction
+ !---------------------------------------------------------------------------
+!
+ ! WENO scheme order 1, IE+1
+ PR(IE+1,:,:) = PSRC(IE,:,:) * (0.5+SIGN(0.5,PRUCT(IE+1,:,:))) + &
PSRC(IE+1,:,:) * (0.5-SIGN(0.5,PRUCT(IE+1,:,:)))
!
- ZFPOS1(IE,:,:) = 0.5 * (3.0*PSRC(IE-1,:,:) - PSRC(IE-2,:,:))
- ZFPOS2(IE,:,:) = 0.5 * (PSRC(IE, :,:) + PSRC(IE-1,:,:))
- ZBPOS1(IE,:,:) = (PSRC(IE-1,:,:) - PSRC(IE-2,:,:))**2
- ZBPOS2(IE,:,:) = (PSRC(IE, :,:) - PSRC(IE-1,:,:))**2
-!
- ZFNEG1(IE,:,:) = 0.5 * (3.0*PSRC(IE,:,:) - PSRC(IE+1,:,:))
- ZFNEG2(IE,:,:) = 0.5 * (PSRC(IE, :,:) + PSRC(IE-1,:,:))
- ZBNEG1(IE,:,:) = (PSRC(IE, :,:) - PSRC(IE+1,:,:))**2
- ZBNEG2(IE,:,:) = (PSRC(IE-1,:,:) - PSRC(IE, :,:))**2
-!
- ZOMP1(IE,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(IE,:,:))**2
- ZOMP2(IE,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(IE,:,:))**2
- ZOMN1(IE,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(IE,:,:))**2
- ZOMN2(IE,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(IE,:,:))**2
-!
- PR(IE,:,:) = (ZOMP2(IE,:,:)/(ZOMP1(IE,:,:)+ZOMP2(IE,:,:)) * ZFPOS2(IE,:,:) + &
- ZOMP1(IE,:,:)/(ZOMP1(IE,:,:)+ZOMP2(IE,:,:)) * ZFPOS1(IE,:,:)) *&
- (0.5+SIGN(0.5,PRUCT(IE,:,:))) &
- + (ZOMN2(IE,:,:)/(ZOMN1(IE,:,:)+ZOMN2(IE,:,:)) * ZFNEG2(IE,:,:) + &
- ZOMN1(IE,:,:)/(ZOMN1(IE,:,:)+ZOMN2(IE,:,:)) * ZFNEG1(IE,:,:)) *&
- (0.5-SIGN(0.5,PRUCT(IE,:,:)))
-!
-! PROC. BORDER (EAST)
-!
- ELSEIF(NHALO == 1) THEN
- ZFPOS1(IE+1,:,:) = 0.5 * (3.0*PSRC(IE,:,:) - PSRC(IE-1,:,:))
- ZFPOS2(IE+1,:,:) = 0.5 * (PSRC(IE+1, :,:) + PSRC(IE, :,:))
- ZBPOS1(IE+1,:,:) = (PSRC(IE, :,:) - PSRC(IE-1,:,:))**2
- ZBPOS2(IE+1,:,:) = (PSRC(IE+1,:,:) - PSRC(IE, :,:))**2
-!
- ZFNEG1(IE+1,:,:) = 0.5 * (3.0*PSRC(IE+1,:,:) - TPHALO2%EAST(:,:))
- ZFNEG2(IE+1,:,:) = 0.5 * (PSRC(IE+1, :,:) + PSRC(IE, :,:))
- ZBNEG1(IE+1,:,:) = (PSRC(IE+1,:,:) - TPHALO2%EAST(:,:))**2
- ZBNEG2(IE+1,:,:) = (PSRC(IE, :,:) - PSRC(IE+1, :,:))**2
-!
- ZOMP1(IE+1,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(IE+1,:,:))**2
- ZOMP2(IE+1,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(IE+1,:,:))**2
- ZOMN1(IE+1,:,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(IE+1,:,:))**2
- ZOMN2(IE+1,:,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(IE+1,:,:))**2
-!
- PR(IE+1,:,:) = (ZOMP2(IE+1,:,:)/(ZOMP1(IE+1,:,:)+ZOMP2(IE+1,:,:)) * &
- ZFPOS2(IE+1,:,:) + &
- ZOMP1(IE+1,:,:)/(ZOMP1(IE+1,:,:)+ZOMP2(IE+1,:,:)) * &
- ZFPOS1(IE+1,:,:)) * (0.5+SIGN(0.5,PRUCT(IE+1,:,:))) &
- + (ZOMN2(IE+1,:,:)/(ZOMN1(IE+1,:,:)+ZOMN2(IE+1,:,:)) * &
- ZFNEG2(IE+1,:,:) + &
- ZOMN1(IE+1,:,:)/(ZOMN1(IE+1,:,:)+ZOMN2(IE+1,:,:)) * &
- ZFNEG1(IE+1,:,:)) * (0.5-SIGN(0.5,PRUCT(IE+1,:,:)))
-!
- ZFPOS1(IE,:,:) = 1./6 * (2.0*PSRC(IE-3,:,:) - 7.0*PSRC(IE-2,:,:) + &
- 11.0*PSRC(IE-1,:,:))
- ZFPOS2(IE,:,:) = 1./6 * (-1.0*PSRC(IE-2,:,:) + 5.0*PSRC(IE-1,:,:) + &
- 2.0*PSRC(IE,:,:))
- ZFPOS3(IE,:,:) = 1./6 * (2.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) - &
- PSRC(IE+1,:,:))
-!
- ZBPOS1(IE,:,:) = 13./12 * (PSRC(IE-3,:,:) - 2.0*PSRC(IE-2,:,:) + &
- PSRC(IE-1,:,:))**2 + 1./4 * (PSRC(IE-3,:,:) &
- - 4.0*PSRC(IE-2,:,:) + 3.0*PSRC(IE-1,:,:))**2
- ZBPOS2(IE,:,:) = 13./12 * (PSRC(IE-2,:,:) - 2.0*PSRC(IE-1,:,:) + &
- PSRC(IE,:,:))**2 + 1./4 * &
- (PSRC(IE-2,:,:) - PSRC(IE,:,:))**2
- ZBPOS3(IE,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + &
- PSRC(IE+1,:,:))**2 + 1./4 * &
- ( 3.0*PSRC(IE-1,:,:) - 4.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2
-!
- ZFNEG1(IE,:,:) = 1./6 * (11.0*PSRC(IE, :,:) - 7.0*PSRC(IE+1,:,:) + &
- 2.0*TPHALO2%EAST(:,:))
- ZFNEG2(IE,:,:) = 1./6 * (2.0*PSRC(IE-1, :,:) + 5.0*PSRC(IE, :,:) - &
- PSRC(IE+1,:,:))
- ZFNEG3(IE,:,:) = 1./6 * (-1.0*PSRC(IE-2,:,:) + 5.0*PSRC(IE-1,:,:) + &
- 2.0*PSRC(IE,:,:))
-!
- ZBNEG1(IE,:,:) = 13./12 * (PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + &
- TPHALO2%EAST(:,:))**2 + 1./4 * &
- ( 3.0*PSRC(IE,:,:) - 4.0*PSRC(IE+1,:,:) + TPHALO2%EAST(:,:))**2
- ZBNEG2(IE,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + &
- PSRC(IE+1,:,:))**2 + 1./4 * &
- (PSRC(IE-1,:,:) - PSRC(IE+1,:,:))**2
- ZBNEG3(IE,:,:) = 13./12 * (PSRC(IE-2,:,:) - 2.0*PSRC(IE-1,:,:) + &
- PSRC(IE,:,:))**2 + 1./4 * &
- ( PSRC(IE-2,:,:) - 4.0*PSRC(IE-1,:,:) + &
- 3.0*PSRC(IE,:,:))**2
-!
- ZOMP1(IE,:,:) = ZGAMMA1 / (ZEPS + ZBPOS1(IE,:,:))**2
- ZOMP2(IE,:,:) = ZGAMMA2 / (ZEPS + ZBPOS2(IE,:,:))**2
- ZOMP3(IE,:,:) = ZGAMMA3 / (ZEPS + ZBPOS3(IE,:,:))**2
- ZOMN1(IE,:,:) = ZGAMMA1 / (ZEPS + ZBNEG1(IE,:,:))**2
- ZOMN2(IE,:,:) = ZGAMMA2 / (ZEPS + ZBNEG2(IE,:,:))**2
- ZOMN3(IE,:,:) = ZGAMMA3 / (ZEPS + ZBNEG3(IE,:,:))**2
-!
- PR(IE,:,:) = (ZOMP2(IE,:,:)/(ZOMP1(IE,:,:)+ZOMP2(IE,:,:)+ &
- ZOMP3(IE,:,:)) * ZFPOS2(IE,:,:) &
- + ZOMP1(IE,:,:)/(ZOMP1(IE,:,:)+ZOMP2(IE,:,:)+ &
- ZOMP3(IE,:,:)) * ZFPOS1(IE,:,:) &
- + ZOMP3(IE,:,:)/(ZOMP1(IE,:,:)+ZOMP2(IE,:,:)+ &
- ZOMP3(IE,:,:)) * ZFPOS3(IE,:,:)) * &
- (0.5+SIGN(0.5,PRUCT(IE,:,:))) &
- + (ZOMN2(IE,:,:)/(ZOMN1(IE,:,:)+ZOMN2(IE,:,:)+ &
- ZOMN3(IE,:,:)) * ZFNEG2(IE,:,:) &
- + ZOMN1(IE,:,:)/(ZOMN1(IE,:,:)+ZOMN2(IE,:,:)+ &
- ZOMN3(IE,:,:)) * ZFNEG1(IE,:,:) &
- + ZOMN3(IE,:,:)/(ZOMN1(IE,:,:)+ZOMN2(IE,:,:)+ &
- ZOMN3(IE,:,:)) * ZFNEG3(IE,:,:)) * &
- (0.5-SIGN(0.5,PRUCT(IE,:,:)))
-!
- ENDIF
-!
-! USE A FIFTH ORDER UPSTREAM WENO SCHEME ELSEWHERE (IW+2 --> IE-1)
-!
- ZFPOS1(IW+2:IE-1,:,:) = 1./6 * (2.0*PSRC(IW-1:IE-4,:,:) - &
- 7.0*PSRC(IW:IE-3, :,:) + 11.0*PSRC(IW+1:IE-2,:,:))
- ZFPOS2(IW+2:IE-1,:,:) = 1./6 * (-1.0*PSRC(IW:IE-3, :,:) + &
- 5.0*PSRC(IW+1:IE-2,:,:) + 2.0*PSRC(IW+2:IE-1, :,:))
- ZFPOS3(IW+2:IE-1,:,:) = 1./6 * (2.0*PSRC(IW+1:IE-2,:,:) + &
- 5.0*PSRC(IW+2:IE-1,:,:) - PSRC(IW+3:IE, :,:))
-!
- ZBPOS1(IW+2:IE-1,:,:) = 13./12 * (PSRC(IW-1:IE-4,:,:) - &
- 2.0*PSRC(IW:IE-3,:,:) + PSRC(IW+1:IE-2,:,:))**2 + &
- 1./4 * (PSRC(IW-1:IE-4,:,:) - 4.0*PSRC(IW:IE-3,:,:) + &
- 3.0*PSRC(IW+1:IE-2,:,:))**2
- ZBPOS2(IW+2:IE-1,:,:) = 13./12 * (PSRC(IW:IE-3,:,:) - &
- 2.0*PSRC(IW+1:IE-2,:,:) + PSRC(IW+2:IE-1,:,:))**2 + &
- 1./4 * (PSRC(IW:IE-3,:,:) - PSRC(IW+2:IE-1,:,:))**2
- ZBPOS3(IW+2:IE-1,:,:) = 13./12 * (PSRC(IW+1:IE-2,:,:) - &
- 2.0*PSRC(IW+2:IE-1,:,:) + PSRC(IW+3:IE,:,:))**2 + &
- 1./4 * (3.0*PSRC(IW+1:IE-2,:,:) - 4.0*PSRC(IW+2:IE-1,:,:) + &
- PSRC(IW+3:IE,:,:))**2
-!
- ZFNEG1(IW+2:IE-1,:,:) = 1./6 * (11.0*PSRC(IW+2:IE-1,:,:) - &
- 7.0*PSRC(IW+3:IE,:,:) + 2.0*PSRC(IW+4:IE+1,:,:))
- ZFNEG2(IW+2:IE-1,:,:) = 1./6 * (2.0*PSRC(IW+1:IE-2,:,:) + &
- 5.0*PSRC(IW+2:IE-1,:,:) - PSRC(IW+3:IE,:,:))
- ZFNEG3(IW+2:IE-1,:,:) = 1./6 * (-1.0*PSRC(IW:IE-3,:,:) + &
- 5.0*PSRC(IW+1:IE-2,:,:) + 2.0*PSRC(IW+2:IE-1,:,:))
-!
- ZBNEG1(IW+2:IE-1,:,:) = 13./12 * (PSRC(IW+2:IE-1,:,:) - &
- 2.0*PSRC(IW+3:IE,:,:) + PSRC(IW+4:IE+1,:,:))**2 + &
- 1./4 * ( 3.0*PSRC(IW+2:IE-1,:,:) - 4.0*PSRC(IW+3:IE,:,:) + &
- PSRC(IW+4:IE+1,:,:))**2
- ZBNEG2(IW+2:IE-1,:,:) = 13./12 * (PSRC(IW+1:IE-2,:,:) - &
- 2.0*PSRC(IW+2:IE-1,:,:) + PSRC(IW+3:IE,:,:))**2 + &
- 1./4 * (PSRC(IW+1:IE-2,:,:) - PSRC(IW+3:IE,:,:))**2
- ZBNEG3(IW+2:IE-1,:,:) = 13./12 * (PSRC(IW:IE-3,:,:) - &
- 2.0*PSRC(IW+1:IE-2,:,:) + PSRC(IW+2:IE-1,:,:))**2 + &
- 1./4 * ( PSRC(IW:IE-3,:,:) - 4.0*PSRC(IW+1:IE-2,:,:) + &
- 3.0*PSRC(IW+2:IE-1,:,:))**2
-!
- ZOMP1(IW+2:IE-1,:,:) = ZGAMMA1 / (ZEPS + ZBPOS1(IW+2:IE-1,:,:))**2
- ZOMP2(IW+2:IE-1,:,:) = ZGAMMA2 / (ZEPS + ZBPOS2(IW+2:IE-1,:,:))**2
- ZOMP3(IW+2:IE-1,:,:) = ZGAMMA3 / (ZEPS + ZBPOS3(IW+2:IE-1,:,:))**2
- ZOMN1(IW+2:IE-1,:,:) = ZGAMMA1 / (ZEPS + ZBNEG1(IW+2:IE-1,:,:))**2
- ZOMN2(IW+2:IE-1,:,:) = ZGAMMA2 / (ZEPS + ZBNEG2(IW+2:IE-1,:,:))**2
- ZOMN3(IW+2:IE-1,:,:) = ZGAMMA3 / (ZEPS + ZBNEG3(IW+2:IE-1,:,:))**2
-!
- PR(IW+2:IE-1,:,:) = (ZOMP2(IW+2:IE-1,:,:)/(ZOMP1(IW+2:IE-1,:,:)+ &
- ZOMP2(IW+2:IE-1,:,:)+ &
- ZOMP3(IW+2:IE-1,:,:)) * ZFPOS2(IW+2:IE-1,:,:) + &
- ZOMP1(IW+2:IE-1,:,:)/(ZOMP1(IW+2:IE-1,:,:)+ZOMP2(IW+2:IE-1,:,:)+ &
- ZOMP3(IW+2:IE-1,:,:)) * ZFPOS1(IW+2:IE-1,:,:) + &
- ZOMP3(IW+2:IE-1,:,:)/(ZOMP1(IW+2:IE-1,:,:)+ZOMP2(IW+2:IE-1,:,:)+ &
- ZOMP3(IW+2:IE-1,:,:)) * ZFPOS3(IW+2:IE-1,:,:)) * &
- (0.5+SIGN(0.5,PRUCT(IW+2:IE-1,:,:))) + &
- (ZOMN2(IW+2:IE-1,:,:)/(ZOMN1(IW+2:IE-1,:,:)+ZOMN2(IW+2:IE-1,:,:)+&
- ZOMN3(IW+2:IE-1,:,:)) * ZFNEG2(IW+2:IE-1,:,:) + &
- ZOMN1(IW+2:IE-1,:,:)/(ZOMN1(IW+2:IE-1,:,:)+ZOMN2(IW+2:IE-1,:,:)+ &
- ZOMN3(IW+2:IE-1,:,:)) * ZFNEG1(IW+2:IE-1,:,:) + &
- ZOMN3(IW+2:IE-1,:,:)/(ZOMN1(IW+2:IE-1,:,:)+ZOMN2(IW+2:IE-1,:,:)+ &
- ZOMN3(IW+2:IE-1,:,:)) * ZFNEG3(IW+2:IE-1,:,:)) * &
- (0.5-SIGN(0.5,PRUCT(IW+2:IE-1,:,:)))
-!
-END SELECT
-!
-PR = PR * PRUCT
+! ! WENO scheme order 3, IE
+ ZFPOS1(IE,:,:) = 0.5 * (3.0*PSRC(IE-1,:,:) - PSRC(IE-2,:,:)) ! First positive flux
+ ZFPOS2(IE,:,:) = 0.5 * ( PSRC(IE-1,:,:) + PSRC(IE,:,:)) ! Second positive flux
+ ZBPOS1(IE,:,:) = (PSRC(IE-1,:,:) - PSRC(IE-2,:,:))**2 ! First positive smoothness indicator
+ ZBPOS2(IE,:,:) = (PSRC(IE,:,:) - PSRC(IE-1,:,:))**2 ! Second positive smoothness indicator
+!
+ ZFNEG1(IE,:,:) = 0.5 * (3.0*PSRC(IE,:,:) - PSRC(IE+1,:,:)) ! First negative flux
+ ZFNEG2(IE,:,:) = 0.5 * ( PSRC(IE-1,:,:) + PSRC(IE,:,:)) ! Second negative flux
+ ZBNEG1(IE,:,:) = (PSRC(IE,:,:) - PSRC(IE+1,:,:))**2 ! First negative smoothness indicator
+ ZBNEG2(IE,:,:) = (PSRC(IE-1,:,:) - PSRC(IE,:,:))**2 ! Second negative smoothness indicator
+!
+ ZOMP1(IE,:,:) = 1./3. / (ZEPS + ZBPOS1(IE,:,:))**2 ! First positive non-normalized weight
+ ZOMP2(IE,:,:) = 2./3. / (ZEPS + ZBPOS2(IE,:,:))**2 ! Second positive non-normalized weight
+ ZOMN1(IE,:,:) = 1./3. / (ZEPS + ZBNEG1(IE,:,:))**2 ! First negative non-normalized weight
+ ZOMN2(IE,:,:) = 2./3. / (ZEPS + ZBNEG2(IE,:,:))**2 ! Second negative non-normalized weight
+!
+ PR(IE,:,:) = (ZOMN2(IE,:,:)/(ZOMN1(IE,:,:)+ZOMN2(IE,:,:))*ZFNEG2(IE,:,:) + &
+ (ZOMN1(IE,:,:)/(ZOMN1(IE,:,:)+ZOMN2(IE,:,:))*ZFNEG1(IE,:,:))) &
+ *(0.5-SIGN(0.5,PRUCT(IE,:,:))) + &
+ (ZOMP2(IE,:,:)/(ZOMP1(IE,:,:)+ZOMP2(IE,:,:))*ZFPOS2(IE,:,:) + &
+ (ZOMP1(IE,:,:)/(ZOMP1(IE,:,:)+ZOMP2(IE,:,:))*ZFPOS1(IE,:,:))) &
+ *(0.5+SIGN(0.5,PRUCT(IE,:,:))) ! Total flux
+!
+ END SELECT ! SELECT CASE (HLBCX(2)) ! X direction LBC type on right side
+!
+ELSE
+ !-----------------------------------------------------------------------------
+ ! East border is proc border -- IE,IE+1
+ !-----------------------------------------------------------------------------
+!
+ IF (NHALO<3) THEN
+ PRINT *,'WARNING : WENO5 not parallelisable with NHALO < 3'
+ CALL ABORT
+ ELSEIF (NHALO>=3) THEN
+ !---------------------------------------------------------------------------
+ ! NHALO >= 3 => WENO5 for all boundary points
+ !---------------------------------------------------------------------------
+!
+ ! ----- Positive fluxes -----
+!
+ ! First positive stencil, needs indices i-3, i-2, i-1
+ ZFPOS1(IE,:,:) = 1./6. * (2.0*PSRC(IE-3,:,:) - 7.0*PSRC(IE-2,:,:) + 11.0*PSRC(IE-1,:,:)) ! Flux IE
+ ZFPOS1(IE+1,:,:) = 1./6. * (2.0*PSRC(IE-2,:,:) - 7.0*PSRC(IE-1,:,:) + 11.0*PSRC(IE,:,:)) ! Flux IE+1
+ ZBPOS1(IE,:,:) = 13./12. * (PSRC(IE-3,:,:) - 2.0*PSRC(IE-2,:,:) + PSRC(IE-1,:,:))**2 &
+ + 1./4 * (PSRC(IE-3,:,:) - 4.0*PSRC(IE-2,:,:) + 3.0*PSRC(IE-1,:,:))**2 ! Smoothness indicator IE
+ ZBPOS1(IE+1,:,:) = 13./12. * (PSRC(IE-2,:,:) - 2.0*PSRC(IE-1,:,:) + PSRC(IE,:,:))**2 &
+ + 1./4 * (PSRC(IE-2,:,:) - 4.0*PSRC(IE-1,:,:) + 3.0*PSRC(IE,:,:))**2 ! Smoothness indicator IE+1
+ ZOMP1(IE:IE+1,:,:) = 1./10. / (ZEPS + ZBPOS1(IE:IE+1,:,:))**2 ! Non-normalized weight IE,IE+1
+!
+ ! Second positive stencil, needs indices i-2, i-1, i
+ ZFPOS2(IE,:,:) = 1./6. * (-1.0*PSRC(IE-2,:,:) + 5.0*PSRC(IE-1,:,:) + 2.0*PSRC(IE,:,:)) ! Flux IE
+ ZFPOS2(IE+1,:,:) = 1./6. * (-1.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) + 2.0*PSRC(IE+1,:,:)) ! Flux IE+1
+ ZBPOS2(IE,:,:) = 13./12 * (PSRC(IE-2,:,:) - 2.0*PSRC(IE-1,:,:) + PSRC(IE,:,:))**2 &
+ + 1./4 * (PSRC(IE-2,:,:) - PSRC(IE,:,:))**2 ! Smoothness indicator IE
+ ZBPOS2(IE+1,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (PSRC(IE-1,:,:) - PSRC(IE+1,:,:))**2 ! Smoothness indicator IE+1
+ ZOMP2(IE:IE+1,:,:) = 3./5. / (ZEPS + ZBPOS2(IE:IE+1,:,:))**2 ! Non-normalized weight IE,IE+1
+!
+ ! Third positive stencil, needs indices i, i+1, i+2
+ ZFPOS3(IE,:,:) = 1./6 * (2.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) - PSRC(IE+1,:,:)) ! Flux IE
+ ZFPOS3(IE+1,:,:) = 1./6 * (2.0*PSRC(IE,:,:) + 5.0*PSRC(IE+1,:,:) - PSRC(IE+2,:,:)) ! Flux IE+1
+ ZBPOS3(IE,:,:) = 13./12 * ( PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE-1,:,:) - 4.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 ! Smoothness indicator IE
+ ZBPOS3(IE+1,:,:) = 13./12 * ( PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE,:,:) - 4.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 ! Smoothness indicator IE+1
+ ZOMP3(IE:IE+1,:,:) = 3./10. / (ZEPS + ZBPOS3(IE:IE+1,:,:))**2 ! Non-normalized weight IE,IE+1
+!
+ ! ----- Negative fluxes -----
+!
+ ! First negative stencil, needs indices i, i+1, i+2
+ ZFNEG1(IE,:,:) = 1./6. * (11.0*PSRC(IE,:,:) - 7.0*PSRC(IE+1,:,:) + 2.0*PSRC(IE+2,:,:)) ! Flux IE
+ ZFNEG1(IE+1,:,:) = 1./6. * (11.0*PSRC(IE+1,:,:) - 7.0*PSRC(IE+2,:,:) + 2.0*PSRC(IE+3,:,:)) ! Flux IE+1
+ ZBNEG1(IE,:,:) = 13./12. * ( PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE,:,:) - 4.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 ! Smoothness indicator IE
+ ZBNEG1(IE+1,:,:) = 13./12. * ( PSRC(IE+1,:,:) - 2.0*PSRC(IE+2,:,:) + PSRC(IE+3,:,:))**2 &
+ + 1./4 * (3.0*PSRC(IE+1,:,:) - 4.0*PSRC(IE+2,:,:) + PSRC(IE+3,:,:))**2 ! Smoothness indicator IE+1
+ ZOMN1(IE:IE+1,:,:) = 1./10. / (ZEPS + ZBNEG1(IE:IE+1,:,:))**2 ! Non-normalized weight IE,IE+1
+!
+ ! Second negative stencil, needs indices i-1, i, i+1
+ ZFNEG2(IE,:,:) = 1./6. * (2.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) - 1.0*PSRC(IE+1,:,:)) ! Flux IE
+ ZFNEG2(IE+1,:,:) = 1./6. * (2.0*PSRC(IE,:,:) + 5.0*PSRC(IE+1,:,:) - 1.0*PSRC(IE+2,:,:)) ! Flux IE+1
+ ZBNEG2(IE,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (PSRC(IE-1,:,:) - PSRC(IE+1,:,:))**2 ! Smoothness indicator IE
+ ZBNEG2(IE+1,:,:) = 13./12 * (PSRC(IE,:,:) - 2.0*PSRC(IE+1,:,:) + PSRC(IE+2,:,:))**2 &
+ + 1./4 * (PSRC(IE,:,:) - PSRC(IE+2,:,:))**2 ! Smoothness indicator IE+1
+ ZOMN2(IE:IE+1,:,:) = 3./5. / (ZEPS + ZBNEG2(IE:IE+1,:,:))**2 ! Non-normalized weight IE,IE+1
+!
+ ! Third negative stencil, needs indices i-2, i-1, i
+ ZFNEG3(IE,:,:) = 1./6 * (-1.0*PSRC(IE-2,:,:) + 5.0*PSRC(IE-1,:,:) + 2.0*PSRC(IE,:,:)) ! Flux IE
+ ZFNEG3(IE+1,:,:) = 1./6 * (-1.0*PSRC(IE-1,:,:) + 5.0*PSRC(IE,:,:) + 2.0*PSRC(IE+1,:,:)) ! Flux IE+1
+ ZBNEG3(IE,:,:) = 13./12 * (PSRC(IE-2,:,:) - 2.0*PSRC(IE-1,:,:) + PSRC(IE,:,:))**2 &
+ + 1./4 * (PSRC(IE-2,:,:) - 4.0*PSRC(IE-1,:,:) + 3.0*PSRC(IE,:,:))**2 ! Smoothness indicator IE
+ ZBNEG3(IE+1,:,:) = 13./12 * (PSRC(IE-1,:,:) - 2.0*PSRC(IE,:,:) + PSRC(IE+1,:,:))**2 &
+ + 1./4 * (PSRC(IE-1,:,:) - 4.0*PSRC(IE,:,:) + 3.0*PSRC(IE+1,:,:))**2 ! Smoothness indicator IE+1
+ ZOMN3(IE:IE+1,:,:) = 3./10. / (ZEPS + ZBNEG3(IE:IE+1,:,:))**2 ! Non-normalized weight IE,IE+1
+!
+ ! ----- Total flux -----
+!
+ PR(IE:IE+1,:,:) = ( ZOMP1(IE:IE+1,:,:)/(ZOMP1(IE:IE+1,:,:)+ZOMP2(IE:IE+1,:,:)+ZOMP3(IE:IE+1,:,:)) * ZFPOS1(IE:IE+1,:,:) &
+ + ZOMP2(IE:IE+1,:,:)/(ZOMP1(IE:IE+1,:,:)+ZOMP2(IE:IE+1,:,:)+ZOMP3(IE:IE+1,:,:)) * ZFPOS2(IE:IE+1,:,:) &
+ + ZOMP3(IE:IE+1,:,:)/(ZOMP1(IE:IE+1,:,:)+ZOMP2(IE:IE+1,:,:)+ZOMP3(IE:IE+1,:,:)) * ZFPOS3(IE:IE+1,:,:)) &
+ * (0.5+SIGN(0.5,PRUCT(IE:IE+1,:,:))) &
+ + ( ZOMN1(IE:IE+1,:,:)/(ZOMN1(IE:IE+1,:,:)+ZOMN2(IE:IE+1,:,:)+ZOMN3(IE:IE+1,:,:)) * ZFNEG1(IE:IE+1,:,:) &
+ + ZOMN2(IE:IE+1,:,:)/(ZOMN1(IE:IE+1,:,:)+ZOMN2(IE:IE+1,:,:)+ZOMN3(IE:IE+1,:,:)) * ZFNEG2(IE:IE+1,:,:) &
+ + ZOMN3(IE:IE+1,:,:)/(ZOMN1(IE:IE+1,:,:)+ZOMN2(IE:IE+1,:,:)+ZOMN3(IE:IE+1,:,:)) * ZFNEG3(IE:IE+1,:,:)) &
+ * (0.5-SIGN(0.5,PRUCT(IE:IE+1,:,:)))
+!
+ END IF ! NHALO
+!
+END IF ! IF(LWEST_ll())
+!-------------------------------------------------------------------------------
+!
+PR = PR * PRUCT ! Add contravariant flux
!
END SUBROUTINE ADVEC_WENO_K_3_MX
!
!-------------------------------------------------------------------------------
!
! ########################################################################
- SUBROUTINE ADVEC_WENO_K_3_MY(HLBCY,PSRC, PRVCT, PR, TPHALO2)
+ SUBROUTINE ADVEC_WENO_K_3_MY(HLBCY,PSRC, PRVCT, PR)
! ########################################################################
!!
!!**** Computes PRVCT * PUT (or PRVCT * PWT). Upstream fluxes of U (or W)
@@ -1387,13 +1428,16 @@ END SUBROUTINE ADVEC_WENO_K_3_MX
!!
!! MODIFICATIONS
!! -------------
+!! T. Lunet 02/10/2014: Correction of periodic boudary conditions
+!! Change of structure in order to adapt WENO to NHALOK
+!! Suppression of second layer HALO pointers
+!! Complete code documentation
!!
!-------------------------------------------------------------------------------
!
USE MODE_ll
USE MODD_LUNIT
USE MODD_CONF
-USE MODD_ARGSLIST_ll, ONLY : HALO2LIST_ll
!
IMPLICIT NONE
!
@@ -1407,7 +1451,6 @@ REAL, DIMENSION(:,:,:), INTENT(IN) :: PRVCT ! contrav. comp. on MASS GRID
! output source term
!
REAL, DIMENSION(:,:,:), INTENT(INOUT) :: PR
-TYPE(HALO2_ll), OPTIONAL, POINTER :: TPHALO2 ! halo2 for the field at t
!
!* 0.2 Declarations of local variables :
!
@@ -1423,7 +1466,6 @@ INTEGER:: ILUOUT,IRESP ! for prints
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZFPOS1, ZFPOS2, ZFPOS3
!
! intermediate reconstruction fluxes for negative wind case
-! we need only one since ZFNEG2 = ZFPOS2
!
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZFNEG1, ZFNEG2, ZFNEG3
!
@@ -1436,15 +1478,11 @@ REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZBNEG1, ZBNEG2, ZBNEG3
!
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZOMP1, ZOMP2, ZOMP3
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZOMN1, ZOMN2, ZOMN3
+
+REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)) :: ZWORK
!
-! standard weights
-!
-REAL, PARAMETER :: ZGAMMA1 = 1./10.
-REAL, PARAMETER :: ZGAMMA2 = 3./5.
-REAL, PARAMETER :: ZGAMMA3 = 3./10.
-REAL, PARAMETER :: ZGAMMA1_PRIM = 1./3.
-REAL, PARAMETER :: ZGAMMA2_PRIM = 2./3.
-!
+! EPSILON for weno weights calculation
+!
REAL, PARAMETER :: ZEPS = 1.0E-15
!
!-----------------------------------------------------------------------------
@@ -1479,478 +1517,563 @@ ZOMP3 = 0.0
ZOMN1 = 0.0
ZOMN2 = 0.0
ZOMN3 = 0.0
+
+ZWORK = 0.0
!
!-------------------------------------------------------------------------------
+!* 1.1. Interior Fluxes
+! ---------------------
+IS=IJB
+IN=IJE
!
-SELECT CASE ( HLBCY(1) ) !
-!
-!* 1.1 CYCLIC CASE IN THE Y DIRECTION:
-!
-CASE ('CYCL') ! In that case one must have HLBCY(1) == HLBCY(2)
-!
- IF(NHALO == 1) THEN
- IS=IJB
- IN=IJE
- ELSE
- CALL FMLOOK_ll(CLUOUT0,CLUOUT0,ILUOUT,IRESP)
- WRITE(ILUOUT,*) 'ERROR : 4th order advection in CYCLic case '
- WRITE(ILUOUT,*) 'cannot be used with NHALO=2'
- CALL ABORT
- STOP
- END IF
-!
-! Same explanation than for the subroutine ADVEC_WENO_K_3_MX
-!
-! intermediate fluxes for positive wind case
-!
- ZFPOS1(:,IS+2:IN,:) = 1./6 * (2.0*PSRC(:,IS-1:IN-3,:) - &
- 7.0*PSRC(:,IS:IN-2,:) + 11.0*PSRC(:,IS+1:IN-1,:))
- ZFPOS1(:,IS+1, :) = 1./6 * (2.0*TPHALO2%SOUTH(:,:) - &
- 7.0*PSRC(:,IS-1, :) + 11.0*PSRC(:,IS, :))
- ZFPOS1(:,IN+1,:) = 0.5 * (3.0*PSRC(:,IN,:) - PSRC(:,IN-1,:))
- ZFPOS1(:,IS, :) = 0.5 * (3.0*PSRC(:,IS-1, :) - TPHALO2%SOUTH(:,:))
- ZFPOS1(:,IS-1, :) = - 999.
-!
-!
- ZFPOS2(:,IS+1:IN,:) = 1./6 * (-1.0*PSRC(:,IS-1:IN-2,:) + &
- 5.0*PSRC(:,IS:IN-1,:) + 2.0*PSRC(:,IS+1:IN,:))
- ZFPOS2(:,IN+1,:) = 0.5 * (PSRC(:,IN, :) + PSRC(:,IN+1,:))
- ZFPOS2(:,IS, :) = 0.5 * (PSRC(:,IS-1,:) + PSRC(:,IS, :))
- ZFPOS2(:,IS-1,:) = 0.5 * (TPHALO2%SOUTH(:,:) + PSRC(:,IS-1,:))
-!
-!
- ZFPOS3(:,IS+1:IN,:) = 1./6 * (2.0*PSRC(:,IS:IN-1,:) + &
- 5.0*PSRC(:,IS+1:IN,:) - 1.0*PSRC(:,IS+2:IN+1,:))
-!
-! intermediate flux for negative wind case
+!-------------------------------------------------------------------------------
+! Flux calculation in the physical domain far enough from the boundary
+! WENO scheme order 5, IS+2 -> IN-1
+! Computation at the mass point on Vgrid v(i-1/2,j,k)
+!-------------------------------------------------------------------------------
!
- ZFNEG1(:,IS+1:IN-1,:) = 1./6 * (11.0*PSRC(:,IS+1:IN-1,:) - &
- 7.0*PSRC(:,IS+2:IN,:) + 2.0*PSRC(:,IS+3:IN+1,:))
- ZFNEG1(:,IN, :) = 1./6 * (11.0*PSRC(:,IN, :) - &
- 7.0*PSRC(:,IN+1, :) + 2.0*TPHALO2%NORTH(:,:))
- ZFNEG1(:,IS, :) = 0.5 * (3.0*PSRC(:,IS, :) - PSRC(:,IS+1,:))
- ZFNEG1(:,IS-1,:) = 0.5 * (3.0*PSRC(:,IS-1,:) - PSRC(:,IS, :))
- ZFNEG1(:,IN+1,:) = 0.5 * (3.0*PSRC(:,IN+1,:) - TPHALO2%NORTH(:,:))
+! ----- Positive fluxes -----
+!
+! First positive stencil, needs indices i-3, i-2, i-1
+ZFPOS1(:,IS+2:IN-1,:) = 1./6. * (2.0*PSRC(:,IS-1:IN-4,:)- 7.0*PSRC(:,IS:IN-3,:)+ 11.0*PSRC(:,IS+1:IN-2,:)) ! Flux
+ZBPOS1(:,IS+2:IN-1,:) = 13./12. * ( PSRC(:,IS-1:IN-4,:)- 2.0*PSRC(:,IS:IN-3,:)+ PSRC(:,IS+1:IN-2,:))**2 &
+ + 1./4 * ( PSRC(:,IS-1:IN-4,:)- 4.0*PSRC(:,IS:IN-3,:)+ 3.0* PSRC(:,IS+1:IN-2,:))**2 ! Smoothness indicator
+ZOMP1(:,IS+2:IN-1,:) = 1./10. / (ZEPS + ZBPOS1(:,IS+2:IN-1,:))**2 ! Non-normalized weight
+!
+! Second positive stencil, needs indices i-2, i-1, i
+ZFPOS2(:,IS+2:IN-1,:) = 1./6. * (-1.0*PSRC(:,IS:IN-3,:) + 5.0*PSRC(:,IS+1:IN-2,:) + 2.0*PSRC(:,IS+2:IN-1,:)) ! Flux
+ZBPOS2(:,IS+2:IN-1,:) = 13./12 * ( PSRC(:,IS:IN-3,:) - 2.0*PSRC(:,IS+1:IN-2,:) + PSRC(:,IS+2:IN-1,:))**2 &
+ + 1./4 * ( PSRC(:,IS:IN-3,:) - PSRC(:,IS+2:IN-1,:))**2 ! Smoothness indicator
+ZOMP2(:,IS+2:IN-1,:) = 3./5. / (ZEPS + ZBPOS2(:,IS+2:IN-1,:))**2 ! Non-normalized weight
+!
+! Third positive stencil, needs indices i-1, i, i+1
+ZFPOS3(:,IS+2:IN-1,:) = 1./6 * (2.0*PSRC(:,IS+1:IN-2,:) + 5.0*PSRC(:,IS+2:IN-1,:) - PSRC(:,IS+3:IN,:)) ! Flux
+ZBPOS3(:,IS+2:IN-1,:) = 13./12 * ( PSRC(:,IS+1:IN-2,:) - 2.0*PSRC(:,IS+2:IN-1,:) + PSRC(:,IS+3:IN,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS+1:IN-2,:) - 4.0*PSRC(:,IS+2:IN-1,:) + PSRC(:,IS+3:IN,:))**2 ! Smoothness indicator
+ZOMP3(:,IS+2:IN-1,:) = 3./10. / (ZEPS + ZBPOS3(:,IS+2:IN-1,:))**2 ! Non-normalized weight
+!
+! ----- Negative fluxes -----
+!
+! First negative stencil, needs indices i, i+1, i+2
+ZFNEG1(:,IS+2:IN-1,:) = 1./6. * (11.0*PSRC(:,IS+2:IN-1,:) - 7.0*PSRC(:,IS+3:IN,:) + 2.0*PSRC(:,IS+4:IN+1,:)) ! Flux
+ZBNEG1(:,IS+2:IN-1,:) = 13./12. * ( PSRC(:,IS+2:IN-1,:) - 2.0*PSRC(:,IS+3:IN,:) + PSRC(:,IS+4:IN+1,:))**2 &
+ + 1./4 * (3.0* PSRC(:,IS+2:IN-1,:) - 4.0*PSRC(:,IS+3:IN,:) + PSRC(:,IS+4:IN+1,:))**2 ! Smoothness indicator
+ZOMN1(:,IS+2:IN-1,:) = 1./10. / (ZEPS + ZBNEG1(:,IS+2:IN-1,:))**2 ! Non-normalized weight
+!
+! Second negative stencil, needs indices i-1, i, i+1
+ZFNEG2(:,IS+2:IN-1,:) = 1./6. * (2.0*PSRC(:,IS+1:IN-2,:) + 5.0*PSRC(:,IS+2:IN-1,:) - 1.0*PSRC(:,IS+3:IN,:)) ! Flux
+ZBNEG2(:,IS+2:IN-1,:) = 13./12 * ( PSRC(:,IS+1:IN-2,:) - 2.0*PSRC(:,IS+2:IN-1,:) + PSRC(:,IS+3:IN,:))**2 &
+ + 1./4 * ( PSRC(:,IS+1:IN-2,:) - PSRC(:,IS+3:IN,:))**2 ! Smoothness indicator
+ZOMN2(:,IS+2:IN-1,:) = 3./5. / (ZEPS + ZBNEG2(:,IS+2:IN-1,:))**2 ! Non-normalized weight
+!
+! Third negative stencil, needs indices i-2, i-1, i
+ZFNEG3(:,IS+2:IN-1,:) = 1./6 * (-1.0*PSRC(:,IS:IN-3,:) + 5.0*PSRC(:,IS+1:IN-2,:) + 2.0*PSRC(:,IS+2:IN-1,:)) ! Flux
+ZBNEG3(:,IS+2:IN-1,:) = 13./12 * ( PSRC(:,IS:IN-3,:) - 2.0*PSRC(:,IS+1:IN-2,:) + PSRC(:,IS+2:IN-1,:))**2 &
+ + 1./4 * ( PSRC(:,IS:IN-3,:) - 4.0*PSRC(:,IS+1:IN-2,:) + 3.0*PSRC(:,IS+2:IN-1,:))**2 ! Smoothness indicator
+ZOMN3(:,IS+2:IN-1,:) = 3./10. / (ZEPS + ZBNEG3(:,IS+2:IN-1,:))**2 ! Non-normalized weight
+!
+! ----- Total flux -----
+!
+PR(:,IS+2:IN-1,:) = (ZOMP1(:,IS+2:IN-1,:)/(ZOMP1(:,IS+2:IN-1,:)+ZOMP2(:,IS+2:IN-1,:)+ZOMP3(:,IS+2:IN-1,:)) &
+ * ZFPOS1(:,IS+2:IN-1,:) + &
+ ZOMP2(:,IS+2:IN-1,:)/(ZOMP1(:,IS+2:IN-1,:)+ZOMP2(:,IS+2:IN-1,:)+ZOMP3(:,IS+2:IN-1,:)) &
+ * ZFPOS2(:,IS+2:IN-1,:) + &
+ ZOMP3(:,IS+2:IN-1,:)/(ZOMP1(:,IS+2:IN-1,:)+ZOMP2(:,IS+2:IN-1,:)+ZOMP3(:,IS+2:IN-1,:)) &
+ * ZFPOS3(:,IS+2:IN-1,:)) &
+ * (0.5+SIGN(0.5,PRVCT(:,IS+2:IN-1,:))) &
+ + (ZOMN1(:,IS+2:IN-1,:)/(ZOMN1(:,IS+2:IN-1,:)+ZOMN2(:,IS+2:IN-1,:)+ZOMN3(:,IS+2:IN-1,:)) &
+ * ZFNEG1(:,IS+2:IN-1,:) &
+ + ZOMN2(:,IS+2:IN-1,:)/(ZOMN1(:,IS+2:IN-1,:)+ZOMN2(:,IS+2:IN-1,:)+ZOMN3(:,IS+2:IN-1,:)) &
+ * ZFNEG2(:,IS+2:IN-1,:) &
+ + ZOMN3(:,IS+2:IN-1,:)/(ZOMN1(:,IS+2:IN-1,:)+ZOMN2(:,IS+2:IN-1,:)+ZOMN3(:,IS+2:IN-1,:)) &
+ * ZFNEG3(:,IS+2:IN-1,:)) &
+ * (0.5-SIGN(0.5,PRVCT(:,IS+2:IN-1,:)))
!
+!-------------------------------------------------------------------------------
+!* 1.2. South border
+! ---------------------
!
- ZFNEG2(:,IS+1:IN,:) = 1./6 * (2.0*PSRC(:,IS:IN-1,:) + &
- 5.0*PSRC(:,IS+1:IN,:) - 1.0*PSRC(:,IS+2:IN+1,:))
- ZFNEG2(:,IN+1,:) = 0.5 * (PSRC(:,IN+1,:) + PSRC(:,IN, :))
- ZFNEG2(:,IS, :) = 0.5 * (PSRC(:,IS, :) + PSRC(:,IS-1,:))
- ZFNEG2(:,IS-1,:) = 0.5 * (PSRC(:,IS-1,:) + TPHALO2%SOUTH(:,:))
+IF(LSOUTH_ll() .AND. .FALSE. ) THEN
+ !-----------------------------------------------------------------------------
+ ! South border is physical -- IS+1,IS
+ !-----------------------------------------------------------------------------
+ SELECT CASE (HLBCY(1)) ! Y direction LBC type on south side
!
+ CASE ('CYCL')
+ !---------------------------------------------------------------------------
+ ! Periodic boundary condition
+ !---------------------------------------------------------------------------
+!
+ IF(LNORTH_ll() .AND. .FALSE. ) THEN ! North border is physical
+!
+ ! First positive stencil, needs indices i-3, i-2, i-1
+ ZFPOS1(:,IS+1,:) = 1./6. * (2.0*PSRC(:,IN,:) - 7.0*PSRC(:,IS-1,:) + 11.0*PSRC(:,IS,:)) ! Flux IS+1
+ ZFPOS1(:,IS,:) = 1./6. * (2.0*PSRC(:,IN-1,:) - 7.0*PSRC(:,IN,:) + 11.0*PSRC(:,IS-1,:)) ! Flux IS
+ ZBPOS1(:,IS+1,:) = 13./12. * (PSRC(:,IN,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IN,:) - 4.0*PSRC(:,IS-1,:) + 3.0*PSRC(:,IS,:))**2 ! Smoothness indicator IS+1
+ ZBPOS1(:,IS,:) = 13./12. * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IS-1,:))**2 &
+ + 1./4 * (PSRC(:,IN-1,:) - 4.0*PSRC(:,IN,:) + 3.0*PSRC(:,IS-1,:))**2 ! Smoothness indicator IS
+ ZOMP1(:,IS:IS+1,:) = 1./10. / (ZEPS + ZBPOS1(:,IS:IS+1,:))**2 ! Non-normalized weight IS+1,IS
+!
+ ! Second positive stencil, needs indices i-2, i-1, i
+ ZFPOS2(:,IS+1,:) = 1./6.* (-1.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) + 2.0*PSRC(:,IS+1,:)) ! Flux IS+1
+ ZFPOS2(:,IS,:) = 1./6.* (-1.0*PSRC(:,IN,:) + 5.0*PSRC(:,IS-1,:) + 2.0*PSRC(:,IS,:)) ! Flux IS
+ ZBPOS2(:,IS+1,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (PSRC(:,IS-1,:) - PSRC(:,IS+1,:))**2 ! Smoothness indicator IS+1
+ ZBPOS2(:,IS,:) = 13./12 * (PSRC(:,IN,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IN,:) - PSRC(:,IS,:))**2 ! Smoothness indicator IS
+ ZOMP2(:,IS:IS+1,:) = 3./5. / (ZEPS + ZBPOS2(:,IS:IS+1,:))**2 ! Non-normalized weight IS+1,IS
+!
+ ! Third negative stencil, needs indices i-2, i-1, i
+ ZFNEG3(:,IS+1,:) = 1./6 * (-1.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) + 2.0*PSRC(:,IS+1,:)) ! Flux IS+1
+ ZFNEG3(:,IS,:) = 1./6 * (-1.0*PSRC(:,IN,:) + 5.0*PSRC(:,IS-1,:) + 2.0*PSRC(:,IS,:)) ! Flux IS
+ ZBNEG3(:,IS+1,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (PSRC(:,IS-1,:) - 4.0*PSRC(:,IS,:) + 3.0*PSRC(:,IS+1,:))**2 ! Smoothness indicator IS+1
+ ZBNEG3(:,IS,:) = 13./12 * (PSRC(:,IN,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IN,:) - 4.0*PSRC(:,IS-1,:) + 3.0*PSRC(:,IS,:))**2 ! Smoothness indicator IS
+ ZOMN3(:,IS:IS+1,:) = 3./10. / (ZEPS + ZBNEG3(:,IS:IS+1,:))**2 ! Non-normalized weight IS+1,IS
+!
+ ELSEIF(IS>3) THEN ! North boundary is proc border, with minimum 3 HALO points on sounth side
+!
+ ! First positive stencil, needs indices i-3, i-2, i-1
+ ZFPOS1(:,IS+1,:) = 1./6. * (2.0*PSRC(:,IS-2,:) - 7.0*PSRC(:,IS-1,:) + 11.0*PSRC(:,IS,:)) ! Flux IS+1
+ ZFPOS1(:,IS,:) = 1./6. * (2.0*PSRC(:,IS-3,:) - 7.0*PSRC(:,IS-2,:) + 11.0*PSRC(:,IS-1,:)) ! Flux IS
+ ZBPOS1(:,IS+1,:) = 13./12. * (PSRC(:,IS-2,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IS-2,:) - 4.0*PSRC(:,IS-1,:) + 3.0*PSRC(:,IS,:))**2 ! Smoothness indicator IS+1
+ ZBPOS1(:,IS,:) = 13./12. * (PSRC(:,IS-3,:) - 2.0*PSRC(:,IS-2,:) + PSRC(:,IS-1,:))**2 &
+ + 1./4 * (PSRC(:,IS-3,:) - 4.0*PSRC(:,IS-2,:) + 3.0*PSRC(:,IS-1,:))**2 ! Smoothness indicator IS
+ ZOMP1(:,IS:IS+1,:) = 1./10. / (ZEPS + ZBPOS1(:,IS:IS+1,:))**2 ! Non-normalized weight IS+1,IS
+!
+ ! Second positive stencil, needs indices i-2, i-1, i
+ ZFPOS2(:,IS+1,:) = 1./6.* (-1.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) + 2.0*PSRC(:,IS+1,:)) ! Flux IS+1
+ ZFPOS2(:,IS,:) = 1./6.* (-1.0*PSRC(:,IS-2,:) + 5.0*PSRC(:,IS-1,:) + 2.0*PSRC(:,IS,:)) ! Flux IS
+ ZBPOS2(:,IS+1,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (PSRC(:,IS-1,:) - PSRC(:,IS+1,:))**2 ! Smoothness indicator IS+1
+ ZBPOS2(:,IS,:) = 13./12 * (PSRC(:,IS-2,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IS-2,:) - PSRC(:,IS,:))**2 ! Smoothness indicator IS
+ ZOMP2(:,IS:IS+1,:) = 3./5. / (ZEPS + ZBPOS2(:,IS:IS+1,:))**2 ! Non-normalized weight IS+1,IS
+!
+ ! Third negative stencil, needs indices i-2, i-1, i
+ ZFNEG3(:,IS+1,:) = 1./6 * (-1.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) + 2.0*PSRC(:,IS+1,:)) ! Flux IS+1
+ ZFNEG3(:,IS,:) = 1./6 * (-1.0*PSRC(:,IS-2,:) + 5.0*PSRC(:,IS-1,:) + 2.0*PSRC(:,IS,:)) ! Flux IS
+ ZBNEG3(:,IS+1,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (PSRC(:,IS-1,:) - 4.0*PSRC(:,IS,:) + 3.0*PSRC(:,IS+1,:))**2 ! Smoothness indicator IS+1
+ ZBNEG3(:,IS,:) = 13./12 * (PSRC(:,IS-2,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IS-2,:) - 4.0*PSRC(:,IS-1,:) + 3.0*PSRC(:,IS,:))**2 ! Smoothness indicator IS
+ ZOMN3(:,IS:IS+1,:) = 3./10. / (ZEPS + ZBNEG3(:,IS:IS+1,:))**2 ! Non-normalized weight IS+1,IS
+!
+ ELSE ! North boundary is proc border, with NHALO < 3 on south side
+ PRINT *,'WARNING : WENO5 fluxes calculation needs NHALO >= 3 on south side'
+ CALL ABORT
+ ENDIF
+!
+ ! Third positive stencil, needs indices i-1, i, i+1
+ ZFPOS3(:,IS+1,:) = 1./6 * (2.0*PSRC(:,IS,:) + 5.0*PSRC(:,IS+1,:) - PSRC(:,IS+2,:)) ! Flux IS+1
+ ZFPOS3(:,IS,:) = 1./6 * (2.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) - PSRC(:,IS+1,:)) ! Flux IS
+ ZBPOS3(:,IS+1,:) = 13./12 * ( PSRC(:,IS,:) - 2.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS,:) - 4.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 ! Smoothness indicator IS+1
+ ZBPOS3(:,IS,:) = 13./12 * ( PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS-1,:) - 4.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 ! Smoothness indicator IS
+ ZOMP3(:,IS:IS+1,:) = 3./10. / (ZEPS + ZBPOS3(:,IS:IS+1,:))**2 ! Non-normalized weight IS+1,IS
+!
+ ! ----- Negative fluxes -----
+!
+ ! First negative stencil, needs indices i, i+1, i+2
+ ZFNEG1(:,IS+1,:) = 1./6. * (11.0*PSRC(:,IS+1,:) - 7.0*PSRC(:,IS+2,:) + 2.0*PSRC(:,IS+3,:)) ! Flux IS+1
+ ZFNEG1(:,IS,:) = 1./6. * (11.0*PSRC(:,IS,:) - 7.0*PSRC(:,IS+1,:) + 2.0*PSRC(:,IS+2,:)) ! Flux IS
+ ZBNEG1(:,IS+1,:) = 13./12. * ( PSRC(:,IS+1,:) - 2.0*PSRC(:,IS+2,:) + PSRC(:,IS+3,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS+1,:) - 4.0*PSRC(:,IS+2,:) + PSRC(:,IS+3,:))**2 ! Smoothness indicator IS+1
+ ZBNEG1(:,IS,:) = 13./12. * ( PSRC(:,IS,:) - 2.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS,:) - 4.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 ! Smoothness indicator IS
+ ZOMN1(:,IS:IS+1,:) = 1./10. / (ZEPS + ZBNEG1(:,IS:IS+1,:))**2 ! Non-normalized weight IS+1,IS
+!
+ ! Second negative stencil, needs indices i-1, i, i+1
+ ZFNEG2(:,IS+1,:) = 1./6. * (2.0*PSRC(:,IS,:) + 5.0*PSRC(:,IS+1,:) - 1.0*PSRC(:,IS+2,:)) ! Flux IS+1
+ ZFNEG2(:,IS,:) = 1./6. * (2.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) - 1.0*PSRC(:,IS+1,:)) ! Flux IS
+ ZBNEG2(:,IS+1,:) = 13./12 * (PSRC(:,IS,:) - 2.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 &
+ + 1./4 * (PSRC(:,IS,:) - PSRC(:,IS+2,:))**2 ! Smoothness indicator IS+1
+ ZBNEG2(:,IS,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (PSRC(:,IS-1,:) - PSRC(:,IS+1,:))**2 ! Smoothness indicator IS
+ ZOMN2(:,IS:IS+1,:) = 3./5. / (ZEPS + ZBNEG2(:,IS:IS+1,:))**2 ! Non-normalized weight IS+1,IS
+!
+ ! ----- Total flux -----
+!
+ PR(:,IS:IS+1,:) = ( ZOMP1(:,IS:IS+1,:)/(ZOMP1(:,IS:IS+1,:)+ZOMP2(:,IS:IS+1,:)+ZOMP3(:,IS:IS+1,:)) * ZFPOS1(:,IS:IS+1,:) &
+ + ZOMP2(:,IS:IS+1,:)/(ZOMP1(:,IS:IS+1,:)+ZOMP2(:,IS:IS+1,:)+ZOMP3(:,IS:IS+1,:)) * ZFPOS2(:,IS:IS+1,:) &
+ + ZOMP3(:,IS:IS+1,:)/(ZOMP1(:,IS:IS+1,:)+ZOMP2(:,IS:IS+1,:)+ZOMP3(:,IS:IS+1,:)) * ZFPOS3(:,IS:IS+1,:)) &
+ * (0.5+SIGN(0.5,PRVCT(:,IS:IS+1,:))) &
+ + ( ZOMN1(:,IS:IS+1,:)/(ZOMN1(:,IS:IS+1,:)+ZOMN2(:,IS:IS+1,:)+ZOMN3(:,IS:IS+1,:)) * ZFNEG1(:,IS:IS+1,:) &
+ + ZOMN2(:,IS:IS+1,:)/(ZOMN1(:,IS:IS+1,:)+ZOMN2(:,IS:IS+1,:)+ZOMN3(:,IS:IS+1,:)) * ZFNEG2(:,IS:IS+1,:) &
+ + ZOMN3(:,IS:IS+1,:)/(ZOMN1(:,IS:IS+1,:)+ZOMN2(:,IS:IS+1,:)+ZOMN3(:,IS:IS+1,:)) * ZFNEG3(:,IS:IS+1,:)) &
+ * (0.5-SIGN(0.5,PRVCT(:,IS:IS+1,:)))
+!
+!
+ CASE ('OPEN','WALL','NEST')
+ !---------------------------------------------------------------------------
+ ! Open, or Wall, or Nest boundary condition => WENO order reduction
+ !---------------------------------------------------------------------------
+!
+ ! WENO scheme order 1, IS
+ PR(:,IS,:) = PSRC(:,IS-1,:) * (0.5+SIGN(0.5,PRVCT(:,IS,:))) + &
+ PSRC(:,IS,:) * (0.5-SIGN(0.5,PRVCT(:,IS,:)))
+!
+! ! WENO scheme order 3, IS+1
+ ZFPOS1(:,IS+1,:) = 0.5 * (3.0*PSRC(:,IS,:) - PSRC(:,IS-1,:)) ! First positive flux
+ ZFPOS2(:,IS+1,:) = 0.5 * ( PSRC(:,IS,:) + PSRC(:,IS+1,:)) ! Second positive flux
+ ZBPOS1(:,IS+1,:) = (PSRC(:,IS,:) - PSRC(:,IS-1,:))**2 ! First positive smoothness indicator
+ ZBPOS2(:,IS+1,:) = (PSRC(:,IS+1,:) - PSRC(:,IS,:))**2 ! Second positive smoothness indicator
+!
+ ZFNEG1(:,IS+1,:) = 0.5 * (3.0*PSRC(:,IS+1,:) - PSRC(:,IS+2,:)) ! First negative flux
+ ZFNEG2(:,IS+1,:) = 0.5 * ( PSRC(:,IS+1,:) + PSRC(:,IS,:)) ! Second negative flux
+ ZBNEG1(:,IS+1,:) = (PSRC(:,IS+1,:) - PSRC(:,IS+2,:))**2 ! First negative smoothness indicator
+ ZBNEG2(:,IS+1,:) = (PSRC(:,IS,:) - PSRC(:,IS+1,:))**2 ! Second negative smoothness indicator
+!
+ ZOMP1(:,IS+1,:) = 1./3. / (ZEPS + ZBPOS1(:,IS+1,:))**2 ! First positive non-normalized weight
+ ZOMP2(:,IS+1,:) = 2./3. / (ZEPS + ZBPOS2(:,IS+1,:))**2 ! Second positive non-normalized weight
+ ZOMN1(:,IS+1,:) = 1./3. / (ZEPS + ZBNEG1(:,IS+1,:))**2 ! First negative non-normalized weight
+ ZOMN2(:,IS+1,:) = 2./3. / (ZEPS + ZBNEG2(:,IS+1,:))**2 ! Second negative non-normalized weight
+!
+ PR(:,IS+1,:) = (ZOMP2(:,IS+1,:)/(ZOMP1(:,IS+1,:)+ZOMP2(:,IS+1,:)) * ZFPOS2(:,IS+1,:) + &
+ (ZOMP1(:,IS+1,:)/(ZOMP1(:,IS+1,:)+ZOMP2(:,IS+1,:)) * ZFPOS1(:,IS+1,:))) &
+ *(0.5+SIGN(0.5,PRVCT(:,IS+1,:))) + &
+ (ZOMN2(:,IS+1,:)/(ZOMN1(:,IS+1,:)+ZOMN2(:,IS+1,:)) * ZFNEG2(:,IS+1,:) + &
+ (ZOMN1(:,IS+1,:)/(ZOMN1(:,IS+1,:)+ZOMN2(:,IS+1,:)) * ZFNEG1(:,IS+1,:))) &
+ *(0.5-SIGN(0.5,PRVCT(:,IS+1,:))) ! Total flux
+!
+ END SELECT ! SELECT CASE (HLBCY(1)) ! Y direction LBC type on south side
+!
+ELSE
+ !-----------------------------------------------------------------------------
+ ! South border is proc border -- IS,IS-1
+ !-----------------------------------------------------------------------------
+!
+ IF (NHALO<3) THEN
+ PRINT *,'WARNING : WENO5 not parallelisable with NHALO < 3'
+ CALL ABORT
+ ELSEIF (NHALO>=3) THEN
+ !---------------------------------------------------------------------------
+ ! NHALO >3 => WENO5 for all boundary points
+ !---------------------------------------------------------------------------
+!
+ ! ----- Positive fluxes -----
+!
+ ! First positive stencil, needs indices i-3, i-2, i-1
+ ZFPOS1(:,IS+1,:) = 1./6. * (2.0*PSRC(:,IS-2,:) - 7.0*PSRC(:,IS-1,:) + 11.0*PSRC(:,IS,:)) ! Flux IS+1
+ ZFPOS1(:,IS,:) = 1./6. * (2.0*PSRC(:,IS-3,:) - 7.0*PSRC(:,IS-2,:) + 11.0*PSRC(:,IS-1,:)) ! Flux IS
+ ZBPOS1(:,IS+1,:) = 13./12. * (PSRC(:,IS-2,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IS-2,:) - 4.0*PSRC(:,IS-1,:) + 3.0*PSRC(:,IS,:))**2 ! Smoothness indicator IS+1
+ ZBPOS1(:,IS,:) = 13./12. * (PSRC(:,IS-3,:) - 2.0*PSRC(:,IS-2,:) + PSRC(:,IS-1,:))**2 &
+ + 1./4 * (PSRC(:,IS-3,:) - 4.0*PSRC(:,IS-2,:) + 3.0*PSRC(:,IS-1,:))**2 ! Smoothness indicator IS
+ ZOMP1(:,IS:IS+1,:) = 1./10. / (ZEPS + ZBPOS1(:,IS:IS+1,:))**2 ! Non-normalized weight IS+1,IS
+!
+ ! Second positive stencil, needs indices i-2, i-1, i
+ ZFPOS2(:,IS+1,:) = 1./6.* (-1.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) + 2.0*PSRC(:,IS+1,:)) ! Flux IS+1
+ ZFPOS2(:,IS,:) = 1./6.* (-1.0*PSRC(:,IS-2,:) + 5.0*PSRC(:,IS-1,:) + 2.0*PSRC(:,IS,:)) ! Flux IS
+ ZBPOS2(:,IS+1,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (PSRC(:,IS-1,:) - PSRC(:,IS+1,:))**2 ! Smoothness indicator IS+1
+ ZBPOS2(:,IS,:) = 13./12 * (PSRC(:,IS-2,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IS-2,:) - PSRC(:,IS,:))**2 ! Smoothness indicator IS
+ ZOMP2(:,IS:IS+1,:) = 3./5. / (ZEPS + ZBPOS2(:,IS:IS+1,:))**2 ! Non-normalized weight IS+1,IS
+!
+ ! Third positive stencil, needs indices i-1, i, i+1
+ ZFPOS3(:,IS+1,:) = 1./6 * (2.0*PSRC(:,IS,:) + 5.0*PSRC(:,IS+1,:) - PSRC(:,IS+2,:)) ! Flux IS+1
+ ZFPOS3(:,IS,:) = 1./6 * (2.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) - PSRC(:,IS+1,:)) ! Flux IS
+ ZBPOS3(:,IS+1,:) = 13./12 * ( PSRC(:,IS,:) - 2.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS,:) - 4.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 ! Smoothness indicator IS+1
+ ZBPOS3(:,IS,:) = 13./12 * ( PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS-1,:) - 4.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 ! Smoothness indicator IS
+ ZOMP3(:,IS:IS+1,:) = 3./10. / (ZEPS + ZBPOS3(:,IS:IS+1,:))**2 ! Non-normalized weight IS+1,IS
+!
+ ! ----- Negative fluxes -----
+!
+ ! First negative stencil, needs indices i, i+1, i+2
+ ZFNEG1(:,IS+1,:) = 1./6. * (11.0*PSRC(:,IS+1,:) - 7.0*PSRC(:,IS+2,:) + 2.0*PSRC(:,IS+3,:)) ! Flux IS+1
+ ZFNEG1(:,IS,:) = 1./6. * (11.0*PSRC(:,IS,:) - 7.0*PSRC(:,IS+1,:) + 2.0*PSRC(:,IS+2,:)) ! Flux IS
+ ZBNEG1(:,IS+1,:) = 13./12. * ( PSRC(:,IS+1,:) - 2.0*PSRC(:,IS+2,:) + PSRC(:,IS+3,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS+1,:) - 4.0*PSRC(:,IS+2,:) + PSRC(:,IS+3,:))**2 ! Smoothness indicator IS+1
+ ZBNEG1(:,IS,:) = 13./12. * ( PSRC(:,IS,:) - 2.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS,:) - 4.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 ! Smoothness indicator IS
+ ZOMN1(:,IS:IS+1,:) = 1./10. / (ZEPS + ZBNEG1(:,IS:IS+1,:))**2 ! Non-normalized weight IS+1,IS
+!
+ ! Second negative stencil, needs indices i-1, i, i+1
+ ZFNEG2(:,IS+1,:) = 1./6. * (2.0*PSRC(:,IS,:) + 5.0*PSRC(:,IS+1,:) - 1.0*PSRC(:,IS+2,:)) ! Flux IS+1
+ ZFNEG2(:,IS,:) = 1./6. * (2.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) - 1.0*PSRC(:,IS+1,:)) ! Flux IS
+ ZBNEG2(:,IS+1,:) = 13./12 * (PSRC(:,IS,:) - 2.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 &
+ + 1./4 * (PSRC(:,IS,:) - PSRC(:,IS+2,:))**2 ! Smoothness indicator IS+1
+ ZBNEG2(:,IS,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (PSRC(:,IS-1,:) - PSRC(:,IS+1,:))**2 ! Smoothness indicator IS
+ ZOMN2(:,IS:IS+1,:) = 3./5. / (ZEPS + ZBNEG2(:,IS:IS+1,:))**2 ! Non-normalized weight IS+1,IS
+!
+ ! Third negative stencil, needs indices i-2, i-1, i
+ ZFNEG3(:,IS+1,:) = 1./6 * (-1.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) + 2.0*PSRC(:,IS+1,:)) ! Flux IS+1
+ ZFNEG3(:,IS,:) = 1./6 * (-1.0*PSRC(:,IS-2,:) + 5.0*PSRC(:,IS-1,:) + 2.0*PSRC(:,IS,:)) ! Flux IS
+ ZBNEG3(:,IS+1,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (PSRC(:,IS-1,:) - 4.0*PSRC(:,IS,:) + 3.0*PSRC(:,IS+1,:))**2 ! Smoothness indicator IS+1
+ ZBNEG3(:,IS,:) = 13./12 * (PSRC(:,IS-2,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IS-2,:) - 4.0*PSRC(:,IS-1,:) + 3.0*PSRC(:,IS,:))**2 ! Smoothness indicator IS
+ ZOMN3(:,IS:IS+1,:) = 3./10. / (ZEPS + ZBNEG3(:,IS:IS+1,:))**2 ! Non-normalized weight IS+1,IS
+!
+ ! ----- Total flux -----
+!
+ PR(:,IS:IS+1,:) = ( ZOMP1(:,IS:IS+1,:)/(ZOMP1(:,IS:IS+1,:)+ZOMP2(:,IS:IS+1,:)+ZOMP3(:,IS:IS+1,:)) * ZFPOS1(:,IS:IS+1,:) &
+ + ZOMP2(:,IS:IS+1,:)/(ZOMP1(:,IS:IS+1,:)+ZOMP2(:,IS:IS+1,:)+ZOMP3(:,IS:IS+1,:)) * ZFPOS2(:,IS:IS+1,:) &
+ + ZOMP3(:,IS:IS+1,:)/(ZOMP1(:,IS:IS+1,:)+ZOMP2(:,IS:IS+1,:)+ZOMP3(:,IS:IS+1,:)) * ZFPOS3(:,IS:IS+1,:)) &
+ * (0.5+SIGN(0.5,PRVCT(:,IS:IS+1,:))) &
+ + ( ZOMN1(:,IS:IS+1,:)/(ZOMN1(:,IS:IS+1,:)+ZOMN2(:,IS:IS+1,:)+ZOMN3(:,IS:IS+1,:)) * ZFNEG1(:,IS:IS+1,:) &
+ + ZOMN2(:,IS:IS+1,:)/(ZOMN1(:,IS:IS+1,:)+ZOMN2(:,IS:IS+1,:)+ZOMN3(:,IS:IS+1,:)) * ZFNEG2(:,IS:IS+1,:) &
+ + ZOMN3(:,IS:IS+1,:)/(ZOMN1(:,IS:IS+1,:)+ZOMN2(:,IS:IS+1,:)+ZOMN3(:,IS:IS+1,:)) * ZFNEG3(:,IS:IS+1,:)) &
+ * (0.5-SIGN(0.5,PRVCT(:,IS:IS+1,:)))
!
- ZFNEG3(:,IS+1:IN,:) = 1./6 * (-1.0*PSRC(:,IS-1:IN-2,:) + &
- 5.0*PSRC(:,IS:IN-1,:) + 2.0*PSRC(:,IS+1:IN,:))
-!
-! smoothness indicators for positive wind case
-!
- ZBPOS1(:,IS+2:IN,:) = 13./12 * (PSRC(:,IS-1:IN-3,:) - 2.0*PSRC(:,IS:IN-2,:) + &
- PSRC(:,IS+1:IN-1,:))**2 + 1./4 * (PSRC(:,IS-1:IN-3,:) - 4.0*PSRC(:,IS:IN-2,:) +&
- 3.0*PSRC(:,IS+1:IN-1,:))**2
- ZBPOS1(:,IS+1,:) = 13./12 * (TPHALO2%SOUTH(:,:) - 2.0*PSRC(:,IS-1,:) + &
- PSRC(:,IS,:))**2 + &
- 1./4 * (TPHALO2%SOUTH(:,:) - 4.0*PSRC(:,IS-1,:) + 3.0*PSRC(:,IS,:))**2
- ZBPOS1(:,IN+1,:) = (PSRC(:,IN, :) - PSRC(:,IN-1,:))**2
- ZBPOS1(:,IS, :) = (PSRC(:,IS-1,:) - TPHALO2%SOUTH(:,:))**2
- ZBPOS1(:,IS-1,:) = - 999.
-!
- ZBPOS2(:,IS+1:IN,:) = 13./12 * (PSRC(:,IS-1:IN-2,:) - 2.0*PSRC(:,IS:IN-1,:) + &
- PSRC(:,IS+1:IN,:))**2 + 1./4 * (PSRC(:,IS-1:IN-2,:) - PSRC(:,IS+1:IN,:))**2
- ZBPOS2(:,IN+1,:) = (PSRC(:,IN+1,:) - PSRC(:,IN, :))**2
- ZBPOS2(:,IS-1,:) = (PSRC(:,IS-1,:) - TPHALO2%SOUTH(:,:))**2
- ZBPOS2(:,IS, :) = (PSRC(:,IS, :) - PSRC(:,IS-1,:))**2
-!
-!
- ZBPOS3(:,IS+1:IN,:) = 13./12 * (PSRC(:,IS:IN-1,:) - 2.0*PSRC(:,IS+1:IN,:) + &
- PSRC(:,IS+2:IN+1,:))**2 + 1./4 * ( 3.0*PSRC(:,IS:IN-1,:) - 4.0*PSRC(:,IS+1:IN,:) + PSRC(:,IS+2:IN+1,:))**2
-!
-! smoothness indicators for negative wind case
-!
- ZBNEG1(:,IS+1:IN-1,:) = 13./12 * (PSRC(:,IS+1:IN-1,:) - 2.0*PSRC(:,IS+2:IN,:) + &
- PSRC(:,IS+3:IN+1,:))**2 + 1./4 * ( 3.0*PSRC(:,IS+1:IN-1,:) - &
- 4.0*PSRC(:,IS+2:IN,:) + PSRC(:,IS+3:IN+1,:))**2
- ZBNEG1(:,IN, :) = 13./12 * (PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + &
- TPHALO2%NORTH(:,:))**2 + &
- 1./4 * ( 3.0*PSRC(:,IN,:) - 4.0*PSRC(:,IN+1,:) + TPHALO2%NORTH(:,:))**2
- ZBNEG1(:,IS-1,:) = (PSRC(:,IS-1,:) - PSRC(:,IS,:))**2
- ZBNEG1(:,IS, :) = (PSRC(:,IS, :) - PSRC(:,IS+1,:))**2
- ZBNEG1(:,IN+1,:) = (PSRC(:,IN+1,:) - TPHALO2%NORTH(:,:))**2
-!
-!
- ZBNEG2(:,IS+1:IN,:) = 13./12 * (PSRC(:,IS:IN-1,:) - 2.0*PSRC(:,IS+1:IN,:) + &
- PSRC(:,IS+2:IN+1,:))**2 + &
- 1./4 * (PSRC(:,IS:IN-1,:) - PSRC(:,IS+2:IN+1,:))**2
- ZBNEG2(:,IN+1,:) = (PSRC(:,IN ,:) - PSRC(:,IN+1,:))**2
- ZBNEG2(:,IS, :) = (PSRC(:,IS-1,:) - PSRC(:,IS, :))**2
- ZBNEG2(:,IS-1,:) = (TPHALO2%SOUTH(:,:) - PSRC(:,IS-1,:))**2
+ END IF ! NHALO
!
+END IF ! IF(LSOUTH_ll())
!
- ZBNEG3(:,IS+1:IN,:) = 13./12 * (PSRC(:,IS-1:IN-2,:) - 2.0*PSRC(:,IS:IN-1,:) + &
- PSRC(:,IS+1:IN,:))**2 + &
- 1./4 * ( PSRC(:,IS-1:IN-2,:) - 4.0*PSRC(:,IS:IN-1,:) + 3.0*PSRC(:,IS+1:IN,:))**2
+!-------------------------------------------------------------------------------
+!* 1.3. East border
+! ---------------------
!
-! WENO weights
+IF(LNORTH_ll() .AND. .FALSE. ) THEN
+ !-----------------------------------------------------------------------------
+ ! North border is physical -- IN,IN+1
+ !-----------------------------------------------------------------------------
+ SELECT CASE (HLBCY(2)) ! Y direction LBC type on north side
+!
+ CASE ('CYCL')
+ !---------------------------------------------------------------------------
+ ! Periodic boundary condition
+ !---------------------------------------------------------------------------
!
- ZOMP1(:,IS+1:IN,:) = ZGAMMA1 / (ZEPS + ZBPOS1(:,IS+1:IN,:))**2
- ZOMP2(:,IS+1:IN,:) = ZGAMMA2 / (ZEPS + ZBPOS2(:,IS+1:IN,:))**2
- ZOMP3(:,IS+1:IN,:) = ZGAMMA3 / (ZEPS + ZBPOS3(:,IS+1:IN,:))**2
- ZOMN1(:,IS+1:IN,:) = ZGAMMA1 / (ZEPS + ZBNEG1(:,IS+1:IN,:))**2
- ZOMN2(:,IS+1:IN,:) = ZGAMMA2 / (ZEPS + ZBNEG2(:,IS+1:IN,:))**2
- ZOMN3(:,IS+1:IN,:) = ZGAMMA3 / (ZEPS + ZBNEG3(:,IS+1:IN,:))**2
-!
- ZOMP1(:,IN+1,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,IN+1,:))**2
- ZOMP2(:,IN+1,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,IN+1,:))**2
- ZOMN1(:,IN+1,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,IN+1,:))**2
- ZOMN2(:,IN+1,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,IN+1,:))**2
- ZOMP1(:,IS, :) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,IS, :))**2
- ZOMP2(:,IS, :) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,IS, :))**2
- ZOMN1(:,IS, :) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,IS, :))**2
- ZOMN2(:,IS, :) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,IS, :))**2
- ZOMP1(:,IS-1,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,IS-1,:))**2
- ZOMP2(:,IS-1,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,IS-1,:))**2
- ZOMN1(:,IS-1,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,IS-1,:))**2
- ZOMN2(:,IS-1,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,IS-1,:))**2
-!
-! WENO fluxes (5th order)
-!
- PR(:,IS+1:IN,:) = (ZOMP2(:,IS+1:IN,:)/(ZOMP1(:,IS+1:IN,:)+ZOMP2(:,IS+1:IN,:)+&
- ZOMP3(:,IS+1:IN,:)) * ZFPOS2(:,IS+1:IN,:) &
- + ZOMP1(:,IS+1:IN,:)/(ZOMP1(:,IS+1:IN,:)+ZOMP2(:,IS+1:IN,:)+&
- ZOMP3(:,IS+1:IN,:)) * ZFPOS1(:,IS+1:IN,:) &
- + ZOMP3(:,IS+1:IN,:)/(ZOMP1(:,IS+1:IN,:)+ZOMP2(:,IS+1:IN,:)+&
- ZOMP3(:,IS+1:IN,:)) * ZFPOS3(:,IS+1:IN,:)) * &
- (0.5+SIGN(0.5,PRVCT(:,IS+1:IN,:))) &
- + (ZOMN2(:,IS+1:IN,:)/(ZOMN1(:,IS+1:IN,:)+ZOMN2(:,IS+1:IN,:)+&
- ZOMN3(:,IS+1:IN,:)) * ZFNEG2(:,IS+1:IN,:) &
- + ZOMN1(:,IS+1:IN,:)/(ZOMN1(:,IS+1:IN,:)+ZOMN2(:,IS+1:IN,:)+&
- ZOMN3(:,IS+1:IN,:)) * ZFNEG1(:,IS+1:IN,:) &
- + ZOMN3(:,IS+1:IN,:)/(ZOMN1(:,IS+1:IN,:)+ZOMN2(:,IS+1:IN,:)+&
- ZOMN3(:,IS+1:IN,:)) * ZFNEG3(:,IS+1:IN,:)) * &
- (0.5-SIGN(0.5,PRVCT(:,IS+1:IN,:)))
-!
-! WENO fluxes (3rd order)
-!
- PR(:,IS-1,:) = (ZOMP2(:,IS-1,:)/(ZOMP1(:,IS-1,:)+ZOMP2(:,IS-1,:)) * &
- ZFPOS2(:,IS-1,:) &
- + ZOMP1(:,IS-1,:)/(ZOMP1(:,IS-1,:)+ZOMP2(:,IS-1,:)) * &
- ZFPOS1(:,IS-1,:)) * (0.5+SIGN(0.5,PRVCT(:,IS-1,:))) &
- + (ZOMN2(:,IS-1,:)/(ZOMN1(:,IS-1,:)+ZOMN2(:,IS-1,:)) * &
- ZFNEG2(:,IS-1,:) &
- + ZOMN1(:,IS-1,:)/(ZOMN1(:,IS-1,:)+ZOMN2(:,IS-1,:)) * &
- ZFNEG1(:,IS-1,:)) * (0.5-SIGN(0.5,PRVCT(:,IS-1,:)))
-!
- PR(:,IS, :) = (ZOMP2(:,IS, :)/(ZOMP1(:,IS, :)+ZOMP2(:,IS, :)) * &
- ZFPOS2(:,IS, :) &
- + ZOMP1(:,IS, :)/(ZOMP1(:,IS, :)+ZOMP2(:,IS, :)) * &
- ZFPOS1(:,IS, :)) * (0.5+SIGN(0.5,PRVCT(:,IS, :))) &
- + (ZOMN2(:,IS, :)/(ZOMN1(:,IS, :)+ZOMN2(:,IS, :)) * &
- ZFNEG2(:,IS, :) &
- + ZOMN1(:,IS, :)/(ZOMN1(:,IS, :)+ZOMN2(:,IS, :)) * &
- ZFNEG1(:,IS, :)) * (0.5-SIGN(0.5,PRVCT(:,IS, :)))
-!
- PR(:,IN+1,:) = (ZOMP2(:,IN+1,:)/(ZOMP1(:,IN+1,:)+ZOMP2(:,IN+1,:)) * &
- ZFPOS2(:,IN+1,:) &
- + ZOMP1(:,IN+1,:)/(ZOMP1(:,IN+1,:)+ZOMP2(:,IN+1,:)) * &
- ZFPOS1(:,IN+1,:)) * (0.5+SIGN(0.5,PRVCT(:,IN+1,:))) &
- + (ZOMN2(:,IN+1,:)/(ZOMN1(:,IN+1,:)+ZOMN2(:,IN+1,:)) * &
- ZFNEG2(:,IN+1,:) &
- + ZOMN1(:,IN+1,:)/(ZOMN1(:,IN+1,:)+ZOMN2(:,IN+1,:)) * &
- ZFNEG1(:,IN+1,:)) * (0.5-SIGN(0.5,PRVCT(:,IN+1,:)))
-!
-!
-! OPEN, WALL, NEST CASE IN THE Y DIRECTION
-!
-CASE ('OPEN','WALL','NEST')
-!
- IS=IJB
- IN=IJE
-!
- IF(LSOUTH_ll()) THEN
- PR(:,IS,:) = PSRC(:,IS-1,:) * (0.5+SIGN(0.5,PRVCT(:,IS,:))) + &
- PSRC(:,IS,:) * (0.5-SIGN(0.5,PRVCT(:,IS,:)))
-!
- ZFPOS1(:,IS+1,:) = 0.5 * (3.0*PSRC(:,IS,:) - PSRC(:,IS-1,:))
- ZFPOS2(:,IS+1,:) = 0.5 * (PSRC(:,IS, :) + PSRC(:,IS+1,:))
- ZBPOS1(:,IS+1,:) = (PSRC(:,IS, :) - PSRC(:,IS-1,:))**2
- ZBPOS2(:,IS+1,:) = (PSRC(:,IS+1,:) - PSRC(:,IS, :))**2
-!
- ZFNEG1(:,IS+1,:) = 0.5 * (3.0*PSRC(:,IS+1,:) - PSRC(:,IS+2,:))
- ZFNEG2(:,IS+1,:) = 0.5 * (PSRC(:,IS+1, :) + PSRC(:,IS,:))
- ZBNEG1(:,IS+1,:) = (PSRC(:,IS+1,:) - PSRC(:,IS+2,:))**2
- ZBNEG2(:,IS+1,:) = (PSRC(:,IS, :) - PSRC(:,IS+1,:))**2
-!
- ZOMP1(:,IS+1,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,IS+1,:))**2
- ZOMP2(:,IS+1,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,IS+1,:))**2
- ZOMN1(:,IS+1,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,IS+1,:))**2
- ZOMN2(:,IS+1,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,IS+1,:))**2
-!
- PR(:,IS+1, :) = (ZOMP2(:,IS+1,:)/(ZOMP1(:,IS+1,:)+ZOMP2(:,IS+1,:)) * &
- ZFPOS2(:,IS+1,:) &
- + ZOMP1(:,IS+1,:)/(ZOMP1(:,IS+1,:)+ZOMP2(:,IS+1,:)) * &
- ZFPOS1(:,IS+1,:)) * (0.5+SIGN(0.5,PRVCT(:,IS+1,:))) &
- + (ZOMN2(:,IS+1,:)/(ZOMN1(:,IS+1,:)+ZOMN2(:,IS+1,:)) * &
- ZFNEG2(:,IS+1,:) &
- + ZOMN1(:,IS+1,:)/(ZOMN1(:,IS+1,:)+ZOMN2(:,IS+1,:)) * &
- ZFNEG1(:,IS+1,:)) * (0.5-SIGN(0.5,PRVCT(:,IS+1,:)))
-!
- ELSEIF(NHALO == 1) THEN
- ZFPOS1(:,IS,:) = 0.5 * (3.0*PSRC(:,IS-1, :) - TPHALO2%SOUTH(:,:))
- ZFPOS2(:,IS,:) = 0.5 * (PSRC(:,IS-1, :) + PSRC(:,IS,:))
- ZBPOS1(:,IS,:) = (PSRC(:,IS-1,:) - TPHALO2%SOUTH(:,:))**2
- ZBPOS2(:,IS,:) = (PSRC(:,IS, :) - PSRC(:,IS-1,:))**2
-!
- ZFNEG1(:,IS,:) = 0.5 * (3.0*PSRC(:,IS, :) - PSRC(:,IS+1,:))
- ZFNEG2(:,IS,:) = 0.5 * (PSRC(:,IS, :) + PSRC(:,IS-1,:))
- ZBNEG1(:,IS,:) = (PSRC(:,IS, :) - PSRC(:,IS+1,:))**2
- ZBNEG2(:,IS,:) = (PSRC(:,IS-1,:) - PSRC(:,IS, :))**2
-!
- ZOMP1(:,IS,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,IS,:))**2
- ZOMP2(:,IS,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,IS,:))**2
- ZOMN1(:,IS,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,IS,:))**2
- ZOMN2(:,IS,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,IS,:))**2
-!
- PR(:,IS,:) = (ZOMP2(:,IS,:)/(ZOMP1(:,IS,:)+ZOMP2(:,IS,:)) * ZFPOS2(:,IS,:) &
- + ZOMP1(:,IS,:)/(ZOMP1(:,IS,:)+ZOMP2(:,IS,:)) * ZFPOS1(:,IS,:)) *&
- (0.5+SIGN(0.5,PRVCT(:,IS,:))) &
- + (ZOMN2(:,IS,:)/(ZOMN1(:,IS,:)+ZOMN2(:,IS,:)) * ZFNEG2(:,IS,:) &
- + ZOMN1(:,IS,:)/(ZOMN1(:,IS,:)+ZOMN2(:,IS,:)) * ZFNEG1(:,IS,:)) *&
- (0.5-SIGN(0.5,PRVCT(:,IS,:)))
-!
- ZFPOS1(:,IS+1,:) = 1./6 * (2.0*TPHALO2%SOUTH(:,:) - 7.0*PSRC(:,IS-1,:) + &
- 11.0*PSRC(:,IS,:))
- ZFPOS2(:,IS+1,:) = 1./6 * (-1.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) + &
- 2.0*PSRC(:,IS+1,:))
- ZFPOS3(:,IS+1,:) = 1./6 * (2.0*PSRC(:,IS,:) + 5.0*PSRC(:,IS+1,:) - &
- 1.0*PSRC(:,IS+2,:))
-!
- ZBPOS1(:,IS+1,:) = 13./12 * (TPHALO2%SOUTH(:,:) - 2.0*PSRC(:,IS-1,:) + &
- PSRC(:,IS,:))**2 + &
- 1./4 * (TPHALO2%SOUTH(:,:) - 4.0*PSRC(:,IS-1,:) + 3.0*PSRC(:,IS,:))**2
- ZBPOS2(:,IS+1,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + &
- PSRC(:,IS+1,:))**2 + &
- 1./4 * (PSRC(:,IS-1,:) - PSRC(:,IS+1,:))**2
- ZBPOS3(:,IS+1,:) = 13./12 * (PSRC(:,IS,:) - 2.0*PSRC(:,IS+1,:) + &
- PSRC(:,IS+2,:))**2 + &
- 1./4 * ( 3.0*PSRC(:,IS,:) - 4.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2
-!
- ZFNEG1(:,IS+1,:) = 1./6 * (11.0*PSRC(:,IS+1,:) - 7.0*PSRC(:,IS+2,:) + &
- 2.0*PSRC(:,IS+3,:))
- ZFNEG2(:,IS+1,:) = 1./6 * (2.0*PSRC(:,IS,:) + 5.0*PSRC(:,IS+1,:) - &
- 1.0*PSRC(:,IS+2,:))
- ZFNEG3(:,IS+1,:) = 1./6 * (-1.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) + &
- 2.0*PSRC(:,IS+1,:))
-!
- ZBNEG1(:,IS+1,:) = 13./12 * (PSRC(:,IS+1,:) - 2.0*PSRC(:,IS+2,:) + &
- PSRC(:,IS+3,:))**2 + &
- 1./4 * ( 3.0*PSRC(:,IS+1,:) - 4.0*PSRC(:,IS+2,:) + PSRC(:,IS+3,:))**2
- ZBNEG2(:,IS+1,:) = 13./12 * (PSRC(:,IS,:) - 2.0*PSRC(:,IS+1,:) + &
- PSRC(:,IS+2,:))**2 + &
- 1./4 * (PSRC(:,IS,:) - PSRC(:,IS+2,:))**2
- ZBNEG3(:,IS+1,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + &
- PSRC(:,IS+1,:))**2 + &
- 1./4 * ( PSRC(:,IS-1,:) - 4.0*PSRC(:,IS,:) + 3.0*PSRC(:,IS+1,:))**2
-!
- ZOMP1(:,IS+1,:) = ZGAMMA1 / (ZEPS + ZBPOS1(:,IS+1,:))**2
- ZOMP2(:,IS+1,:) = ZGAMMA2 / (ZEPS + ZBPOS2(:,IS+1,:))**2
- ZOMP3(:,IS+1,:) = ZGAMMA3 / (ZEPS + ZBPOS3(:,IS+1,:))**2
- ZOMN1(:,IS+1,:) = ZGAMMA1 / (ZEPS + ZBNEG1(:,IS+1,:))**2
- ZOMN2(:,IS+1,:) = ZGAMMA2 / (ZEPS + ZBNEG2(:,IS+1,:))**2
- ZOMN3(:,IS+1,:) = ZGAMMA3 / (ZEPS + ZBNEG3(:,IS+1,:))**2
-!
- PR(:,IS+1,:) = (ZOMP2(:,IS+1,:)/(ZOMP1(:,IS+1,:)+ZOMP2(:,IS+1,:)+ &
- ZOMP3(:,IS+1,:)) * ZFPOS2(:,IS+1,:) &
- + ZOMP1(:,IS+1,:)/(ZOMP1(:,IS+1,:)+ZOMP2(:,IS+1,:)+ &
- ZOMP3(:,IS+1,:)) * ZFPOS1(:,IS+1,:) &
- + ZOMP3(:,IS+1,:)/(ZOMP1(:,IS+1,:)+ZOMP2(:,IS+1,:)+ &
- ZOMP3(:,IS+1,:)) * ZFPOS3(:,IS+1,:)) *&
- (0.5+SIGN(0.5,PRVCT(:,IS+1,:))) &
- + (ZOMN2(:,IS+1,:)/(ZOMN1(:,IS+1,:)+ZOMN2(:,IS+1,:)+ &
- ZOMN3(:,IS+1,:)) * ZFNEG2(:,IS+1,:) &
- + ZOMN1(:,IS+1,:)/(ZOMN1(:,IS+1,:)+ZOMN2(:,IS+1,:)+ &
- ZOMN3(:,IS+1,:)) * ZFNEG1(:,IS+1,:) &
- + ZOMN3(:,IS+1,:)/(ZOMN1(:,IS+1,:)+ZOMN2(:,IS+1,:)+ &
- ZOMN3(:,IS+1,:)) * ZFNEG3(:,IS+1,:)) *&
- (0.5-SIGN(0.5,PRVCT(:,IS+1,:)))
-!
- ENDIF
-!
- IF(LNORTH_ll()) THEN
- PR(:,IN+1,:) = PSRC(:,IN,:) * (0.5+SIGN(0.5,PRVCT(:,IN+1,:))) + &
+ IF (LSOUTH_ll() .AND. .FALSE. ) THEN ! South border is physical
+!
+ ! Third positive stencil, needs indices i, i+1, i+2
+ ZFPOS3(:,IN,:) = 1./6 * (2.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) - PSRC(:,IN+1,:)) ! Flux IN
+ ZFPOS3(:,IN+1,:) = 1./6 * (2.0*PSRC(:,IN,:) + 5.0*PSRC(:,IN+1,:) - PSRC(:,IS,:)) ! Flux IN+1
+ ZBPOS3(:,IN,:) = 13./12 * ( PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN-1,:) - 4.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 ! Smoothness indicator IN
+ ZBPOS3(:,IN+1,:) = 13./12 * ( PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN,:) - 4.0*PSRC(:,IN+1,:) + PSRC(:,IS,:))**2 ! Smoothness indicator IN+1
+ ZOMP3(:,IN:IN+1,:) = 3./10. / (ZEPS + ZBPOS3(:,IN:IN+1,:))**2 ! Non-normalized weight IN,IN+1
+!
+ ! First negative stencil, needs indices i, i+1, i+2
+ ZFNEG1(:,IN,:) = 1./6. * (11.0*PSRC(:,IN,:) - 7.0*PSRC(:,IN+1,:) + 2.0*PSRC(:,IS,:)) ! Flux IN
+ ZFNEG1(:,IN+1,:) = 1./6. * (11.0*PSRC(:,IN+1,:) - 7.0*PSRC(:,IS,:) + 2.0*PSRC(:,IS+1,:)) ! Flux IN+1
+ ZBNEG1(:,IN,:) = 13./12. * ( PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN,:) - 4.0*PSRC(:,IN+1,:) + PSRC(:,IS,:))**2 ! Smoothness indicator IN
+ ZBNEG1(:,IN+1,:) = 13./12. * ( PSRC(:,IN+1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN+1,:) - 4.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 ! Smoothness indicator IN+1
+ ZOMN1(:,IN:IN+1,:) = 1./10. / (ZEPS + ZBNEG1(:,IN:IN+1,:))**2 ! Non-normalized weight IN,IN+1
+!
+ ! Second negative stencil, needs indices i-1, i, i+1
+ ZFNEG2(:,IN,:) = 1./6. * (2.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) - 1.0*PSRC(:,IN+1,:)) ! Flux IN
+ ZFNEG2(:,IN+1,:) = 1./6. * (2.0*PSRC(:,IN,:) + 5.0*PSRC(:,IN+1,:) - 1.0*PSRC(:,IS,:)) ! Flux IN+1
+ ZBNEG2(:,IN,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (PSRC(:,IN-1,:) - PSRC(:,IN+1,:))**2 ! Smoothness indicator IN
+ ZBNEG2(:,IN+1,:) = 13./12 * (PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IN,:) - PSRC(:,IS,:))**2 ! Smoothness indicator IN+1
+ ZOMN2(:,IN:IN+1,:) = 3./5. / (ZEPS + ZBNEG2(:,IN:IN+1,:))**2 ! Non-normalized weight IN,IN+1
+!
+ ELSEIF(IN<=SIZE(PSRC,2)-3) THEN ! South boundary is proc border, with minimum 3 HALO points on north side
+!
+ ! Third positive stencil, needs indices i, i+1, i+2
+ ZFPOS3(:,IN,:) = 1./6 * (2.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) - PSRC(:,IN+1,:)) ! Flux IN
+ ZFPOS3(:,IN+1,:) = 1./6 * (2.0*PSRC(:,IN,:) + 5.0*PSRC(:,IN+1,:) - PSRC(:,IN+2,:)) ! Flux IN+1
+ ZBPOS3(:,IN,:) = 13./12 * ( PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN-1,:) - 4.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 ! Smoothness indicator IN
+ ZBPOS3(:,IN+1,:) = 13./12 * ( PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN,:) - 4.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 ! Smoothness indicator IN+1
+ ZOMP3(:,IN:IN+1,:) = 3./10. / (ZEPS + ZBPOS3(:,IN:IN+1,:))**2 ! Non-normalized weight IN,IN+1
+!
+ ! First negative stencil, needs indices i, i+1, i+2
+ ZFNEG1(:,IN,:) = 1./6. * (11.0*PSRC(:,IN,:) - 7.0*PSRC(:,IN+1,:) + 2.0*PSRC(:,IN+2,:)) ! Flux IN
+ ZFNEG1(:,IN+1,:) = 1./6. * (11.0*PSRC(:,IN+1,:) - 7.0*PSRC(:,IN+2,:) + 2.0*PSRC(:,IN+3,:)) ! Flux IN+1
+ ZBNEG1(:,IN,:) = 13./12. * ( PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN,:) - 4.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 ! Smoothness indicator IN
+ ZBNEG1(:,IN+1,:) = 13./12. * ( PSRC(:,IN+1,:) - 2.0*PSRC(:,IN+2,:) + PSRC(:,IN+3,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN+1,:) - 4.0*PSRC(:,IN+2,:) + PSRC(:,IN+3,:))**2 ! Smoothness indicator IN+1
+ ZOMN1(:,IN:IN+1,:) = 1./10. / (ZEPS + ZBNEG1(:,IN:IN+1,:))**2 ! Non-normalized weight IN,IN+1
+!
+ ! Second negative stencil, needs indices i-1, i, i+1
+ ZFNEG2(:,IN,:) = 1./6. * (2.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) - 1.0*PSRC(:,IN+1,:)) ! Flux IN
+ ZFNEG2(:,IN+1,:) = 1./6. * (2.0*PSRC(:,IN,:) + 5.0*PSRC(:,IN+1,:) - 1.0*PSRC(:,IN+2,:)) ! Flux IN+1
+ ZBNEG2(:,IN,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (PSRC(:,IN-1,:) - PSRC(:,IN+1,:))**2 ! Smoothness indicator IN
+ ZBNEG2(:,IN+1,:) = 13./12 * (PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 &
+ + 1./4 * (PSRC(:,IN,:) - PSRC(:,IN+2,:))**2 ! Smoothness indicator IN+1
+ ZOMN2(:,IN:IN+1,:) = 3./5. / (ZEPS + ZBNEG2(:,IN:IN+1,:))**2 ! Non-normalized weight IN,IN+1
+!
+ ELSE ! South boundary is proc border, with NHALO < 3 on south side
+ PRINT *,'WARNING : WENO5 fluxes calculation needs NHALO >= 3 on south side'
+ CALL ABORT
+ ENDIF
+!
+ ! First positive stencil, needs indices i-3, i-2, i-1
+ ZFPOS1(:,IN,:) = 1./6. * (2.0*PSRC(:,IN-3,:) - 7.0*PSRC(:,IN-2,:) + 11.0*PSRC(:,IN-1,:)) ! Flux IN
+ ZFPOS1(:,IN+1,:) = 1./6. * (2.0*PSRC(:,IN-2,:) - 7.0*PSRC(:,IN-1,:) + 11.0*PSRC(:,IN,:)) ! Flux IN+1
+ ZBPOS1(:,IN,:) = 13./12. * (PSRC(:,IN-3,:) - 2.0*PSRC(:,IN-2,:) + PSRC(:,IN-1,:))**2 &
+ + 1./4 * (PSRC(:,IN-3,:) - 4.0*PSRC(:,IN-2,:) + 3.0*PSRC(:,IN-1,:))**2 ! Smoothness indicator IN
+ ZBPOS1(:,IN+1,:) = 13./12. * (PSRC(:,IN-2,:) - 2.0*PSRC(:,IN-1,:) + PSRC(:,IN,:))**2 &
+ + 1./4 * (PSRC(:,IN-2,:) - 4.0*PSRC(:,IN-1,:) + 3.0*PSRC(:,IN,:))**2 ! Smoothness indicator IN+1
+ ZOMP1(:,IN:IN+1,:) = 1./10. / (ZEPS + ZBPOS1(:,IN:IN+1,:))**2 ! Non-normalized weight IN,IN+1
+!
+ ! Second positive stencil, needs indices i-2, i-1, i
+ ZFPOS2(:,IN,:) = 1./6. * (-1.0*PSRC(:,IN-2,:) + 5.0*PSRC(:,IN-1,:) + 2.0*PSRC(:,IN,:)) ! Flux IN
+ ZFPOS2(:,IN+1,:) = 1./6. * (-1.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) + 2.0*PSRC(:,IN+1,:)) ! Flux IN+1
+ ZBPOS2(:,IN,:) = 13./12 * (PSRC(:,IN-2,:) - 2.0*PSRC(:,IN-1,:) + PSRC(:,IN,:))**2 &
+ + 1./4 * (PSRC(:,IN-2,:) - PSRC(:,IN,:))**2 ! Smoothness indicator IN
+ ZBPOS2(:,IN+1,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (PSRC(:,IN-1,:) - PSRC(:,IN+1,:))**2 ! Smoothness indicator IN+1
+ ZOMP2(:,IN:IN+1,:) = 3./5. / (ZEPS + ZBPOS2(:,IN:IN+1,:))**2 ! Non-normalized weight IN,IN+1
+!
+ ! Third negative stencil, needs indices i-2, i-1, i
+ ZFNEG3(:,IN,:) = 1./6 * (-1.0*PSRC(:,IN-2,:) + 5.0*PSRC(:,IN-1,:) + 2.0*PSRC(:,IN,:)) ! Flux IN
+ ZFNEG3(:,IN+1,:) = 1./6 * (-1.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) + 2.0*PSRC(:,IN+1,:)) ! Flux IN+1
+ ZBNEG3(:,IN,:) = 13./12 * (PSRC(:,IN-2,:) - 2.0*PSRC(:,IN-1,:) + PSRC(:,IN,:))**2 &
+ + 1./4 * (PSRC(:,IN-2,:) - 4.0*PSRC(:,IN-1,:) + 3.0*PSRC(:,IN,:))**2 ! Smoothness indicator IN
+ ZBNEG3(:,IN+1,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (PSRC(:,IN-1,:) - 4.0*PSRC(:,IN,:) + 3.0*PSRC(:,IN+1,:))**2 ! Smoothness indicator IN+1
+ ZOMN3(:,IN:IN+1,:) = 3./10. / (ZEPS + ZBNEG3(:,IN:IN+1,:))**2 ! Non-normalized weight IN,IN+1
+!
+ ! ----- Total flux -----
+!
+ PR(:,IN:IN+1,:) = ( ZOMP1(:,IN:IN+1,:)/(ZOMP1(:,IN:IN+1,:)+ZOMP2(:,IN:IN+1,:)+ZOMP3(:,IN:IN+1,:)) * ZFPOS1(:,IN:IN+1,:) &
+ + ZOMP2(:,IN:IN+1,:)/(ZOMP1(:,IN:IN+1,:)+ZOMP2(:,IN:IN+1,:)+ZOMP3(:,IN:IN+1,:)) * ZFPOS2(:,IN:IN+1,:) &
+ + ZOMP3(:,IN:IN+1,:)/(ZOMP1(:,IN:IN+1,:)+ZOMP2(:,IN:IN+1,:)+ZOMP3(:,IN:IN+1,:)) * ZFPOS3(:,IN:IN+1,:)) &
+ * (0.5+SIGN(0.5,PRVCT(:,IN:IN+1,:))) &
+ + ( ZOMN1(:,IN:IN+1,:)/(ZOMN1(:,IN:IN+1,:)+ZOMN2(:,IN:IN+1,:)+ZOMN3(:,IN:IN+1,:)) * ZFNEG1(:,IN:IN+1,:) &
+ + ZOMN2(:,IN:IN+1,:)/(ZOMN1(:,IN:IN+1,:)+ZOMN2(:,IN:IN+1,:)+ZOMN3(:,IN:IN+1,:)) * ZFNEG2(:,IN:IN+1,:) &
+ + ZOMN3(:,IN:IN+1,:)/(ZOMN1(:,IN:IN+1,:)+ZOMN2(:,IN:IN+1,:)+ZOMN3(:,IN:IN+1,:)) * ZFNEG3(:,IN:IN+1,:)) &
+ * (0.5-SIGN(0.5,PRVCT(:,IN:IN+1,:)))
+!
+!
+ CASE ('OPEN','WALL','NEST')
+ !---------------------------------------------------------------------------
+ ! Open, or Wall, or Nest boundary condition => WENO order reduction
+ !---------------------------------------------------------------------------
+!
+ ! WENO scheme order 1, IN+1
+ PR(:,IN+1,:) = PSRC(:,IN,:) * (0.5+SIGN(0.5,PRVCT(:,IN+1,:))) + &
PSRC(:,IN+1,:) * (0.5-SIGN(0.5,PRVCT(:,IN+1,:)))
!
- ZFPOS1(:,IN,:) = 0.5 * (3.0*PSRC(:,IN-1,:) - PSRC(:,IN-2,:))
- ZFPOS2(:,IN,:) = 0.5 * (PSRC(:,IN-1, :) + PSRC(:,IN, :))
- ZBPOS1(:,IN,:) = (PSRC(:,IN-1,:) - PSRC(:,IN-2,:))**2
- ZBPOS2(:,IN,:) = (PSRC(:,IN, :) - PSRC(:,IN-1,:))**2
-!
- ZFNEG1(:,IN,:) = 0.5 * (3.0*PSRC(:,IN,:) - PSRC(:,IN+1,:))
- ZFNEG2(:,IN,:) = 0.5 * (PSRC(:,IN, :) + PSRC(:,IN-1,:))
- ZBNEG1(:,IN,:) = (PSRC(:,IN, :) - PSRC(:,IN+1,:))**2
- ZBNEG2(:,IN,:) = (PSRC(:,IN-1,:) - PSRC(:,IN, :))**2
-!
- ZOMP1(:,IN,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,IN,:))**2
- ZOMP2(:,IN,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,IN,:))**2
- ZOMN1(:,IN,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,IN,:))**2
- ZOMN2(:,IN,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,IN,:))**2
-!
- PR(:,IN,:) = (ZOMP2(:,IN,:)/(ZOMP1(:,IN,:)+ZOMP2(:,IN,:)) * ZFPOS2(:,IN,:) &
- + ZOMP1(:,IN,:)/(ZOMP1(:,IN,:)+ZOMP2(:,IN,:)) * ZFPOS1(:,IN,:)) *&
- (0.5+SIGN(0.5,PRVCT(:,IN,:))) &
- + (ZOMN2(:,IN,:)/(ZOMN1(:,IN,:)+ZOMN2(:,IN,:)) * ZFNEG2(:,IN,:) &
- + ZOMN1(:,IN,:)/(ZOMN1(:,IN,:)+ZOMN2(:,IN,:)) * ZFNEG1(:,IN,:)) *&
- (0.5-SIGN(0.5,PRVCT(:,IN,:)))
+! ! WENO scheme order 3, IN
+ ZFPOS1(:,IN,:) = 0.5 * (3.0*PSRC(:,IN-1,:) - PSRC(:,IN-2,:)) ! First positive flux
+ ZFPOS2(:,IN,:) = 0.5 * ( PSRC(:,IN-1,:) + PSRC(:,IN,:)) ! Second positive flux
+ ZBPOS1(:,IN,:) = (PSRC(:,IN-1,:) - PSRC(:,IN-2,:))**2 ! First positive smoothness indicator
+ ZBPOS2(:,IN,:) = (PSRC(:,IN,:) - PSRC(:,IN-1,:))**2 ! Second positive smoothness indicator
+!
+ ZFNEG1(:,IN,:) = 0.5 * (3.0*PSRC(:,IN,:) - PSRC(:,IN+1,:)) ! First negative flux
+ ZFNEG2(:,IN,:) = 0.5 * ( PSRC(:,IN,:) + PSRC(:,IN-1,:)) ! Second negative flux
+ ZBNEG1(:,IN,:) = (PSRC(:,IN,:) - PSRC(:,IN+1,:))**2 ! First negative smoothness indicator
+ ZBNEG2(:,IN,:) = (PSRC(:,IN-1,:) - PSRC(:,IN,:))**2 ! Second negative smoothness indicator
+!
+ ZOMP1(:,IN,:) = 1./3. / (ZEPS + ZBPOS1(:,IN,:))**2 ! First positive non-normalized weight
+ ZOMP2(:,IN,:) = 2./3. / (ZEPS + ZBPOS2(:,IN,:))**2 ! Second positive non-normalized weight
+ ZOMN1(:,IN,:) = 1./3. / (ZEPS + ZBNEG1(:,IN,:))**2 ! First negative non-normalized weight
+ ZOMN2(:,IN,:) = 2./3. / (ZEPS + ZBNEG2(:,IN,:))**2 ! Second negative non-normalized weight
+!
+ PR(:,IN,:) = (ZOMP2(:,IN,:)/(ZOMP1(:,IN,:)+ZOMP2(:,IN,:))*ZFPOS2(:,IN,:) + &
+ (ZOMP1(:,IN,:)/(ZOMP1(:,IN,:)+ZOMP2(:,IN,:))*ZFPOS1(:,IN,:))) &
+ *(0.5+SIGN(0.5,PRVCT(:,IN,:))) + &
+ (ZOMN2(:,IN,:)/(ZOMN1(:,IN,:)+ZOMN2(:,IN,:))*ZFNEG2(:,IN,:) + &
+ (ZOMN1(:,IN,:)/(ZOMN1(:,IN,:)+ZOMN2(:,IN,:))*ZFNEG1(:,IN,:))) &
+ *(0.5-SIGN(0.5,PRVCT(:,IN,:))) ! Total flux
+!
+ END SELECT ! SELECT CASE (HLBCX(2)) ! X direction LBC type on right side
+!
+ELSE
+ !-----------------------------------------------------------------------------
+ ! North border is proc border -- IN,IN+1
+ !-----------------------------------------------------------------------------
+!
+ IF (NHALO<3) THEN
+ PRINT *,'WARNING : WENO5 not parallelisable with NHALO < 3'
+ CALL ABORT
+ ELSEIF (NHALO>=3) THEN
+ !---------------------------------------------------------------------------
+ ! NHALO >= 3 => WENO5 for all boundary points
+ !---------------------------------------------------------------------------
+!
+ ! ----- Positive fluxes -----
+!
+ ! First positive stencil, needs indices i-3, i-2, i-1
+ ZFPOS1(:,IN,:) = 1./6. * (2.0*PSRC(:,IN-3,:) - 7.0*PSRC(:,IN-2,:) + 11.0*PSRC(:,IN-1,:)) ! Flux IN
+ ZFPOS1(:,IN+1,:) = 1./6. * (2.0*PSRC(:,IN-2,:) - 7.0*PSRC(:,IN-1,:) + 11.0*PSRC(:,IN,:)) ! Flux IN+1
+ ZBPOS1(:,IN,:) = 13./12. * (PSRC(:,IN-3,:) - 2.0*PSRC(:,IN-2,:) + PSRC(:,IN-1,:))**2 &
+ + 1./4 * (PSRC(:,IN-3,:) - 4.0*PSRC(:,IN-2,:) + 3.0*PSRC(:,IN-1,:))**2 ! Smoothness indicator IN
+ ZBPOS1(:,IN+1,:) = 13./12. * (PSRC(:,IN-2,:) - 2.0*PSRC(:,IN-1,:) + PSRC(:,IN,:))**2 &
+ + 1./4 * (PSRC(:,IN-2,:) - 4.0*PSRC(:,IN-1,:) + 3.0*PSRC(:,IN,:))**2 ! Smoothness indicator IN+1
+ ZOMP1(:,IN:IN+1,:) = 1./10. / (ZEPS + ZBPOS1(:,IN:IN+1,:))**2 ! Non-normalized weight IN,IN+1
+!
+ ! Second positive stencil, needs indices i-2, i-1, i
+ ZFPOS2(:,IN,:) = 1./6. * (-1.0*PSRC(:,IN-2,:) + 5.0*PSRC(:,IN-1,:) + 2.0*PSRC(:,IN,:)) ! Flux IN
+ ZFPOS2(:,IN+1,:) = 1./6. * (-1.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) + 2.0*PSRC(:,IN+1,:)) ! Flux IN+1
+ ZBPOS2(:,IN,:) = 13./12 * (PSRC(:,IN-2,:) - 2.0*PSRC(:,IN-1,:) + PSRC(:,IN,:))**2 &
+ + 1./4 * (PSRC(:,IN-2,:) - PSRC(:,IN,:))**2 ! Smoothness indicator IN
+ ZBPOS2(:,IN+1,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (PSRC(:,IN-1,:) - PSRC(:,IN+1,:))**2 ! Smoothness indicator IN+1
+ ZOMP2(:,IN:IN+1,:) = 3./5. / (ZEPS + ZBPOS2(:,IN:IN+1,:))**2 ! Non-normalized weight IN,IN+1
+!
+ ! Third positive stencil, needs indices i, i+1, i+2
+ ZFPOS3(:,IN,:) = 1./6 * (2.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) - PSRC(:,IN+1,:)) ! Flux IN
+ ZFPOS3(:,IN+1,:) = 1./6 * (2.0*PSRC(:,IN,:) + 5.0*PSRC(:,IN+1,:) - PSRC(:,IN+2,:)) ! Flux IN+1
+ ZBPOS3(:,IN,:) = 13./12 * ( PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN-1,:) - 4.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 ! Smoothness indicator IN
+ ZBPOS3(:,IN+1,:) = 13./12 * ( PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN,:) - 4.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 ! Smoothness indicator IN+1
+ ZOMP3(:,IN:IN+1,:) = 3./10. / (ZEPS + ZBPOS3(:,IN:IN+1,:))**2 ! Non-normalized weight IN,IN+1
+!
+ ! ----- Negative fluxes -----
+!
+ ! First negative stencil, needs indices i, i+1, i+2
+ ZFNEG1(:,IN,:) = 1./6. * (11.0*PSRC(:,IN,:) - 7.0*PSRC(:,IN+1,:) + 2.0*PSRC(:,IN+2,:)) ! Flux IN
+ ZFNEG1(:,IN+1,:) = 1./6. * (11.0*PSRC(:,IN+1,:) - 7.0*PSRC(:,IN+2,:) + 2.0*PSRC(:,IN+3,:)) ! Flux IN+1
+ ZBNEG1(:,IN,:) = 13./12. * ( PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN,:) - 4.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 ! Smoothness indicator IN
+ ZBNEG1(:,IN+1,:) = 13./12. * ( PSRC(:,IN+1,:) - 2.0*PSRC(:,IN+2,:) + PSRC(:,IN+3,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN+1,:) - 4.0*PSRC(:,IN+2,:) + PSRC(:,IN+3,:))**2 ! Smoothness indicator IN+1
+ ZOMN1(:,IN:IN+1,:) = 1./10. / (ZEPS + ZBNEG1(:,IN:IN+1,:))**2 ! Non-normalized weight IN,IN+1
+!
+ ! Second negative stencil, needs indices i-1, i, i+1
+ ZFNEG2(:,IN,:) = 1./6. * (2.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) - 1.0*PSRC(:,IN+1,:)) ! Flux IN
+ ZFNEG2(:,IN+1,:) = 1./6. * (2.0*PSRC(:,IN,:) + 5.0*PSRC(:,IN+1,:) - 1.0*PSRC(:,IN+2,:)) ! Flux IN+1
+ ZBNEG2(:,IN,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (PSRC(:,IN-1,:) - PSRC(:,IN+1,:))**2 ! Smoothness indicator IN
+ ZBNEG2(:,IN+1,:) = 13./12 * (PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 &
+ + 1./4 * (PSRC(:,IN,:) - PSRC(:,IN+2,:))**2 ! Smoothness indicator IN+1
+ ZOMN2(:,IN:IN+1,:) = 3./5. / (ZEPS + ZBNEG2(:,IN:IN+1,:))**2 ! Non-normalized weight IN,IN+1
+!
+ ! Third negative stencil, needs indices i-2, i-1, i
+ ZFNEG3(:,IN,:) = 1./6 * (-1.0*PSRC(:,IN-2,:) + 5.0*PSRC(:,IN-1,:) + 2.0*PSRC(:,IN,:)) ! Flux IN
+ ZFNEG3(:,IN+1,:) = 1./6 * (-1.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) + 2.0*PSRC(:,IN+1,:)) ! Flux IN+1
+ ZBNEG3(:,IN,:) = 13./12 * (PSRC(:,IN-2,:) - 2.0*PSRC(:,IN-1,:) + PSRC(:,IN,:))**2 &
+ + 1./4 * (PSRC(:,IN-2,:) - 4.0*PSRC(:,IN-1,:) + 3.0*PSRC(:,IN,:))**2 ! Smoothness indicator IN
+ ZBNEG3(:,IN+1,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (PSRC(:,IN-1,:) - 4.0*PSRC(:,IN,:) + 3.0*PSRC(:,IN+1,:))**2 ! Smoothness indicator IN+1
+ ZOMN3(:,IN:IN+1,:) = 3./10. / (ZEPS + ZBNEG3(:,IN:IN+1,:))**2 ! Non-normalized weight IN,IN+1
+!
+ ! ----- Total flux -----
+!
+ PR(:,IN:IN+1,:) = ( ZOMP1(:,IN:IN+1,:)/(ZOMP1(:,IN:IN+1,:)+ZOMP2(:,IN:IN+1,:)+ZOMP3(:,IN:IN+1,:)) * ZFPOS1(:,IN:IN+1,:) &
+ + ZOMP2(:,IN:IN+1,:)/(ZOMP1(:,IN:IN+1,:)+ZOMP2(:,IN:IN+1,:)+ZOMP3(:,IN:IN+1,:)) * ZFPOS2(:,IN:IN+1,:) &
+ + ZOMP3(:,IN:IN+1,:)/(ZOMP1(:,IN:IN+1,:)+ZOMP2(:,IN:IN+1,:)+ZOMP3(:,IN:IN+1,:)) * ZFPOS3(:,IN:IN+1,:)) &
+ * (0.5+SIGN(0.5,PRVCT(:,IN:IN+1,:))) &
+ + ( ZOMN1(:,IN:IN+1,:)/(ZOMN1(:,IN:IN+1,:)+ZOMN2(:,IN:IN+1,:)+ZOMN3(:,IN:IN+1,:)) * ZFNEG1(:,IN:IN+1,:) &
+ + ZOMN2(:,IN:IN+1,:)/(ZOMN1(:,IN:IN+1,:)+ZOMN2(:,IN:IN+1,:)+ZOMN3(:,IN:IN+1,:)) * ZFNEG2(:,IN:IN+1,:) &
+ + ZOMN3(:,IN:IN+1,:)/(ZOMN1(:,IN:IN+1,:)+ZOMN2(:,IN:IN+1,:)+ZOMN3(:,IN:IN+1,:)) * ZFNEG3(:,IN:IN+1,:)) &
+ * (0.5-SIGN(0.5,PRVCT(:,IN:IN+1,:)))
+!
+ END IF ! NHALO
+!
+END IF ! IF(LNORTH_ll())
+!-------------------------------------------------------------------------------
!
- ELSEIF(NHALO == 1) THEN
- ZFPOS1(:,IN+1,:) = 0.5 * (3.0*PSRC(:,IN,:) - PSRC(:,IN-1,:))
- ZFPOS2(:,IN+1,:) = 0.5 * (PSRC(:,IN, :) + PSRC(:,IN+1,:))
- ZBPOS1(:,IN+1,:) = (PSRC(:,IN, :) - PSRC(:,IN-1,:))**2
- ZBPOS2(:,IN+1,:) = (PSRC(:,IN+1,:) - PSRC(:,IN, :))**2
-!
- ZFNEG1(:,IN+1,:) = 0.5 * (3.0*PSRC(:,IN+1,:) - TPHALO2%NORTH(:,:))
- ZFNEG2(:,IN+1,:) = 0.5 * (PSRC(:,IN+1, :) + PSRC(:,IN, :))
- ZBNEG1(:,IN+1,:) = (PSRC(:,IN+1,:) - TPHALO2%NORTH(:,:))**2
- ZBNEG2(:,IN+1,:) = (PSRC(:,IN ,:) - PSRC(:,IN+1,:))**2
-!
- ZOMP1(:,IN+1,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,IN+1,:))**2
- ZOMP2(:,IN+1,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,IN+1,:))**2
- ZOMN1(:,IN+1,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,IN+1,:))**2
- ZOMN2(:,IN+1,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,IN+1,:))**2
-!
- PR(:,IN+1,:) = (ZOMP2(:,IN+1,:)/(ZOMP1(:,IN+1,:)+ZOMP2(:,IN+1,:))*&
- ZFPOS2(:,IN+1,:) &
- + ZOMP1(:,IN+1,:)/(ZOMP1(:,IN+1,:)+ZOMP2(:,IN+1,:)) * &
- ZFPOS1(:,IN+1,:)) * (0.5+SIGN(0.5,PRVCT(:,IN+1,:))) &
- + (ZOMN2(:,IN+1,:)/(ZOMN1(:,IN+1,:)+ZOMN2(:,IN+1,:)) * &
- ZFNEG2(:,IN+1,:) &
- + ZOMN1(:,IN+1,:)/(ZOMN1(:,IN+1,:)+ZOMN2(:,IN+1,:)) * &
- ZFNEG1(:,IN+1,:)) * (0.5-SIGN(0.5,PRVCT(:,IN+1,:)))
-!
- ZFPOS1(:,IN,:) = 1./6 * (2.0*PSRC(:,IN-3,:) - 7.0*PSRC(:,IN-2,:) + &
- 11.0*PSRC(:,IN-1,:))
- ZFPOS2(:,IN,:) = 1./6 * (-1.0*PSRC(:,IN-2,:) + 5.0*PSRC(:,IN-1,:) + &
- 2.0*PSRC(:,IN,:))
- ZFPOS3(:,IN,:) = 1./6 * (2.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) - &
- 1.0*PSRC(:,IN+1,:))
-!
- ZBPOS1(:,IN,:) = 13./12 * (PSRC(:,IN-3,:) - 2.0*PSRC(:,IN-2,:) + &
- PSRC(:,IN-1,:))**2 + &
- 1./4 * (PSRC(:,IN-3,:) - 4.0*PSRC(:,IN-2,:) + 3.0*PSRC(:,IN-1,:))**2
- ZBPOS2(:,IN,:) = 13./12 * (PSRC(:,IN-2,:) - 2.0*PSRC(:,IN-1,:) + &
- PSRC(:,IN,:))**2 + &
- 1./4 * (PSRC(:,IN-2,:) - PSRC(:,IN,:))**2
- ZBPOS3(:,IN,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + &
- PSRC(:,IN+1,:))**2 + &
- 1./4 * ( 3.0*PSRC(:,IN-1,:) - 4.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2
-!
- ZFNEG1(:,IN,:) = 1./6 * (11.0*PSRC(:,IN,:) - 7.0*PSRC(:,IN+1,:) + &
- 2.0*TPHALO2%NORTH(:,:))
- ZFNEG2(:,IN,:) = 1./6 * (2.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) - &
- 1.0*PSRC(:,IN+1,:))
- ZFNEG3(:,IN,:) = 1./6 * (-1.0*PSRC(:,IN-2,:) + 5.0*PSRC(:,IN-1,:) + &
- 2.0*PSRC(:,IN,:))
-!
- ZBNEG1(:,IN,:) = 13./12 * (PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + &
- TPHALO2%NORTH(:,:))**2 + &
- 1./4 * ( 3.0*PSRC(:,IN,:) - 4.0*PSRC(:,IN+1,:) + TPHALO2%NORTH(:,:))**2
- ZBNEG2(:,IN,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + &
- PSRC(:,IN+1,:))**2 + &
- 1./4 * (PSRC(:,IN-1,:) - PSRC(:,IN+1,:))**2
- ZBNEG3(:,IN,:) = 13./12 * (PSRC(:,IN-2,:) - 2.0*PSRC(:,IN-1,:) +&
- PSRC(:,IN,:))**2 + &
- 1./4 * ( PSRC(:,IN-2,:) - 4.0*PSRC(:,IN-1,:) + 3.0*PSRC(:,IN,:))**2
-!
- ZOMP1(:,IN,:) = ZGAMMA1 / (ZEPS + ZBPOS1(:,IN,:))**2
- ZOMP2(:,IN,:) = ZGAMMA2 / (ZEPS + ZBPOS2(:,IN,:))**2
- ZOMP3(:,IN,:) = ZGAMMA3 / (ZEPS + ZBPOS3(:,IN,:))**2
- ZOMN1(:,IN,:) = ZGAMMA1 / (ZEPS + ZBNEG1(:,IN,:))**2
- ZOMN2(:,IN,:) = ZGAMMA2 / (ZEPS + ZBNEG2(:,IN,:))**2
- ZOMN3(:,IN,:) = ZGAMMA3 / (ZEPS + ZBNEG3(:,IN,:))**2
-!
- PR(:,IN,:) = (ZOMP2(:,IN,:)/(ZOMP1(:,IN,:)+ZOMP2(:,IN,:)+ZOMP3(:,IN,:)) * &
- ZFPOS2(:,IN,:) &
- + ZOMP1(:,IN,:)/(ZOMP1(:,IN,:)+ZOMP2(:,IN,:)+ZOMP3(:,IN,:)) * ZFPOS1(:,IN,:) &
- + ZOMP3(:,IN,:)/(ZOMP1(:,IN,:)+ZOMP2(:,IN,:)+ZOMP3(:,IN,:)) * ZFPOS3(:,IN,:)) &
- * (0.5+SIGN(0.5,PRVCT(:,IN,:))) &
- + (ZOMN2(:,IN,:)/(ZOMN1(:,IN,:)+ZOMN2(:,IN,:)+ZOMN3(:,IN,:)) * ZFNEG2(:,IN,:) &
- + ZOMN1(:,IN,:)/(ZOMN1(:,IN,:)+ZOMN2(:,IN,:)+ZOMN3(:,IN,:)) * ZFNEG1(:,IN,:) &
- + ZOMN3(:,IN,:)/(ZOMN1(:,IN,:)+ZOMN2(:,IN,:)+ZOMN3(:,IN,:)) * ZFNEG3(:,IN,:)) &
- * (0.5-SIGN(0.5,PRVCT(:,IN,:)))
-!
- ENDIF
-!
-! USE A FIFTH ORDER UPSTREAM WENO SCHEME ELSEWHERE (IS+2 --> IN-1)
-!
- ZFPOS1(:,IS+2:IN-1,:) = 1./6 * (2.0*PSRC(:,IS-1:IN-4,:) - &
- 7.0*PSRC(:,IS:IN-3, :) + 11.0*PSRC(:,IS+1:IN-2,:))
- ZFPOS2(:,IS+2:IN-1,:) = 1./6 * (-1.0*PSRC(:,IS:IN-3, :) + &
- 5.0*PSRC(:,IS+1:IN-2,:) + 2.0*PSRC(:,IS+2:IN-1, :))
- ZFPOS3(:,IS+2:IN-1,:) = 1./6 * (2.0*PSRC(:,IS+1:IN-2,:) + &
- 5.0*PSRC(:,IS+2:IN-1,:) - 1.0*PSRC(:,IS+3:IN, :))
-!
- ZBPOS1(:,IS+2:IN-1,:) = 13./12 * (PSRC(:,IS-1:IN-4,:) - &
- 2.0*PSRC(:,IS:IN-3,:) + PSRC(:,IS+1:IN-2,:))**2 + &
- 1./4 * (PSRC(:,IS-1:IN-4,:) - 4.0*PSRC(:,IS:IN-3,:) + &
- 3.0*PSRC(:,IS+1:IN-2,:))**2
- ZBPOS2(:,IS+2:IN-1,:) = 13./12 * (PSRC(:,IS:IN-3,:) - &
- 2.0*PSRC(:,IS+1:IN-2,:) + PSRC(:,IS+2:IN-1,:))**2 + &
- 1./4 * (PSRC(:,IS:IN-3,:) - PSRC(:,IS+2:IN-1,:))**2
- ZBPOS3(:,IS+2:IN-1,:) = 13./12 * (PSRC(:,IS+1:IN-2,:) - &
- 2.0*PSRC(:,IS+2:IN-1,:) + PSRC(:,IS+3:IN,:))**2 + &
- 1./4 * ( 3.0*PSRC(:,IS+1:IN-2,:) - 4.0*PSRC(:,IS+2:IN-1,:) +&
- PSRC(:,IS+3:IN,:))**2
-!
- ZFNEG1(:,IS+2:IN-1,:) = 1./6 * (11.0*PSRC(:,IS+2:IN-1,:) - &
- 7.0*PSRC(:,IS+3:IN,:) + 2.0*PSRC(:,IS+4:IN+1,:))
- ZFNEG2(:,IS+2:IN-1,:) = 1./6 * (2.0*PSRC(:,IS+1:IN-2,:) + &
- 5.0*PSRC(:,IS+2:IN-1,:) - 1.0*PSRC(:,IS+3:IN,:))
- ZFNEG3(:,IS+2:IN-1,:) = 1./6 * (-1.0*PSRC(:,IS:IN-3,:) + &
- 5.0*PSRC(:,IS+1:IN-2,:) + 2.0*PSRC(:,IS+2:IN-1,:))
-!
- ZBNEG1(:,IS+2:IN-1,:) = 13./12 * (PSRC(:,IS+2:IN-1,:) - &
- 2.0*PSRC(:,IS+3:IN,:) + PSRC(:,IS+4:IN+1,:))**2 + &
- 1./4 * ( 3.0*PSRC(:,IS+2:IN-1,:) - 4.0*PSRC(:,IS+3:IN,:) + &
- PSRC(:,IS+4:IN+1,:))**2
- ZBNEG2(:,IS+2:IN-1,:) = 13./12 * (PSRC(:,IS+1:IN-2,:) - &
- 2.0*PSRC(:,IS+2:IN-1,:) + PSRC(:,IS+3:IN,:))**2 + &
- 1./4 * (PSRC(:,IS+1:IN-2,:) - PSRC(:,IS+3:IN,:))**2
- ZBNEG3(:,IS+2:IN-1,:) = 13./12 * (PSRC(:,IS:IN-3,:) - &
- 2.0*PSRC(:,IS+1:IN-2,:) + PSRC(:,IS+2:IN-1,:))**2 + &
- 1./4 * ( PSRC(:,IS:IN-3,:) - 4.0*PSRC(:,IS+1:IN-2,:) + &
- 3.0*PSRC(:,IS+2:IN-1,:))**2
-!
- ZOMP1(:,IS+2:IN-1,:) = ZGAMMA1 / (ZEPS + ZBPOS1(:,IS+2:IN-1,:))**2
- ZOMP2(:,IS+2:IN-1,:) = ZGAMMA2 / (ZEPS + ZBPOS2(:,IS+2:IN-1,:))**2
- ZOMP3(:,IS+2:IN-1,:) = ZGAMMA3 / (ZEPS + ZBPOS3(:,IS+2:IN-1,:))**2
- ZOMN1(:,IS+2:IN-1,:) = ZGAMMA1 / (ZEPS + ZBNEG1(:,IS+2:IN-1,:))**2
- ZOMN2(:,IS+2:IN-1,:) = ZGAMMA2 / (ZEPS + ZBNEG2(:,IS+2:IN-1,:))**2
- ZOMN3(:,IS+2:IN-1,:) = ZGAMMA3 / (ZEPS + ZBNEG3(:,IS+2:IN-1,:))**2
-!
- PR(:,IS+2:IN-1,:) = (ZOMP2(:,IS+2:IN-1,:)/(ZOMP1(:,IS+2:IN-1,:)+&
- ZOMP2(:,IS+2:IN-1,:)+ZOMP3(:,IS+2:IN-1,:)) * ZFPOS2(:,IS+2:IN-1,:) &
- + ZOMP1(:,IS+2:IN-1,:)/(ZOMP1(:,IS+2:IN-1,:)+&
- ZOMP2(:,IS+2:IN-1,:)+ZOMP3(:,IS+2:IN-1,:)) * ZFPOS1(:,IS+2:IN-1,:) &
- + ZOMP3(:,IS+2:IN-1,:)/(ZOMP1(:,IS+2:IN-1,:)+ZOMP2(:,IS+2:IN-1,:)+ &
- ZOMP3(:,IS+2:IN-1,:)) * ZFPOS3(:,IS+2:IN-1,:)) &
- * (0.5+SIGN(0.5,PRVCT(:,IS+2:IN-1,:))) &
- + (ZOMN2(:,IS+2:IN-1,:)/(ZOMN1(:,IS+2:IN-1,:)+ZOMN2(:,IS+2:IN-1,:)+ &
- ZOMN3(:,IS+2:IN-1,:)) * ZFNEG2(:,IS+2:IN-1,:) &
- + ZOMN1(:,IS+2:IN-1,:)/(ZOMN1(:,IS+2:IN-1,:)+ZOMN2(:,IS+2:IN-1,:)+ &
- ZOMN3(:,IS+2:IN-1,:)) * ZFNEG1(:,IS+2:IN-1,:) &
- + ZOMN3(:,IS+2:IN-1,:)/(ZOMN1(:,IS+2:IN-1,:)+ZOMN2(:,IS+2:IN-1,:)+&
- ZOMN3(:,IS+2:IN-1,:)) * ZFNEG3(:,IS+2:IN-1,:)) &
- * (0.5-SIGN(0.5,PRVCT(:,IS+2:IN-1,:)))
-!
-END SELECT
-!
-PR = PR * PRVCT
+PR = PR * PRVCT ! Add contravariant flux
!
END SUBROUTINE ADVEC_WENO_K_3_MY
!
!-------------------------------------------------------------------------------
!
! #############################################################
- SUBROUTINE ADVEC_WENO_K_3_VY(HLBCY, PSRC, PRVCT, PR, TPHALO2)
+ SUBROUTINE ADVEC_WENO_K_3_VY(HLBCY, PSRC, PRVCT, PR)
! #############################################################
!!
!!**** Computes PRVCT * PVT. Upstream fluxes of V in Y direction.
@@ -1963,13 +2086,16 @@ END SUBROUTINE ADVEC_WENO_K_3_MY
!!
!! MODIFICATIONS
!! -------------
+!! T. Lunet 02/10/2014: Correction of periodic boudary conditions
+!! Change of structure in order to adapt WENO to NHALOK
+!! Suppression of second layer HALO pointers
+!! Complete code documentation
!!
!-------------------------------------------------------------------------------
!
USE MODE_ll
USE MODD_LUNIT
USE MODD_CONF
-USE MODD_ARGSLIST_ll, ONLY : HALO2LIST_ll
!
IMPLICIT NONE
!
@@ -1982,13 +2108,12 @@ REAL, DIMENSION(:,:,:), INTENT(IN) :: PRVCT ! contrav. comp. on MASS GRID
!
! output source term
REAL, DIMENSION(:,:,:), INTENT(INOUT) :: PR
-TYPE(HALO2_ll), OPTIONAL, POINTER :: TPHALO2 ! halo2 for the field at t
!
!* 0.2 Declarations of local variables :
!
INTEGER :: IIB,IJB ! Begining useful area in x,y,z directions
INTEGER :: IIE,IJE ! End useful area in x,y,z directions
-INTEGER:: IS,IN ! Coordinate of third order diffusion area
+INTEGER:: IS,IN ! Physical boundary index
!
INTEGER:: ILUOUT,IRESP ! for prints
!
@@ -1997,7 +2122,7 @@ INTEGER:: ILUOUT,IRESP ! for prints
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZFPOS1, ZFPOS2, ZFPOS3
!
! intermediate reconstruction fluxes for negative wind case
-! we need only one since ZFNEG2 = ZFPOS2
+!
!
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZFNEG1, ZFNEG2, ZFNEG3
!
@@ -2011,15 +2136,9 @@ REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZBNEG1, ZBNEG2, ZBNEG3
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)) :: ZOMP1, ZOMP2, ZOMP3
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)) :: ZOMN1, ZOMN2, ZOMN3
!
-! standard weights
-!
-REAL, PARAMETER :: ZGAMMA1 = 1./10.
-REAL, PARAMETER :: ZGAMMA2 = 3./5.
-REAL, PARAMETER :: ZGAMMA3 = 3./10.
-REAL, PARAMETER :: ZGAMMA1_PRIM = 1./3.
-REAL, PARAMETER :: ZGAMMA2_PRIM = 2./3.
-!
- REAL, PARAMETER :: ZEPS = 1.0E-15
+! EPSILON for weno weights calculation
+!
+REAL, PARAMETER :: ZEPS = 1.0E-15
!
!----------------------------------------------------------------------------
!
@@ -2055,468 +2174,556 @@ ZOMN2 = 0.0
ZOMN3 = 0.0
!
!-------------------------------------------------------------------------------
+!-------------------------------------------------------------------------------
+!* 1.1. Interior Fluxes
+! ---------------------
+IS=IJB
+IN=IJE
!
-SELECT CASE ( HLBCY(1) ) ! Y direction LBC type: (1) for left side
-!
-!* 1.1 CYCLIC CASE IN THE Y DIRECTION:
-!
-CASE ('CYCL') ! In that case one must have HLBCX(1) == HLBCX(2)
-!
- IF(NHALO == 1) THEN
- IS=IJB
- IN=IJE
- ELSE
- CALL FMLOOK_ll(CLUOUT0,CLUOUT0,ILUOUT,IRESP)
- WRITE(ILUOUT,*) 'ERROR : 4th order advection in CYCLic case '
- WRITE(ILUOUT,*) 'cannot be used with NHALO=2'
- CALL ABORT
- STOP
- END IF
-!
-! Same explanation than for the subroutine ADVEC_WENO_K_3_UX
-!
-! intermediate fluxes for positive wind case
-!
- ZFPOS1(:,IS+1:IN-1,:) = 1./6 * (2.0*PSRC(:,IS-1:IN-3,:) - 7.0*PSRC(:,IS:IN-2,:) +&
- 11.0*PSRC(:,IS+1:IN-1,:))
- ZFPOS1(:,IS, :) = 1./6 * (2.0*TPHALO2%SOUTH(:,:) - 7.0*PSRC(:,IS-1, :) +&
- 11.0*PSRC(:,IS, :))
- ZFPOS1(:,IS-1,:) = 0.5 * (3.0*PSRC(:,IS-1,:) - TPHALO2%SOUTH(:,:))
- ZFPOS1(:,IN, :) = 0.5 * (3.0*PSRC(:,IN, :) - PSRC(:,IN-1,:))
- ZFPOS1(:,IN+1,:) = 0.5 * (3.0*PSRC(:,IN+1,:) - PSRC(:,IN, :))
-!
-!
- ZFPOS2(:,IS:IN-1,:) = 1./6 * (-1.0*PSRC(:,IS-1:IN-2,:) + 5.0*PSRC(:,IS:IN-1,:) +&
- 2.0*PSRC(:,IS+1:IN,:))
- ZFPOS2(:,IS-1,:) = 0.5 * (PSRC(:,IS-1,:) + PSRC(:,IS, :))
- ZFPOS2(:,IN, :) = 0.5 * (PSRC(:,IN, :) + PSRC(:,IN+1,:))
- ZFPOS2(:,IN+1,:) = 0.5 * (PSRC(:,IN+1,:) + TPHALO2%NORTH(:,:))
-!
-!
- ZFPOS3(:,IS:IN-1,:) = 1./6 * (2.0*PSRC(:,IS:IN-1,:) + 5.0*PSRC(:,IS+1:IN,:) - &
- 1.0*PSRC(:,IS+2:IN+1,:))
+!-------------------------------------------------------------------------------
+! Flux calculation in the physical domain far enough from the boundary
+! WENO scheme order 5, IS+1 -> IN-2
+! Computation at the mass point on Vgrid v(i+1/2,j,k)
+!-------------------------------------------------------------------------------
!
-! intermediate flux for negative wind case
+! ----- Positive fluxes -----
+!
+! First positive stencil, needs indices i-2, i-1, i
+ZFPOS1(:,IS+1:IN-2,:) = 1./6. * (2.0*PSRC(:,IS-1:IN-4,:) - 7.0*PSRC(:,IS:IN-3,:) + 11.0*PSRC(:,IS+1:IN-2,:)) ! Flux
+ZBPOS1(:,IS+1:IN-2,:) = 13./12. * ( PSRC(:,IS-1:IN-4,:) - 2.0*PSRC(:,IS:IN-3,:) + PSRC(:,IS+1:IN-2,:))**2 &
+ + 1./4 * ( PSRC(:,IS-1:IN-4,:) - 4.0*PSRC(:,IS:IN-3,:) + 3.0* PSRC(:,IS+1:IN-2,:))**2 ! Smoothness indicator
+ZOMP1(:,IS+1:IN-2,:) = 1./10. / (ZEPS + ZBPOS1(:,IS+1:IN-2,:))**2 ! Non-normalized weight
+!
+! Second positive stencil, needs indices i-1, i, i+1
+ZFPOS2(:,IS+1:IN-2,:) = 1./6. * (-1.0*PSRC(:,IS:IN-3,:) + 5.0*PSRC(:,IS+1:IN-2,:) + 2.0*PSRC(:,IS+2:IN-1,:)) ! Flux
+ZBPOS2(:,IS+1:IN-2,:) = 13./12 * ( PSRC(:,IS:IN-3,:) - 2.0*PSRC(:,IS+1:IN-2,:) + PSRC(:,IS+2:IN-1,:))**2 &
+ + 1./4 * ( PSRC(:,IS:IN-3,:) - PSRC(:,IS+2:IN-1,:))**2 ! Smoothness indicator
+ZOMP2(:,IS+1:IN-2,:) = 3./5. / (ZEPS + ZBPOS2(:,IS+1:IN-2,:))**2 ! Non-normalized weight
+!
+! Third positive stencil, needs indices i, i+1, i+2
+ZFPOS3(:,IS+1:IN-2,:) = 1./6 * (2.0*PSRC(:,IS+1:IN-2,:) + 5.0*PSRC(:,IS+2:IN-1,:) - PSRC(:,IS+3:IN,:)) ! Flux
+ZBPOS3(:,IS+1:IN-2,:) = 13./12 * ( PSRC(:,IS+1:IN-2,:) - 2.0*PSRC(:,IS+2:IN-1,:) + PSRC(:,IS+3:IN,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS+1:IN-2,:) - 4.0*PSRC(:,IS+2:IN-1,:) + PSRC(:,IS+3:IN,:))**2 ! Smoothness indicator
+ZOMP3(:,IS+1:IN-2,:) = 3./10. / (ZEPS + ZBPOS3(:,IS+1:IN-2,:))**2 ! Non-normalized weight
+!
+! ----- Negative fluxes -----
+!
+! First negative stencil, needs indices i+1, i+2, i+3
+ZFNEG1(:,IS+1:IN-2,:) = 1./6. * (11.0*PSRC(:,IS+2:IN-1,:) - 7.0*PSRC(:,IS+3:IN,:) + 2.0*PSRC(:,IS+4:IN+1,:)) ! Flux
+ZBNEG1(:,IS+1:IN-2,:) = 13./12. * ( PSRC(:,IS+2:IN-1,:) - 2.0*PSRC(:,IS+3:IN,:) + PSRC(:,IS+4:IN+1,:))**2 &
+ + 1./4 * (3.0* PSRC(:,IS+2:IN-1,:) - 4.0*PSRC(:,IS+3:IN,:) + PSRC(:,IS+4:IN+1,:))**2 ! Smoothness indicator
+ZOMN1(:,IS+1:IN-2,:) = 1./10. / (ZEPS + ZBNEG1(:,IS+1:IN-2,:))**2 ! Non-normalized weight
+!
+! Second negative stencil, needs indices i, i+1, i+2
+ZFNEG2(:,IS+1:IN-2,:) = 1./6. * (2.0*PSRC(:,IS+1:IN-2,:) + 5.0*PSRC(:,IS+2:IN-1,:) - 1.0*PSRC(:,IS+3:IN,:)) ! Flux
+ZBNEG2(:,IS+1:IN-2,:) = 13./12 * ( PSRC(:,IS+1:IN-2,:) - 2.0*PSRC(:,IS+2:IN-1,:) + PSRC(:,IS+3:IN,:))**2 &
+ + 1./4 * ( PSRC(:,IS+1:IN-2,:) - PSRC(:,IS+3:IN,:))**2 ! Smoothness indicator
+ZOMN2(:,IS+1:IN-2,:) = 3./5. / (ZEPS + ZBNEG2(:,IS+1:IN-2,:))**2 ! Non-normalized weight
+!
+! Third negative stencil, needs indices i-1, i, i+1
+ZFNEG3(:,IS+1:IN-2,:) = 1./6 * (-1.0*PSRC(:,IS:IN-3,:) + 5.0*PSRC(:,IS+1:IN-2,:) + 2.0*PSRC(:,IS+2:IN-1,:)) ! Flux
+ZBNEG3(:,IS+1:IN-2,:) = 13./12 * ( PSRC(:,IS:IN-3,:) - 2.0*PSRC(:,IS+1:IN-2,:) + PSRC(:,IS+2:IN-1,:))**2 &
+ + 1./4 * ( PSRC(:,IS:IN-3,:) - 4.0*PSRC(:,IS+1:IN-2,:) + 3.0*PSRC(:,IS+2:IN-1,:))**2 ! Smoothness indicator
+ZOMN3(:,IS+1:IN-2,:) = 3./10. / (ZEPS + ZBNEG3(:,IS+1:IN-2,:))**2 ! Non-normalized weight
+!
+!
+! ----- Total flux -----
+!
+PR(:,IS+1:IN-2,:) = (ZOMP1(:,IS+1:IN-2,:)/(ZOMP1(:,IS+1:IN-2,:)+ZOMP2(:,IS+1:IN-2,:)+ZOMP3(:,IS+1:IN-2,:)) &
+ * ZFPOS1(:,IS+1:IN-2,:) + &
+ ZOMP2(:,IS+1:IN-2,:)/(ZOMP1(:,IS+1:IN-2,:)+ZOMP2(:,IS+1:IN-2,:)+ZOMP3(:,IS+1:IN-2,:)) &
+ * ZFPOS2(:,IS+1:IN-2,:) + &
+ ZOMP3(:,IS+1:IN-2,:)/(ZOMP1(:,IS+1:IN-2,:)+ZOMP2(:,IS+1:IN-2,:)+ZOMP3(:,IS+1:IN-2,:)) &
+ * ZFPOS3(:,IS+1:IN-2,:)) &
+ * (0.5+SIGN(0.5,PRVCT(:,IS+1:IN-2,:))) &
+ + (ZOMN1(:,IS+1:IN-2,:)/(ZOMN1(:,IS+1:IN-2,:)+ZOMN2(:,IS+1:IN-2,:)+ZOMN3(:,IS+1:IN-2,:)) &
+ * ZFNEG1(:,IS+1:IN-2,:) &
+ + ZOMN2(:,IS+1:IN-2,:)/(ZOMN1(:,IS+1:IN-2,:)+ZOMN2(:,IS+1:IN-2,:)+ZOMN3(:,IS+1:IN-2,:)) &
+ * ZFNEG2(:,IS+1:IN-2,:) &
+ + ZOMN3(:,IS+1:IN-2,:)/(ZOMN1(:,IS+1:IN-2,:)+ZOMN2(:,IS+1:IN-2,:)+ZOMN3(:,IS+1:IN-2,:)) &
+ * ZFNEG3(:,IS+1:IN-2,:)) &
+ * (0.5-SIGN(0.5,PRVCT(:,IS+1:IN-2,:)))
!
- ZFNEG1(:,IS:IN-2,:) = 1./6 * (11.0*PSRC(:,IS+1:IN-1,:) - 7.0*PSRC(:,IS+2:IN,:) +&
- 2.0*PSRC(:,IS+3:IN+1,:))
- ZFNEG1(:,IN-1, :) = 1./6 * (11.0*PSRC(:,IN, :) - 7.0*PSRC(:,IN+1, :) +&
- 2.0*TPHALO2%NORTH(:,:))
- ZFNEG1(:,IS-1,:) = 0.5 * (3.0*PSRC(:,IS,:) - PSRC(:,IS+1,:))
- ZFNEG1(:,IN+1,:) = - 999.
- ZFNEG1(:,IN, :) = 0.5 * (3.0*PSRC(:,IN+1,:) - TPHALO2%NORTH(:,:))
+!-------------------------------------------------------------------------------
+!* 1.2. South border
+! ---------------------
!
+IF(LSOUTH_ll() .AND. .FALSE. ) THEN
+ !-----------------------------------------------------------------------------
+ ! South border is physical -- IS,IS-1
+ !-----------------------------------------------------------------------------
+ SELECT CASE (HLBCY(1)) ! Y direction LBC type on south side
+!
+ CASE ('CYCL')
+ !---------------------------------------------------------------------------
+ ! Periodic boundary condition
+ !---------------------------------------------------------------------------
+!
+ IF(LNORTH_ll() .AND. .FALSE. ) THEN ! North border is physical
+!
+ ! First positive stencil, needs indices i-2, i-1, i
+ ZFPOS1(:,IS,:) = 1./6. * (2.0*PSRC(:,IN,:) - 7.0*PSRC(:,IS-1,:) + 11.0*PSRC(:,IS,:)) ! Flux IS
+ ZFPOS1(:,IS-1,:) = 1./6. * (2.0*PSRC(:,IN-1,:) - 7.0*PSRC(:,IN,:) + 11.0*PSRC(:,IS-1,:)) ! Flux IS-1
+ ZBPOS1(:,IS,:) = 13./12. * (PSRC(:,IN,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IN,:) - 4.0*PSRC(:,IS-1,:) + 3.0*PSRC(:,IS,:))**2 ! Smoothness indicator IS
+ ZBPOS1(:,IS-1,:) = 13./12. * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IS-1,:))**2 &
+ + 1./4 * (PSRC(:,IN-1,:) - 4.0*PSRC(:,IN,:) + 3.0*PSRC(:,IS-1,:))**2 ! Smoothness indicator IS-1
+ ZOMP1(:,IS-1:IS,:) = 1./10. / (ZEPS + ZBPOS1(:,IS-1:IS,:))**2 ! Non-normalized weight IS,IS-1
+!
+ ! Second positive stencil, needs indices i-1, i, i+1
+ ZFPOS2(:,IS,:) = 1./6.* (-1.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) + 2.0*PSRC(:,IS+1,:)) ! Flux IS
+ ZFPOS2(:,IS-1,:) = 1./6.* (-1.0*PSRC(:,IN,:) + 5.0*PSRC(:,IS-1,:) + 2.0*PSRC(:,IS,:)) ! Flux IS-1
+ ZBPOS2(:,IS,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (PSRC(:,IS-1,:) - PSRC(:,IS+1,:))**2 ! Smoothness indicator IS
+ ZBPOS2(:,IS-1,:) = 13./12 * (PSRC(:,IN,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IN,:) - PSRC(:,IS,:))**2 ! Smoothness indicator IS-1
+ ZOMP2(:,IS-1:IS,:) = 3./5. / (ZEPS + ZBPOS2(:,IS-1:IS,:))**2 ! Non-normalized weight IS,IS-1
+!
+ ! Third negative stencil, needs indices i-1, i, i+1
+ ZFNEG3(:,IS,:) = 1./6 * (-1.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) + 2.0*PSRC(:,IS+1,:)) ! Flux IS
+ ZFNEG3(:,IS-1,:) = 1./6 * (-1.0*PSRC(:,IN,:) + 5.0*PSRC(:,IS-1,:) + 2.0*PSRC(:,IS,:)) ! Flux IS-1
+ ZBNEG3(:,IS,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (PSRC(:,IS-1,:) - 4.0*PSRC(:,IS,:) + 3.0*PSRC(:,IS+1,:))**2 ! Smoothness indicator IS
+ ZBNEG3(:,IS-1,:) = 13./12 * (PSRC(:,IN,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IN,:) - 4.0*PSRC(:,IS-1,:) + 3.0*PSRC(:,IS,:))**2 ! Smoothness indicator IS-1
+ ZOMN3(:,IS-1:IS,:) = 3./10. / (ZEPS + ZBNEG3(:,IS-1:IS,:))**2 ! Non-normalized weight IS,IS-1
+!
+ ELSEIF(IS>3) THEN ! North boundary is proc border, with minimum 3 HALO points on south side
+!
+ ! First positive stencil, needs indices i-2, i-1, i
+ ZFPOS1(:,IS,:) = 1./6. * (2.0*PSRC(:,IS-2,:) - 7.0*PSRC(:,IS-1,:) + 11.0*PSRC(:,IS,:)) ! Flux IS
+ ZFPOS1(:,IS-1,:) = 1./6. * (2.0*PSRC(:,IS+3,:) - 7.0*PSRC(:,IS-2,:) + 11.0*PSRC(:,IS-1,:)) ! Flux IS-1
+ ZBPOS1(:,IS,:) = 13./12. * (PSRC(:,IS-2,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IS-2,:) - 4.0*PSRC(:,IS-1,:) + 3.0*PSRC(:,IS,:))**2 ! Smoothness indicator IS
+ ZBPOS1(:,IS-1,:) = 13./12. * (PSRC(:,IS-3,:) - 2.0*PSRC(:,IS-2,:) + PSRC(:,IS-1,:))**2 &
+ + 1./4 * (PSRC(:,IS-3,:) - 4.0*PSRC(:,IS-2,:) + 3.0*PSRC(:,IS-1,:))**2 ! Smoothness indicator IS-1
+ ZOMP1(:,IS-1:IS,:) = 1./10. / (ZEPS + ZBPOS1(:,IS-1:IS,:))**2 ! Non-normalized weight IS,IS-1
+!
+ ! Second positive stencil, needs indices i-1, i, i+1
+ ZFPOS2(:,IS,:) = 1./6.* (-1.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) + 2.0*PSRC(:,IS+1,:)) ! Flux IS
+ ZFPOS2(:,IS-1,:) = 1./6.* (-1.0*PSRC(:,IS-2,:) + 5.0*PSRC(:,IS-1,:) + 2.0*PSRC(:,IS,:)) ! Flux IS-1
+ ZBPOS2(:,IS,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (PSRC(:,IS-1,:) - PSRC(:,IS+1,:))**2 ! Smoothness indicator IS
+ ZBPOS2(:,IS-1,:) = 13./12 * (PSRC(:,IS-2,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IS-2,:) - PSRC(:,IS,:))**2 ! Smoothness indicator IS-1
+ ZOMP2(:,IS-1:IS,:) = 3./5. / (ZEPS + ZBPOS2(:,IS-1:IS,:))**2 ! Non-normalized weight IS,IS-1
+!
+ ! Third negative stencil, needs indices i-1, i, i+1
+ ZFNEG3(:,IS,:) = 1./6 * (-1.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) + 2.0*PSRC(:,IS+1,:)) ! Flux IS
+ ZFNEG3(:,IS-1,:) = 1./6 * (-1.0*PSRC(:,IS-2,:) + 5.0*PSRC(:,IS-1,:) + 2.0*PSRC(:,IS,:)) ! Flux IS-1
+ ZBNEG3(:,IS,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (PSRC(:,IS-1,:) - 4.0*PSRC(:,IS,:) + 3.0*PSRC(:,IS+1,:))**2 ! Smoothness indicator IS
+ ZBNEG3(:,IS-1,:) = 13./12 * (PSRC(:,IS-2,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IS-2,:) - 4.0*PSRC(:,IS-1,:) + 3.0*PSRC(:,IS,:))**2 ! Smoothness indicator IS-1
+ ZOMN3(:,IS-1:IS,:) = 3./10. / (ZEPS + ZBNEG3(:,IS-1:IS,:))**2 ! Non-normalized weight IS,IS-1
+!
+ ELSE ! North boundary is proc border, with NHALO < 3 on south side
+ PRINT *,'WARNING : WENO5 fluxes calculation needs NHALO >= 3 on south side'
+ CALL ABORT
+ ENDIF
+!
+ ! Third positive stencil, needs indices i, i+1, i+2
+ ZFPOS3(:,IS,:) = 1./6 * (2.0*PSRC(:,IS,:) + 5.0*PSRC(:,IS+1,:) - PSRC(:,IS+2,:)) ! Flux IS
+ ZFPOS3(:,IS-1,:) = 1./6 * (2.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) - PSRC(:,IS+1,:)) ! Flux IS-1
+ ZBPOS3(:,IS,:) = 13./12 * ( PSRC(:,IS,:) - 2.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS,:) - 4.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 ! Smoothness indicator IS
+ ZBPOS3(:,IS-1,:) = 13./12 * ( PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS-1,:) - 4.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 ! Smoothness indicator IS-1
+ ZOMP3(:,IS-1:IS,:) = 3./10. / (ZEPS + ZBPOS3(:,IS-1:IS,:))**2 ! Non-normalized weight IS,IS-1
+!
+ ! ----- Negative fluxes -----
+!
+ ! First negative stencil, needs indices i+1, i+2, i+3
+ ZFNEG1(:,IS,:) = 1./6. * (11.0*PSRC(:,IS+1,:) - 7.0*PSRC(:,IS+2,:) + 2.0*PSRC(:,IS+3,:)) ! Flux IS
+ ZFNEG1(:,IS-1,:) = 1./6. * (11.0*PSRC(:,IS,:) - 7.0*PSRC(:,IS+1,:) + 2.0*PSRC(:,IS+2,:)) ! Flux IS-1
+ ZBNEG1(:,IS,:) = 13./12. * ( PSRC(:,IS+1,:) - 2.0*PSRC(:,IS+2,:) + PSRC(:,IS+3,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS+1,:) - 4.0*PSRC(:,IS+2,:) + PSRC(:,IS+3,:))**2 ! Smoothness indicator IS
+ ZBNEG1(:,IS-1,:) = 13./12. * ( PSRC(:,IS,:) - 2.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS,:) - 4.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 ! Smoothness indicator IS-1
+ ZOMN1(:,IS-1:IS,:) = 1./10. / (ZEPS + ZBNEG1(:,IS-1:IS,:))**2 ! Non-normalized weight IS,IS-1
+!
+ ! Second negative stencil, needs indices i, i+1, i+2
+ ZFNEG2(:,IS,:) = 1./6. * (2.0*PSRC(:,IS,:) + 5.0*PSRC(:,IS+1,:) - 1.0*PSRC(:,IS+2,:)) ! Flux IS
+ ZFNEG2(:,IS-1,:) = 1./6. * (2.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) - 1.0*PSRC(:,IS+1,:)) ! Flux IS-1
+ ZBNEG2(:,IS,:) = 13./12 * (PSRC(:,IS,:) - 2.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 &
+ + 1./4 * (PSRC(:,IS,:) - PSRC(:,IS+2,:))**2 ! Smoothness indicator IS
+ ZBNEG2(:,IS-1,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (PSRC(:,IS-1,:) - PSRC(:,IS+1,:))**2 ! Smoothness indicator IS-1
+ ZOMN2(:,IS-1:IS,:) = 3./5. / (ZEPS + ZBNEG2(:,IS-1:IS,:))**2 ! Non-normalized weight IS,IS-1
+!
+ ! ----- Total flux -----
+!
+ PR(:,IS-1:IS,:) = ( ZOMP1(:,IS-1:IS,:)/(ZOMP1(:,IS-1:IS,:)+ZOMP2(:,IS-1:IS,:)+ZOMP3(:,IS-1:IS,:)) * ZFPOS1(:,IS-1:IS,:) &
+ + ZOMP2(:,IS-1:IS,:)/(ZOMP1(:,IS-1:IS,:)+ZOMP2(:,IS-1:IS,:)+ZOMP3(:,IS-1:IS,:)) * ZFPOS2(:,IS-1:IS,:) &
+ + ZOMP3(:,IS-1:IS,:)/(ZOMP1(:,IS-1:IS,:)+ZOMP2(:,IS-1:IS,:)+ZOMP3(:,IS-1:IS,:)) * ZFPOS3(:,IS-1:IS,:)) &
+ * (0.5+SIGN(0.5,PRVCT(:,IS-1:IS,:))) &
+ + ( ZOMN1(:,IS-1:IS,:)/(ZOMN1(:,IS-1:IS,:)+ZOMN2(:,IS-1:IS,:)+ZOMN3(:,IS-1:IS,:)) * ZFNEG1(:,IS-1:IS,:) &
+ + ZOMN2(:,IS-1:IS,:)/(ZOMN1(:,IS-1:IS,:)+ZOMN2(:,IS-1:IS,:)+ZOMN3(:,IS-1:IS,:)) * ZFNEG2(:,IS-1:IS,:) &
+ + ZOMN3(:,IS-1:IS,:)/(ZOMN1(:,IS-1:IS,:)+ZOMN2(:,IS-1:IS,:)+ZOMN3(:,IS-1:IS,:)) * ZFNEG3(:,IS-1:IS,:)) &
+ * (0.5-SIGN(0.5,PRVCT(:,IS-1:IS,:)))
+!
+!
+ CASE ('OPEN','WALL','NEST')
+ !---------------------------------------------------------------------------
+ ! Open, or Wall, or Nest boundary condition => WENO order reduction
+ !---------------------------------------------------------------------------
+!
+ ! WENO scheme order 1, IS-1
+ PR(:,IS-1,:) = PSRC(:,IS-1,:) * (0.5+SIGN(0.5,PRVCT(:,IS-1,:))) + &
+ PSRC(:,IS,:) * &
+ (0.5-SIGN(0.5,PRVCT(:,IS-1,:)))
+!
+! ! WENO scheme order 3, IS
+ ZFPOS1(:,IS,:) = 0.5 * (3.0*PSRC(:,IS,:) - PSRC(:,IS-1,:)) ! First positive flux
+ ZFPOS2(:,IS,:) = 0.5 * ( PSRC(:,IS,:) + PSRC(:,IS+1,:)) ! Second positive flux
+ ZBPOS1(:,IS,:) = (PSRC(:,IS,:) - PSRC(:,IS-1,:))**2 ! First positive smoothness indicator
+ ZBPOS2(:,IS,:) = (PSRC(:,IS+1,:) - PSRC(:,IS,:))**2 ! Second positive smoothness indicator
+!
+ ZFNEG1(:,IS,:) = 0.5 * (3.0*PSRC(:,IS+1,:) - PSRC(:,IS+2,:)) ! First negative flux
+ ZFNEG2(:,IS,:) = 0.5 * ( PSRC(:,IS,:) + PSRC(:,IS+1,:)) ! Second negative flux
+ ZBNEG1(:,IS,:) = (PSRC(:,IS+1,:) - PSRC(:,IS+2,:))**2 ! First negative smoothness indicator
+ ZBNEG2(:,IS,:) = (PSRC(:,IS,:) - PSRC(:,IS+1,:))**2 ! Second negative smoothness indicator
+!
+ ZOMP1(:,IS,:) = 1./3. / (ZEPS + ZBPOS1(:,IS,:))**2 ! First positive non-normalized weight
+ ZOMP2(:,IS,:) = 2./3. / (ZEPS + ZBPOS2(:,IS,:))**2 ! Second positive non-normalized weight
+ ZOMN1(:,IS,:) = 1./3. / (ZEPS + ZBNEG1(:,IS,:))**2 ! First negative non-normalized weight
+ ZOMN2(:,IS,:) = 2./3. / (ZEPS + ZBNEG2(:,IS,:))**2 ! Second negative non-normalized weight
+!
+ PR(:,IS,:) = (ZOMN2(:,IS,:)/(ZOMN1(:,IS,:)+ZOMN2(:,IS,:)) * ZFNEG2(:,IS,:) + &
+ (ZOMN1(:,IS,:)/(ZOMN1(:,IS,:)+ZOMN2(:,IS,:)) * ZFNEG1(:,IS,:))) &
+ *(0.5-SIGN(0.5,PRVCT(:,IS,:))) + &
+ (ZOMP2(:,IS,:)/(ZOMP1(:,IS,:)+ZOMP2(:,IS,:)) * ZFPOS2(:,IS,:) + &
+ (ZOMP1(:,IS,:)/(ZOMP1(:,IS,:)+ZOMP2(:,IS,:)) * ZFPOS1(:,IS,:))) &
+ *(0.5+SIGN(0.5,PRVCT(:,IS,:))) ! Total flux
+!
+ END SELECT ! SELECT CASE (HLBCY(1)) ! Y direction LBC type on south side
+!
+ELSE
+ !-----------------------------------------------------------------------------
+ ! South border is proc border -- IS,IS-1
+ !-----------------------------------------------------------------------------
+!
+ IF (NHALO<3) THEN
+ PRINT *,'WARNING : WENO5 not parallelisable with NHALO < 3'
+ CALL ABORT
+ ELSEIF (NHALO>=3) THEN
+ !---------------------------------------------------------------------------
+ ! NHALO >3 => WENO5 for all boundary points
+ !---------------------------------------------------------------------------
+!
+ ! ----- Positive fluxes -----
+!
+ ! First positive stencil, needs indices i-2, i-1, i
+ ZFPOS1(:,IS,:) = 1./6. * (2.0*PSRC(:,IS-2,:) - 7.0*PSRC(:,IS-1,:) + 11.0*PSRC(:,IS,:)) ! Flux IS
+ ZFPOS1(:,IS-1,:) = 1./6. * (2.0*PSRC(:,IS-3,:) - 7.0*PSRC(:,IS-2,:) + 11.0*PSRC(:,IS-1,:)) ! Flux IS-1
+ ZBPOS1(:,IS,:) = 13./12. * (PSRC(:,IS-2,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IS-2,:) - 4.0*PSRC(:,IS-1,:) + 3.0*PSRC(:,IS,:))**2 ! Smoothness indicator IS
+ ZBPOS1(:,IS-1,:) = 13./12. * (PSRC(:,IS-3,:) - 2.0*PSRC(:,IS-2,:) + PSRC(:,IS-1,:))**2 &
+ + 1./4 * (PSRC(:,IS-3,:) - 4.0*PSRC(:,IS-2,:) + 3.0*PSRC(:,IS-1,:))**2 ! Smoothness indicator IS-1
+ ZOMP1(:,IS-1:IS,:) = 1./10. / (ZEPS + ZBPOS1(:,IS-1:IS,:))**2 ! Non-normalized weight IS,IS-1
+!
+ ! Second positive stencil, needs indices i-1, i, i+1
+ ZFPOS2(:,IS,:) = 1./6.* (-1.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) + 2.0*PSRC(:,IS+1,:)) ! Flux IS
+ ZFPOS2(:,IS-1,:) = 1./6.* (-1.0*PSRC(:,IS-2,:) + 5.0*PSRC(:,IS-1,:) + 2.0*PSRC(:,IS,:)) ! Flux IS-1
+ ZBPOS2(:,IS,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (PSRC(:,IS-1,:) - PSRC(:,IS+1,:))**2 ! Smoothness indicator IS
+ ZBPOS2(:,IS-1,:) = 13./12 * (PSRC(:,IS-2,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IS-2,:) - PSRC(:,IS,:))**2 ! Smoothness indicator IS-1
+ ZOMP2(:,IS-1:IS,:) = 3./5. / (ZEPS + ZBPOS2(:,IS-1:IS,:))**2 ! Non-normalized weight IS,IS-1
+!
+ ! Third positive stencil, needs indices i, i+1, i+2
+ ZFPOS3(:,IS,:) = 1./6 * (2.0*PSRC(:,IS,:) + 5.0*PSRC(:,IS+1,:) - PSRC(:,IS+2,:)) ! Flux IS
+ ZFPOS3(:,IS-1,:) = 1./6 * (2.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) - PSRC(:,IS+1,:)) ! Flux IS-1
+ ZBPOS3(:,IS,:) = 13./12 * ( PSRC(:,IS,:) - 2.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS,:) - 4.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 ! Smoothness indicator IS
+ ZBPOS3(:,IS-1,:) = 13./12 * ( PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS-1,:) - 4.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 ! Smoothness indicator IS-1
+ ZOMP3(:,IS-1:IS,:) = 3./10. / (ZEPS + ZBPOS3(:,IS-1:IS,:))**2 ! Non-normalized weight IS,IS-1
+!
+ ! ----- Negative fluxes -----
+!
+ ! First negative stencil, needs indices i+1, i+2, i+3
+ ZFNEG1(:,IS,:) = 1./6. * (11.0*PSRC(:,IS+1,:) - 7.0*PSRC(:,IS+2,:) + 2.0*PSRC(:,IS+3,:)) ! Flux IS
+ ZFNEG1(:,IS-1,:) = 1./6. * (11.0*PSRC(:,IS,:) - 7.0*PSRC(:,IS+1,:) + 2.0*PSRC(:,IS+2,:)) ! Flux IS-1
+ ZBNEG1(:,IS,:) = 13./12. * ( PSRC(:,IS+1,:) - 2.0*PSRC(:,IS+2,:) + PSRC(:,IS+3,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS+1,:) - 4.0*PSRC(:,IS+2,:) + PSRC(:,IS+3,:))**2 ! Smoothness indicator IS
+ ZBNEG1(:,IS-1,:) = 13./12. * ( PSRC(:,IS,:) - 2.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IS,:) - 4.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 ! Smoothness indicator IS-1
+ ZOMN1(:,IS-1:IS,:) = 1./10. / (ZEPS + ZBNEG1(:,IS-1:IS,:))**2 ! Non-normalized weight IS,IS-1
+!
+ ! Second negative stencil, needs indices i, i+1, i+2
+ ZFNEG2(:,IS,:) = 1./6. * (2.0*PSRC(:,IS,:) + 5.0*PSRC(:,IS+1,:) - 1.0*PSRC(:,IS+2,:)) ! Flux IS
+ ZFNEG2(:,IS-1,:) = 1./6. * (2.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) - 1.0*PSRC(:,IS+1,:)) ! Flux IS-1
+ ZBNEG2(:,IS,:) = 13./12 * (PSRC(:,IS,:) - 2.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2 &
+ + 1./4 * (PSRC(:,IS,:) - PSRC(:,IS+2,:))**2 ! Smoothness indicator IS
+ ZBNEG2(:,IS-1,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (PSRC(:,IS-1,:) - PSRC(:,IS+1,:))**2 ! Smoothness indicator IS-1
+ ZOMN2(:,IS-1:IS,:) = 3./5. / (ZEPS + ZBNEG2(:,IS-1:IS,:))**2 ! Non-normalized weight IS,IS-1
+!
+ ! Third negative stencil, needs indices i-1, i, i+1
+ ZFNEG3(:,IS,:) = 1./6 * (-1.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS,:) + 2.0*PSRC(:,IS+1,:)) ! Flux IS
+ ZFNEG3(:,IS-1,:) = 1./6 * (-1.0*PSRC(:,IS-2,:) + 5.0*PSRC(:,IS-1,:) + 2.0*PSRC(:,IS,:)) ! Flux IS-1
+ ZBNEG3(:,IS,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (PSRC(:,IS-1,:) - 4.0*PSRC(:,IS,:) + 3.0*PSRC(:,IS+1,:))**2 ! Smoothness indicator IS
+ ZBNEG3(:,IS-1,:) = 13./12 * (PSRC(:,IS-2,:) - 2.0*PSRC(:,IS-1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IS-2,:) - 4.0*PSRC(:,IS-1,:) + 3.0*PSRC(:,IS,:))**2 ! Smoothness indicator IS-1
+ ZOMN3(:,IS-1:IS,:) = 3./10. / (ZEPS + ZBNEG3(:,IS-1:IS,:))**2 ! Non-normalized weight IS,IS-1
+!
+ ! ----- Total flux -----
+!
+ PR(:,IS-1:IS,:) = ( ZOMP1(:,IS-1:IS,:)/(ZOMP1(:,IS-1:IS,:)+ZOMP2(:,IS-1:IS,:)+ZOMP3(:,IS-1:IS,:)) * ZFPOS1(:,IS-1:IS,:) &
+ + ZOMP2(:,IS-1:IS,:)/(ZOMP1(:,IS-1:IS,:)+ZOMP2(:,IS-1:IS,:)+ZOMP3(:,IS-1:IS,:)) * ZFPOS2(:,IS-1:IS,:) &
+ + ZOMP3(:,IS-1:IS,:)/(ZOMP1(:,IS-1:IS,:)+ZOMP2(:,IS-1:IS,:)+ZOMP3(:,IS-1:IS,:)) * ZFPOS3(:,IS-1:IS,:)) &
+ * (0.5+SIGN(0.5,PRVCT(:,IS-1:IS,:))) &
+ + ( ZOMN1(:,IS-1:IS,:)/(ZOMN1(:,IS-1:IS,:)+ZOMN2(:,IS-1:IS,:)+ZOMN3(:,IS-1:IS,:)) * ZFNEG1(:,IS-1:IS,:) &
+ + ZOMN2(:,IS-1:IS,:)/(ZOMN1(:,IS-1:IS,:)+ZOMN2(:,IS-1:IS,:)+ZOMN3(:,IS-1:IS,:)) * ZFNEG2(:,IS-1:IS,:) &
+ + ZOMN3(:,IS-1:IS,:)/(ZOMN1(:,IS-1:IS,:)+ZOMN2(:,IS-1:IS,:)+ZOMN3(:,IS-1:IS,:)) * ZFNEG3(:,IS-1:IS,:)) &
+ * (0.5-SIGN(0.5,PRVCT(:,IS-1:IS,:)))
!
- ZFNEG2(:,IS:IN-1,:) = 1./6 * (2.0*PSRC(:,IS:IN-1,:) + 5.0*PSRC(:,IS+1:IN,:) - &
- 1.0*PSRC(:,IS+2:IN+1,:))
- ZFNEG2(:,IS-1,:) = 0.5 * (PSRC(:,IS-1,:) + PSRC(:,IS, :))
- ZFNEG2(:,IN, :) = 0.5 * (PSRC(:,IN, :) + PSRC(:,IN+1,:))
- ZFNEG2(:,IN+1,:) = 0.5 * (PSRC(:,IN+1,:) + TPHALO2%NORTH(:,:))
+ END IF ! NHALO
!
+END IF ! IF(LSOUTH_ll())
!
- ZFNEG3(:,IS:IN-1,:) = 1./6 * (-1.0*PSRC(:,IS-1:IN-2,:) + 5.0*PSRC(:,IS:IN-1,:) + &
- 2.0*PSRC(:,IS+1:IN,:))
+!-------------------------------------------------------------------------------
+!* 1.3. North border
+! ---------------------
!
-! smoothness indicators for positive wind case
+IF(LNORTH_ll() .AND. .FALSE. ) THEN
+ !-----------------------------------------------------------------------------
+ ! North border is physical -- IN-1,IN
+ !-----------------------------------------------------------------------------
+ SELECT CASE (HLBCY(2)) ! Y direction LBC type on north side
+!
+ CASE ('CYCL')
+ !---------------------------------------------------------------------------
+ ! Periodic boundary condition
+ !---------------------------------------------------------------------------
+!
+ IF(LSOUTH_ll() .AND. .FALSE. ) THEN ! South border is physical
+!
+ ! Third positive stencil, needs indices i, i+1, i+2
+ ZFPOS3(:,IN-1,:) = 1./6 * (2.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) - PSRC(:,IN+1,:)) ! Flux IN-1
+ ZFPOS3(:,IN,:) = 1./6 * (2.0*PSRC(:,IN,:) + 5.0*PSRC(:,IN+1,:) - PSRC(:,IS,:)) ! Flux IN
+ ZBPOS3(:,IN-1,:) = 13./12 * ( PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN-1,:) - 4.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 ! Smoothness indicator IN-1
+ ZBPOS3(:,IN,:) = 13./12 * ( PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN,:) - 4.0*PSRC(:,IN+1,:) + PSRC(:,IS,:))**2 ! Smoothness indicator IN
+ ZOMP3(:,IN-1:IN,:) = 3./10. / (ZEPS + ZBPOS3(:,IN-1:IN,:))**2 ! Non-normalized weight IN-1,IN
+!
+ ! First negative stencil, needs indices i+1, i+2, i+3
+ ZFNEG1(:,IN-1,:) = 1./6. * (11.0*PSRC(:,IN,:) - 7.0*PSRC(:,IN+1,:) + 2.0*PSRC(:,IS,:)) ! Flux IN-1
+ ZFNEG1(:,IN,:) = 1./6. * (11.0*PSRC(:,IN+1,:) - 7.0*PSRC(:,IS,:) + 2.0*PSRC(:,IS+1,:)) ! Flux IN
+ ZBNEG1(:,IN-1,:) = 13./12. * ( PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN,:) - 4.0*PSRC(:,IN+1,:) + PSRC(:,IS,:))**2 ! Smoothness indicator IN-1
+ ZBNEG1(:,IN,:) = 13./12. * ( PSRC(:,IN+1,:) - 2.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN+1,:) - 4.0*PSRC(:,IS,:) + PSRC(:,IS+1,:))**2 ! Smoothness indicator IN
+ ZOMN1(:,IN-1:IN,:) = 1./10. / (ZEPS + ZBNEG1(:,IN-1:IN,:))**2 ! Non-normalized weight IN-1,IN
+!
+ ! Second negative stencil, needs indices i, i+1, i+2
+ ZFNEG2(:,IN-1,:) = 1./6. * (2.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) - 1.0*PSRC(:,IN+1,:)) ! Flux IN-1
+ ZFNEG2(:,IN,:) = 1./6. * (2.0*PSRC(:,IN,:) + 5.0*PSRC(:,IN+1,:) - 1.0*PSRC(:,IS,:)) ! Flux IN
+ ZBNEG2(:,IN-1,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (PSRC(:,IN-1,:) - PSRC(:,IN+1,:))**2 ! Smoothness indicator IN-1
+ ZBNEG2(:,IN,:) = 13./12 * (PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IS,:))**2 &
+ + 1./4 * (PSRC(:,IN,:) - PSRC(:,IS,:))**2 ! Smoothness indicator IN
+ ZOMN2(:,IN-1:IN,:) = 3./5. / (ZEPS + ZBNEG2(:,IN-1:IN,:))**2 ! Non-normalized weight IN-1,IN
+!
+ ELSEIF(IN<=SIZE(PSRC,2)-3) THEN ! South boundary is proc border, with minimum 3 HALO points on north side
+!
+ ! Third positive stencil, needs indices i, i+1, i+2
+ ZFPOS3(:,IN-1,:) = 1./6 * (2.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) - PSRC(:,IN+1,:)) ! Flux IN-1
+ ZFPOS3(:,IN,:) = 1./6 * (2.0*PSRC(:,IN,:) + 5.0*PSRC(:,IN+1,:) - PSRC(:,IN+2,:)) ! Flux IN
+ ZBPOS3(:,IN-1,:) = 13./12 * ( PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN-1,:) - 4.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 ! Smoothness indicator IN-1
+ ZBPOS3(:,IN,:) = 13./12 * ( PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN,:) - 4.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 ! Smoothness indicator IN
+ ZOMP3(:,IN-1:IN,:) = 3./10. / (ZEPS + ZBPOS3(:,IN-1:IN,:))**2 ! Non-normalized weight IN-1,IN
+!
+ ! First negative stencil, needs indices i+1, i+2, i+3
+ ZFNEG1(:,IN-1,:) = 1./6. * (11.0*PSRC(:,IN,:) - 7.0*PSRC(:,IN+1,:) + 2.0*PSRC(:,IN+2,:)) ! Flux IN-1
+ ZFNEG1(:,IN,:) = 1./6. * (11.0*PSRC(:,IN+1,:) - 7.0*PSRC(:,IN+2,:) + 2.0*PSRC(:,IN+3,:)) ! Flux IN
+ ZBNEG1(:,IN-1,:) = 13./12. * ( PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN,:) - 4.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 ! Smoothness indicator IN-1
+ ZBNEG1(:,IN,:) = 13./12. * ( PSRC(:,IN+1,:) - 2.0*PSRC(:,IN+2,:) + PSRC(:,IN+3,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN+1,:) - 4.0*PSRC(:,IN+2,:) + PSRC(:,IN+3,:))**2 ! Smoothness indicator IN
+ ZOMN1(:,IN-1:IN,:) = 1./10. / (ZEPS + ZBNEG1(:,IN-1:IN,:))**2 ! Non-normalized weight IN-1,IN
+!
+ ! Second negative stencil, needs indices i, i+1, i+2
+ ZFNEG2(:,IN-1,:) = 1./6. * (2.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) - 1.0*PSRC(:,IN+1,:)) ! Flux IN-1
+ ZFNEG2(:,IN,:) = 1./6. * (2.0*PSRC(:,IN,:) + 5.0*PSRC(:,IN+1,:) - 1.0*PSRC(:,IN+2,:)) ! Flux IN
+ ZBNEG2(:,IN-1,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (PSRC(:,IN-1,:) - PSRC(:,IN+1,:))**2 ! Smoothness indicator IN-1
+ ZBNEG2(:,IN,:) = 13./12 * (PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 &
+ + 1./4 * (PSRC(:,IN,:) - PSRC(:,IN+2,:))**2 ! Smoothness indicator IN
+ ZOMN2(:,IN-1:IN,:) = 3./5. / (ZEPS + ZBNEG2(:,IN-1:IN,:))**2 ! Non-normalized weight IN-1,IN
+!
+ ELSE ! South boundary is proc border, with NHALO < 3 on north side
+ PRINT *,'WARNING : WENO5 fluxes calculation needs NHALO >= 3 on north side'
+ CALL ABORT
+ ENDIF
+!
+ ! First positive stencil, needs indices i-2, i-1, i
+ ZFPOS1(:,IN-1,:) = 1./6. * (2.0*PSRC(:,IN-3,:) - 7.0*PSRC(:,IN-2,:) + 11.0*PSRC(:,IN-1,:)) ! Flux IN-1
+ ZFPOS1(:,IN,:) = 1./6. * (2.0*PSRC(:,IN-2,:) - 7.0*PSRC(:,IN-1,:) + 11.0*PSRC(:,IN,:)) ! Flux IN
+ ZBPOS1(:,IN-1,:) = 13./12. * (PSRC(:,IN-3,:) - 2.0*PSRC(:,IN-2,:) + PSRC(:,IN-1,:))**2 &
+ + 1./4 * (PSRC(:,IN-3,:) - 4.0*PSRC(:,IN-2,:) + 3.0*PSRC(:,IN-1,:))**2 ! Smoothness indicator IN-1
+ ZBPOS1(:,IN,:) = 13./12. * (PSRC(:,IN-2,:) - 2.0*PSRC(:,IN-1,:) + PSRC(:,IN,:))**2 &
+ + 1./4 * (PSRC(:,IN-2,:) - 4.0*PSRC(:,IN-1,:) + 3.0*PSRC(:,IN,:))**2 ! Smoothness indicator IN
+ ZOMP1(:,IN-1:IN,:) = 1./10. / (ZEPS + ZBPOS1(:,IN-1:IN,:))**2 ! Non-normalized weight IN-1,IN
+!
+ ! Second positive stencil, needs indices i-1, i, i+1
+ ZFPOS2(:,IN-1,:) = 1./6. * (-1.0*PSRC(:,IN-2,:) + 5.0*PSRC(:,IN-1,:) + 2.0*PSRC(:,IN,:)) ! Flux IN-1
+ ZFPOS2(:,IN,:) = 1./6. * (-1.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) + 2.0*PSRC(:,IN+1,:)) ! Flux IN
+ ZBPOS2(:,IN-1,:) = 13./12 * (PSRC(:,IN-2,:) - 2.0*PSRC(:,IN-1,:) + PSRC(:,IN,:))**2 &
+ + 1./4 * (PSRC(:,IN-2,:) - PSRC(:,IN,:))**2 ! Smoothness indicator IN-1
+ ZBPOS2(:,IN,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (PSRC(:,IN-1,:) - PSRC(:,IN+1,:))**2 ! Smoothness indicator IN
+ ZOMP2(:,IN-1:IN,:) = 3./5. / (ZEPS + ZBPOS2(:,IN-1:IN,:))**2 ! Non-normalized weight IN-1,IN
+!
+ ! Third negative stencil, needs indices i-1, i, i+1
+ ZFNEG3(:,IN-1,:) = 1./6 * (-1.0*PSRC(:,IN-2,:) + 5.0*PSRC(:,IN-1,:) + 2.0*PSRC(:,IN,:)) ! Flux IN-1
+ ZFNEG3(:,IN,:) = 1./6 * (-1.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) + 2.0*PSRC(:,IN+1,:)) ! Flux IN
+ ZBNEG3(:,IN-1,:) = 13./12 * (PSRC(:,IN-2,:) - 2.0*PSRC(:,IN-1,:) + PSRC(:,IN,:))**2 &
+ + 1./4 * (PSRC(:,IN-2,:) - 4.0*PSRC(:,IN-1,:) + 3.0*PSRC(:,IN,:))**2 ! Smoothness indicator IN-1
+ ZBNEG3(:,IN,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (PSRC(:,IN-1,:) - 4.0*PSRC(:,IN,:) + 3.0*PSRC(:,IN+1,:))**2 ! Smoothness indicator IN
+ ZOMN3(:,IN-1:IN,:) = 3./10. / (ZEPS + ZBNEG3(:,IN-1:IN,:))**2 ! Non-normalized weight IN-1,IN
+!
+ ! ----- Total flux -----
+!
+ PR(:,IN-1:IN,:) = ( ZOMP1(:,IN-1:IN,:)/(ZOMP1(:,IN-1:IN,:)+ZOMP2(:,IN-1:IN,:)+ZOMP3(:,IN-1:IN,:)) * ZFPOS1(:,IN-1:IN,:) &
+ + ZOMP2(:,IN-1:IN,:)/(ZOMP1(:,IN-1:IN,:)+ZOMP2(:,IN-1:IN,:)+ZOMP3(:,IN-1:IN,:)) * ZFPOS2(:,IN-1:IN,:) &
+ + ZOMP3(:,IN-1:IN,:)/(ZOMP1(:,IN-1:IN,:)+ZOMP2(:,IN-1:IN,:)+ZOMP3(:,IN-1:IN,:)) * ZFPOS3(:,IN-1:IN,:)) &
+ * (0.5+SIGN(0.5,PRVCT(:,IN-1:IN,:))) &
+ + ( ZOMN1(:,IN-1:IN,:)/(ZOMN1(:,IN-1:IN,:)+ZOMN2(:,IN-1:IN,:)+ZOMN3(:,IN-1:IN,:)) * ZFNEG1(:,IN-1:IN,:) &
+ + ZOMN2(:,IN-1:IN,:)/(ZOMN1(:,IN-1:IN,:)+ZOMN2(:,IN-1:IN,:)+ZOMN3(:,IN-1:IN,:)) * ZFNEG2(:,IN-1:IN,:) &
+ + ZOMN3(:,IN-1:IN,:)/(ZOMN1(:,IN-1:IN,:)+ZOMN2(:,IN-1:IN,:)+ZOMN3(:,IN-1:IN,:)) * ZFNEG3(:,IN-1:IN,:)) &
+ * (0.5-SIGN(0.5,PRVCT(:,IN-1:IN,:)))
+!
+!
+ CASE ('OPEN','WALL','NEST')
+ !---------------------------------------------------------------------------
+ ! Open, or Wall, or Nest boundary condition => WENO order reduction
+ !---------------------------------------------------------------------------
+!
+ ! WENO scheme order 1, IN
+ PR(:,IN,:) = PSRC(:,IN,:) * (0.5+SIGN(0.5,PRVCT(:,IN,:))) + &
+ PSRC(:,IN+1,:) * &
+ (0.5-SIGN(0.5,PRVCT(:,IN,:)))
!
- ZBPOS1(:,IS+1:IN-1,:) = 13./12 * (PSRC(:,IS-1:IN-3,:) - 2.0*PSRC(:,IS:IN-2,:) +&
- PSRC(:,IS+1:IN-1,:))**2 + &
- 1./4 * (PSRC(:,IS-1:IN-3,:) - 4.0*PSRC(:,IS:IN-2,:) + 3.0*PSRC(:,IS+1:IN-1,:))**2
- ZBPOS1(:,IS, :) = 13./12 * (TPHALO2%SOUTH(:,:) - 2.0*PSRC(:,IS-1,:) +&
- PSRC(:,IS,:))**2 + &
- 1./4 * (TPHALO2%SOUTH(:,:) - 4.0*PSRC(:,IS-1,:) + 3.0*PSRC(:,IS,:))**2
- ZBPOS1(:,IN+1,:) = (PSRC(:,IN+1,:) - PSRC(:,IN, :))**2
- ZBPOS1(:,IN, :) = (PSRC(:,IN, :) - PSRC(:,IN-1,:))**2
- ZBPOS1(:,IS-1,:) = (PSRC(:,IS-1,:) - TPHALO2%SOUTH(:,:))**2
-!
-!
- ZBPOS2(:,IS:IN-1,:) = 13./12 * (PSRC(:,IS-1:IN-2,:) - 2.0*PSRC(:,IS:IN-1,:) + &
- PSRC(:,IS+1:IN,:))**2 + &
- 1./4 * (PSRC(:,IS-1:IN-2,:) - PSRC(:,IS+1:IN,:))**2
- ZBPOS2(:,IS-1,:) = (PSRC(:,IS, :) - PSRC(:,IS-1,:))**2
- ZBPOS2(:,IN, :) = (PSRC(:,IN+1,:) - PSRC(:,IN, :))**2
- ZBPOS2(:,IN+1,:) = (TPHALO2%NORTH(:,:) - PSRC(:,IN+1,:))**2
-!
- ZBPOS3(:,IS:IN-1,:) = 13./12 * (PSRC(:,IS:IN-1,:) - 2.0*PSRC(:,IS+1:IN,:) + &
- PSRC(:,IS+2:IN+1,:))**2 + &
- 1./4 * ( 3.0*PSRC(:,IS:IN-1,:) - 4.0*PSRC(:,IS+1:IN,:) + PSRC(:,IS+2:IN+1,:))**2
-!
-! smoothness indicators for negative wind case
-!
- ZBNEG1(:,IS:IN-2,:) = 13./12 * (PSRC(:,IS+1:IN-1,:) - 2.0*PSRC(:,IS+2:IN,:) + &
- PSRC(:,IS+3:IN+1,:))**2 + &
- 1./4 * ( 3.0*PSRC(:,IS+1:IN-1,:) - 4.0*PSRC(:,IS+2:IN,:) + &
- PSRC(:,IS+3:IN+1,:))**2
- ZBNEG1(:,IN-1,:) = 13./12 * (PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + &
- TPHALO2%NORTH(:,:))**2 + &
- 1./4 * ( 3.0*PSRC(:,IN,:) - 4.0*PSRC(:,IN+1,:) + TPHALO2%NORTH(:,:))**2
- ZBNEG1(:,IS-1,:) = (PSRC(:,IS,:) - PSRC(:,IS+1,:))**2
- ZBNEG1(:,IN+1,:) = - 999.
- ZBNEG1(:,IN, :) = (PSRC(:,IN+1,:) - TPHALO2%NORTH(:,:))**2
-!
- ZBNEG2(:,IS:IN-1,:) = 13./12 * (PSRC(:,IS:IN-1,:) - 2.0*PSRC(:,IS+1:IN,:) + &
- PSRC(:,IS+2:IN+1,:))**2 + &
- 1./4 * (PSRC(:,IS:IN-1,:) - PSRC(:,IS+2:IN+1,:))**2
- ZBNEG2(:,IS-1,:) = (PSRC(:,IS-1,:) - PSRC(:,IS ,:))**2
- ZBNEG2(:,IN, :) = (PSRC(:,IN, :) - PSRC(:,IN+1,:))**2
- ZBNEG2(:,IN+1,:) = (PSRC(:,IN+1,:) - TPHALO2%NORTH(:,:))**2
-!
-!
- ZBNEG3(:,IS:IN-1,:) = 13./12 * (PSRC(:,IS-1:IN-2,:) - 2.0*PSRC(:,IS:IN-1,:) + &
- PSRC(:,IS+1:IN,:))**2 + &
- 1./4 * ( PSRC(:,IS-1:IN-2,:) - 4.0*PSRC(:,IS:IN-1,:) + 3.0*PSRC(:,IS+1:IN,:))**2
+! ! WENO scheme order 3, IN-1
+ ZFPOS1(:,IN-1,:) = 0.5 * (3.0*PSRC(:,IN-1,:) - PSRC(:,IN-2,:)) ! First positive flux
+ ZFPOS2(:,IN-1,:) = 0.5 * ( PSRC(:,IN-1,:) + PSRC(:,IN,:)) ! Second positive flux
+ ZBPOS1(:,IN-1,:) = (PSRC(:,IN-1,:) - PSRC(:,IN-2,:))**2 ! First positive smoothness indicator
+ ZBPOS2(:,IN-1,:) = (PSRC(:,IN,:) - PSRC(:,IN-1,:))**2 ! Second positive smoothness indicator
+!
+ ZFNEG1(:,IN-1,:) = 0.5 * (3.0*PSRC(:,IN,:) - PSRC(:,IN+1,:)) ! First negative flux
+ ZFNEG2(:,IN-1,:) = 0.5 * ( PSRC(:,IN-1,:) + PSRC(:,IN,:)) ! Second negative flux
+ ZBNEG1(:,IN-1,:) = (PSRC(:,IN,:) - PSRC(:,IN+1,:))**2 ! First negative smoothness indicator
+ ZBNEG2(:,IN-1,:) = (PSRC(:,IN-1,:) - PSRC(:,IN,:))**2 ! Second negative smoothness indicator
+!
+ ZOMP1(:,IN-1,:) = 1./3. / (ZEPS + ZBPOS1(:,IN-1,:))**2 ! First positive non-normalized weight
+ ZOMP2(:,IN-1,:) = 2./3. / (ZEPS + ZBPOS2(:,IN-1,:))**2 ! Second positive non-normalized weight
+ ZOMN1(:,IN-1,:) = 1./3. / (ZEPS + ZBNEG1(:,IN-1,:))**2 ! First negative non-normalized weight
+ ZOMN2(:,IN-1,:) = 2./3. / (ZEPS + ZBNEG2(:,IN-1,:))**2 ! Second negative non-normalized weight
+!
+ PR(:,IN-1,:) = (ZOMN2(:,IN-1,:)/(ZOMN1(:,IN-1,:)+ZOMN2(:,IN-1,:))*ZFNEG2(:,IN-1,:) + &
+ (ZOMN1(:,IN-1,:)/(ZOMN1(:,IN-1,:)+ZOMN2(:,IN-1,:))*ZFNEG1(:,IN-1,:))) &
+ *(0.5-SIGN(0.5,PRVCT(:,IN-1,:))) + &
+ (ZOMP2(:,IN-1,:)/(ZOMP1(:,IN-1,:)+ZOMP2(:,IN-1,:))*ZFPOS2(:,IN-1,:) + &
+ (ZOMP1(:,IN-1,:)/(ZOMP1(:,IN-1,:)+ZOMP2(:,IN-1,:))*ZFPOS1(:,IN-1,:))) &
+ * (0.5+SIGN(0.5,PRVCT(:,IN-1,:))) ! Total flux
+!
+ END SELECT ! SELECT CASE (HLBCY(2)) ! Y direction LBC type on north side
+!
+ELSE
+ !-----------------------------------------------------------------------------
+ ! North border is proc border -- IN-1,IN
+ !-----------------------------------------------------------------------------
+!
+ IF (NHALO<3) THEN
+ PRINT *,'WARNING : WENO5 not parallelisable with NHALO < 3'
+ CALL ABORT
+ ELSEIF (NHALO>=3) THEN
+ !---------------------------------------------------------------------------
+ ! NHALO >= 3 => WENO5 for all boundary points
+ !---------------------------------------------------------------------------
+!
+ ! ----- Positive fluxes -----
+!
+ ! First positive stencil, needs indices i-2, i-1, i
+ ZFPOS1(:,IN-1,:) = 1./6. * (2.0*PSRC(:,IN-3,:) - 7.0*PSRC(:,IN-2,:) + 11.0*PSRC(:,IN-1,:)) ! Flux IN-1
+ ZFPOS1(:,IN,:) = 1./6. * (2.0*PSRC(:,IN-2,:) - 7.0*PSRC(:,IN-1,:) + 11.0*PSRC(:,IN,:)) ! Flux IN
+ ZBPOS1(:,IN-1,:) = 13./12. * (PSRC(:,IN-3,:) - 2.0*PSRC(:,IN-2,:) + PSRC(:,IN-1,:))**2 &
+ + 1./4 * (PSRC(:,IN-3,:) - 4.0*PSRC(:,IN-2,:) + 3.0*PSRC(:,IN-1,:))**2 ! Smoothness indicator IN-1
+ ZBPOS1(:,IN,:) = 13./12. * (PSRC(:,IN-2,:) - 2.0*PSRC(:,IN-1,:) + PSRC(:,IN,:))**2 &
+ + 1./4 * (PSRC(:,IN-2,:) - 4.0*PSRC(:,IN-1,:) + 3.0*PSRC(:,IN,:))**2 ! Smoothness indicator IN
+ ZOMP1(:,IN-1:IN,:) = 1./10. / (ZEPS + ZBPOS1(:,IN-1:IN,:))**2 ! Non-normalized weight IN-1,IN
+!
+ ! Second positive stencil, needs indices i-1, i, i+1
+ ZFPOS2(:,IN-1,:) = 1./6. * (-1.0*PSRC(:,IN-2,:) + 5.0*PSRC(:,IN-1,:) + 2.0*PSRC(:,IN,:)) ! Flux IN-1
+ ZFPOS2(:,IN,:) = 1./6. * (-1.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) + 2.0*PSRC(:,IN+1,:)) ! Flux IN
+ ZBPOS2(:,IN-1,:) = 13./12 * (PSRC(:,IN-2,:) - 2.0*PSRC(:,IN-1,:) + PSRC(:,IN,:))**2 &
+ + 1./4 * (PSRC(:,IN-2,:) - PSRC(:,IN,:))**2 ! Smoothness indicator IN-1
+ ZBPOS2(:,IN,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (PSRC(:,IN-1,:) - PSRC(:,IN+1,:))**2 ! Smoothness indicator IN
+ ZOMP2(:,IN-1:IN,:) = 3./5. / (ZEPS + ZBPOS2(:,IN-1:IN,:))**2 ! Non-normalized weight IN-1,IN
+!
+ ! Third positive stencil, needs indices i, i+1, i+2
+ ZFPOS3(:,IN-1,:) = 1./6 * (2.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) - PSRC(:,IN+1,:)) ! Flux IN-1
+ ZFPOS3(:,IN,:) = 1./6 * (2.0*PSRC(:,IN,:) + 5.0*PSRC(:,IN+1,:) - PSRC(:,IN+2,:)) ! Flux IN
+ ZBPOS3(:,IN-1,:) = 13./12 * ( PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN-1,:) - 4.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 ! Smoothness indicator IN-1
+ ZBPOS3(:,IN,:) = 13./12 * ( PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN,:) - 4.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 ! Smoothness indicator IN
+ ZOMP3(:,IN-1:IN,:) = 3./10. / (ZEPS + ZBPOS3(:,IN-1:IN,:))**2 ! Non-normalized weight IN-1,IN
+!
+ ! ----- Negative fluxes -----
+!
+ ! First negative stencil, needs indices i+1, i+2, i+3
+ ZFNEG1(:,IN-1,:) = 1./6. * (11.0*PSRC(:,IN,:) - 7.0*PSRC(:,IN+1,:) + 2.0*PSRC(:,IN+2,:)) ! Flux IN-1
+ ZFNEG1(:,IN,:) = 1./6. * (11.0*PSRC(:,IN+1,:) - 7.0*PSRC(:,IN+2,:) + 2.0*PSRC(:,IN+3,:)) ! Flux IN
+ ZBNEG1(:,IN-1,:) = 13./12. * ( PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN,:) - 4.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 ! Smoothness indicator IN-1
+ ZBNEG1(:,IN,:) = 13./12. * ( PSRC(:,IN+1,:) - 2.0*PSRC(:,IN+2,:) + PSRC(:,IN+3,:))**2 &
+ + 1./4 * (3.0*PSRC(:,IN+1,:) - 4.0*PSRC(:,IN+2,:) + PSRC(:,IN+3,:))**2 ! Smoothness indicator IN
+ ZOMN1(:,IN-1:IN,:) = 1./10. / (ZEPS + ZBNEG1(:,IN-1:IN,:))**2 ! Non-normalized weight IN-1,IN
+!
+ ! Second negative stencil, needs indices i, i+1, i+2
+ ZFNEG2(:,IN-1,:) = 1./6. * (2.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) - 1.0*PSRC(:,IN+1,:)) ! Flux IN-1
+ ZFNEG2(:,IN,:) = 1./6. * (2.0*PSRC(:,IN,:) + 5.0*PSRC(:,IN+1,:) - 1.0*PSRC(:,IN+2,:)) ! Flux IN
+ ZBNEG2(:,IN-1,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (PSRC(:,IN-1,:) - PSRC(:,IN+1,:))**2 ! Smoothness indicator IN-1
+ ZBNEG2(:,IN,:) = 13./12 * (PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + PSRC(:,IN+2,:))**2 &
+ + 1./4 * (PSRC(:,IN,:) - PSRC(:,IN+2,:))**2 ! Smoothness indicator IN
+ ZOMN2(:,IN-1:IN,:) = 3./5. / (ZEPS + ZBNEG2(:,IN-1:IN,:))**2 ! Non-normalized weight IN-1,IN
+!
+ ! Third negative stencil, needs indices i-1, i, i+1
+ ZFNEG3(:,IN-1,:) = 1./6 * (-1.0*PSRC(:,IN-2,:) + 5.0*PSRC(:,IN-1,:) + 2.0*PSRC(:,IN,:)) ! Flux IN-1
+ ZFNEG3(:,IN,:) = 1./6 * (-1.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) + 2.0*PSRC(:,IN+1,:)) ! Flux IN
+ ZBNEG3(:,IN-1,:) = 13./12 * (PSRC(:,IN-2,:) - 2.0*PSRC(:,IN-1,:) + PSRC(:,IN,:))**2 &
+ + 1./4 * (PSRC(:,IN-2,:) - 4.0*PSRC(:,IN-1,:) + 3.0*PSRC(:,IN,:))**2 ! Smoothness indicator IN-1
+ ZBNEG3(:,IN,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2 &
+ + 1./4 * (PSRC(:,IN-1,:) - 4.0*PSRC(:,IN,:) + 3.0*PSRC(:,IN+1,:))**2 ! Smoothness indicator IN
+ ZOMN3(:,IN-1:IN,:) = 3./10. / (ZEPS + ZBNEG3(:,IN-1:IN,:))**2 ! Non-normalized weight IN-1,IN
+!
+ ! ----- Total flux -----
+!
+ PR(:,IN-1:IN,:) = ( ZOMP1(:,IN-1:IN,:) /(ZOMP1(:,IN-1:IN,:) +ZOMP2(:,IN-1:IN,:) +ZOMP3(:,IN-1:IN,:)) * ZFPOS1(:,IN-1:IN,:) &
+ + ZOMP2(:,IN-1:IN,:) /(ZOMP1(:,IN-1:IN,:) +ZOMP2(:,IN-1:IN,:) +ZOMP3(:,IN-1:IN,:)) * ZFPOS2(:,IN-1:IN,:) &
+ + ZOMP3(:,IN-1:IN,:) /(ZOMP1(:,IN-1:IN,:) +ZOMP2(:,IN-1:IN,:) +ZOMP3(:,IN-1:IN,:)) * ZFPOS3(:,IN-1:IN,:)) &
+ * (0.5+SIGN(0.5,PRVCT(:,IN-1:IN,:))) &
+ + ( ZOMN1(:,IN-1:IN,:)/(ZOMN1(:,IN-1:IN,:)+ZOMN2(:,IN-1:IN,:)+ZOMN3(:,IN-1:IN,:)) * ZFNEG1(:,IN-1:IN,:) &
+ + ZOMN2(:,IN-1:IN,:)/(ZOMN1(:,IN-1:IN,:)+ZOMN2(:,IN-1:IN,:)+ZOMN3(:,IN-1:IN,:)) * ZFNEG2(:,IN-1:IN,:) &
+ + ZOMN3(:,IN-1:IN,:)/(ZOMN1(:,IN-1:IN,:)+ZOMN2(:,IN-1:IN,:)+ZOMN3(:,IN-1:IN,:)) * ZFNEG3(:,IN-1:IN,:)) &
+ * (0.5-SIGN(0.5,PRVCT(:,IN-1:IN,:)))
+!
+ END IF ! NHALO
!
-! WENO weights
+END IF ! IF(LNORTH_ll())
+!-------------------------------------------------------------------------------
!
- ZOMP1(:,IS:IN-1,:) = ZGAMMA1 / (ZEPS + ZBPOS1(:,IS:IN-1,:))**2
- ZOMP2(:,IS:IN-1,:) = ZGAMMA2 / (ZEPS + ZBPOS2(:,IS:IN-1,:))**2
- ZOMP3(:,IS:IN-1,:) = ZGAMMA3 / (ZEPS + ZBPOS3(:,IS:IN-1,:))**2
- ZOMN1(:,IS:IN-1,:) = ZGAMMA1 / (ZEPS + ZBNEG1(:,IS:IN-1,:))**2
- ZOMN2(:,IS:IN-1,:) = ZGAMMA2 / (ZEPS + ZBNEG2(:,IS:IN-1,:))**2
- ZOMN3(:,IS:IN-1,:) = ZGAMMA3 / (ZEPS + ZBNEG3(:,IS:IN-1,:))**2
-!
- ZOMP1(:,IS-1,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,IS-1,:))**2
- ZOMP1(:,IN, :) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,IN, :))**2
- ZOMP1(:,IN+1,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,IN+1,:))**2
- ZOMN1(:,IS-1,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,IS-1,:))**2
- ZOMN1(:,IN, :) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,IN, :))**2
- ZOMN1(:,IN+1,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,IN+1,:))**2
- ZOMP2(:,IS-1,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,IS-1,:))**2
- ZOMP2(:,IN, :) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,IN, :))**2
- ZOMP2(:,IN+1,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,IN+1,:))**2
- ZOMN2(:,IS-1,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,IS-1,:))**2
- ZOMN2(:,IN, :) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,IN, :))**2
- ZOMN2(:,IN+1,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,IN+1,:))**2
-!
-! WENO fluxes (5th order)
-!
- PR(:,IS:IN-1,:) = (ZOMP2(:,IS:IN-1,:)/(ZOMP1(:,IS:IN-1,:)+ZOMP2(:,IS:IN-1,:)+&
- ZOMP3(:,IS:IN-1,:)) * ZFPOS2(:,IS:IN-1,:) &
- + ZOMP1(:,IS:IN-1,:)/(ZOMP1(:,IS:IN-1,:)+ZOMP2(:,IS:IN-1,:)+&
- ZOMP3(:,IS:IN-1,:)) * ZFPOS1(:,IS:IN-1,:) &
- + ZOMP3(:,IS:IN-1,:)/(ZOMP1(:,IS:IN-1,:)+ZOMP2(:,IS:IN-1,:)+&
- ZOMP3(:,IS:IN-1,:)) * ZFPOS3(:,IS:IN-1,:))&
- * (0.5+SIGN(0.5,PRVCT(:,IS:IN-1,:))) &
- + (ZOMN2(:,IS:IN-1,:)/(ZOMN1(:,IS:IN-1,:)+ZOMN2(:,IS:IN-1,:)+&
- ZOMN3(:,IS:IN-1,:)) * ZFNEG2(:,IS:IN-1,:) &
- + ZOMN1(:,IS:IN-1,:)/(ZOMN1(:,IS:IN-1,:)+ZOMN2(:,IS:IN-1,:)+&
- ZOMN3(:,IS:IN-1,:)) * ZFNEG1(:,IS:IN-1,:) &
- + ZOMN3(:,IS:IN-1,:)/(ZOMN1(:,IS:IN-1,:)+ZOMN2(:,IS:IN-1,:)+&
- ZOMN3(:,IS:IN-1,:)) * ZFNEG3(:,IS:IN-1,:))&
- * (0.5-SIGN(0.5,PRVCT(:,IS:IN-1,:)))
-!
- PR(:,IS-1,:) = (ZOMP2(:,IS-1,:)/(ZOMP1(:,IS-1,:)+ZOMP2(:,IS-1,:)) * &
- ZFPOS2(:,IS-1,:) &
- + ZOMP1(:,IS-1,:)/(ZOMP1(:,IS-1,:)+ZOMP2(:,IS-1,:)) * &
- ZFPOS1(:,IS-1,:)) * (0.5+SIGN(0.5,PRVCT(:,IS-1,:))) &
- + (ZOMN2(:,IS-1,:)/(ZOMN1(:,IS-1,:)+ZOMN2(:,IS-1,:)) * &
- ZFNEG2(:,IS-1,:) &
- + ZOMN1(:,IS-1,:)/(ZOMN1(:,IS-1,:)+ZOMN2(:,IS-1,:)) * &
- ZFNEG1(:,IS-1,:)) * (0.5-SIGN(0.5,PRVCT(:,IS-1,:)))
-!
- PR(:,IN, :) = (ZOMP2(:,IN, :)/(ZOMP1(:,IN, :)+ZOMP2(:,IN, :)) * &
- ZFPOS2(:,IN, :) &
- + ZOMP1(:,IN, :)/(ZOMP1(:,IN, :)+ZOMP2(:,IN, :)) * &
- ZFPOS1(:,IN, :)) * (0.5+SIGN(0.5,PRVCT(:,IN, :))) &
- + (ZOMN2(:,IN, :)/(ZOMN1(:,IN, :)+ZOMN2(:,IN, :)) * &
- ZFNEG2(:,IN, :) &
- + ZOMN1(:,IN, :)/(ZOMN1(:,IN, :)+ZOMN2(:,IN, :)) * &
- ZFNEG1(:,IN, :)) * (0.5-SIGN(0.5,PRVCT(:,IN, :)))
-!
- PR(:,IN+1,:) = (ZOMP2(:,IN+1,:)/(ZOMP1(:,IN+1,:)+ZOMP2(:,IN+1,:)) * &
- ZFPOS2(:,IN+1,:) &
- + ZOMP1(:,IN+1,:)/(ZOMP1(:,IN+1,:)+ZOMP2(:,IN+1,:)) * &
- ZFPOS1(:,IN+1,:)) * (0.5+SIGN(0.5,PRVCT(:,IN+1,:))) &
- + (ZOMN2(:,IN+1,:)/(ZOMN1(:,IN+1,:)+ZOMN2(:,IN+1,:)) * &
- ZFNEG2(:,IN+1,:) &
- + ZOMN1(:,IN+1,:)/(ZOMN1(:,IN+1,:)+ZOMN2(:,IN+1,:)) * &
- ZFNEG1(:,IN+1,:)) * (0.5-SIGN(0.5,PRVCT(:,IN+1,:)))
-!
-!
-! OPEN, WALL, NEST CASE IN THE Y DIRECTION
-!
-CASE ('OPEN','WALL','NEST')
-!
- IS=IJB
- IN=IJE
-!
-! USE A FIRST ORDER UPSTREAM SCHEME AT THE PHYSICAL BORDER
-!
- IF(LSOUTH_ll()) THEN
- PR(:,IS-1,:) = PSRC(:,IS-1,:) * (0.5+SIGN(0.5,PRVCT(:,IS-1,:))) + &
- PSRC(:,IS,:) * (0.5-SIGN(0.5,PRVCT(:,IS-1,:)))
-!
- ZFPOS1(:,IS,:) = 0.5 * (3.0*PSRC(:,IS,:) - PSRC(:,IS-1,:))
- ZFPOS2(:,IS,:) = 0.5 * (PSRC(:,IS, :) + PSRC(:,IS+1,:))
- ZBPOS1(:,IS,:) = (PSRC(:,IS, :) - PSRC(:,IS-1,:))**2
- ZBPOS2(:,IS,:) = (PSRC(:,IS+1,:) - PSRC(:,IS, :))**2
-!
- ZFNEG1(:,IS,:) = 0.5 * (3.0*PSRC(:,IS+1,:) - PSRC(:,IS+2,:))
- ZFNEG2(:,IS,:) = 0.5 * (PSRC(:,IS, :) + PSRC(:,IS+1,:))
- ZBNEG1(:,IS,:) = (PSRC(:,IS+1,:) - PSRC(:,IS+2,:))**2
- ZBNEG2(:,IS,:) = (PSRC(:,IS, :) - PSRC(:,IS+1,:))**2
-!
- ZOMP1(:,IS,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,IS,:))**2
- ZOMP2(:,IS,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,IS,:))**2
- ZOMN1(:,IS,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,IS,:))**2
- ZOMN2(:,IS,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,IS,:))**2
-!
- PR(:,IS,:) = (ZOMP2(:,IS,:)/(ZOMP1(:,IS,:)+ZOMP2(:,IS,:)) * ZFPOS2(:,IS,:) &
- + ZOMP1(:,IS,:)/(ZOMP1(:,IS,:)+ZOMP2(:,IS,:)) * ZFPOS1(:,IS,:)) *&
- (0.5+SIGN(0.5,PRVCT(:,IS,:))) &
- + (ZOMN2(:,IS,:)/(ZOMN1(:,IS,:)+ZOMN2(:,IS,:)) * ZFNEG2(:,IS,:) &
- + ZOMN1(:,IS,:)/(ZOMN1(:,IS,:)+ZOMN2(:,IS,:)) * ZFNEG1(:,IS,:)) *&
- (0.5-SIGN(0.5,PRVCT(:,IS,:)))
-!
- ELSEIF(NHALO == 1) THEN
- ZFPOS1(:,IS-1,:) = 0.5 * (3.0*PSRC(:,IS-1,:) - TPHALO2%SOUTH(:,:))
- ZFPOS2(:,IS-1,:) = 0.5 * (PSRC(:,IS-1, :) + PSRC(:,IS,:))
- ZBPOS1(:,IS-1,:) = (PSRC(:,IS-1,:) - TPHALO2%SOUTH(:,:))**2
- ZBPOS2(:,IS-1,:) = (PSRC(:,IS, :) - PSRC(:,IS-1,:))**2
-!
- ZFNEG1(:,IS-1,:) = 0.5 * (3.0*PSRC(:,IS,:) - PSRC(:,IS+1,:))
- ZFNEG2(:,IS-1,:) = 0.5 * (PSRC(:,IS-1, :) + PSRC(:,IS, :))
- ZBNEG1(:,IS-1,:) = (PSRC(:,IS, :) - PSRC(:,IS+1,:))**2
- ZBNEG2(:,IS-1,:) = (PSRC(:,IS-1,:) - PSRC(:,IS, :))**2
-!
- ZOMP1(:,IS-1,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,IS-1,:))**2
- ZOMN1(:,IS-1,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,IS-1,:))**2
- ZOMP2(:,IS-1,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,IS-1,:))**2
- ZOMN2(:,IS-1,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,IS-1,:))**2
-!
- PR(:,IS-1,:) = (ZOMP2(:,IS-1,:)/(ZOMP1(:,IS-1,:)+ZOMP2(:,IS-1,:)) * &
- ZFPOS2(:,IS-1,:) &
- + ZOMP1(:,IS-1,:)/(ZOMP1(:,IS-1,:)+ZOMP2(:,IS-1,:)) * &
- ZFPOS1(:,IS-1,:)) * (0.5+SIGN(0.5,PRVCT(:,IS-1,:))) &
- + (ZOMN2(:,IS-1,:)/(ZOMN1(:,IS-1,:)+ZOMN2(:,IS-1,:)) * &
- ZFNEG2(:,IS-1,:) &
- + ZOMN1(:,IS-1,:)/(ZOMN1(:,IS-1,:)+ZOMN2(:,IS-1,:)) * &
- ZFNEG1(:,IS-1,:)) * (0.5-SIGN(0.5,PRVCT(:,IS-1,:)))
-!
- ZFPOS1(:,IS,:) = 1./6 * (2.0*TPHALO2%SOUTH(:,:) - 7.0*PSRC(:,IS-1,:) + &
- 11.0*PSRC(:,IS,:))
- ZFPOS2(:,IS,:) = 1./6 * (-1.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS, :) + &
- 2.0*PSRC(:,IS+1,:))
- ZFPOS3(:,IS,:) = 1./6 * (2.0*PSRC(:,IS, :) + 5.0*PSRC(:,IS+1,:) - &
- 1.0*PSRC(:,IS+2,:))
-!
- ZFNEG1(:,IS,:) = 1./6 * (11.0*PSRC(:,IS+1,:) - 7.0*PSRC(:,IS+2,:) + &
- 2.0*PSRC(:,IS+3,:))
- ZFNEG2(:,IS,:) = 1./6 * (2.0*PSRC(:,IS, :) + 5.0*PSRC(:,IS+1,:) - &
- 1.0*PSRC(:,IS+2,:))
- ZFNEG3(:,IS,:) = 1./6 * (-1.0*PSRC(:,IS-1,:) + 5.0*PSRC(:,IS, :) + &
- 2.0*PSRC(:,IS+1,:))
-!
- ZBPOS1(:,IS,:) = 13./12 * (TPHALO2%SOUTH(:,:) - 2.0*PSRC(:,IS-1,:) + &
- PSRC(:,IS,:))**2 + &
- 1./4 * (TPHALO2%SOUTH(:,:) - 4.0*PSRC(:,IS-1,:) + 3.0*PSRC(:,IS,:))**2
- ZBPOS2(:,IS,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + &
- PSRC(:,IS+1,:))**2 + &
- 1./4 * (PSRC(:,IS-1,:) - PSRC(:,IS+1,:))**2
- ZBPOS3(:,IS,:) = 13./12 * (PSRC(:,IS,:) - 2.0*PSRC(:,IS+1,:) + &
- PSRC(:,IS+2,:))**2 + &
- 1./4 * ( 3.0*PSRC(:,IS,:) - 4.0*PSRC(:,IS+1,:) + PSRC(:,IS+2,:))**2
-!
- ZBNEG1(:,IS,:) = 13./12 * (PSRC(:,IS+1,:) - 2.0*PSRC(:,IS+2,:) + &
- PSRC(:,IS+3,:))**2 + &
- 1./4 * ( 3.0*PSRC(:,IS+1,:) - 4.0*PSRC(:,IS+2,:) + PSRC(:,IS+3,:))**2
- ZBNEG2(:,IS,:) = 13./12 * (PSRC(:,IS,:) - 2.0*PSRC(:,IS+1,:) + &
- PSRC(:,IS+2,:))**2 + &
- 1./4 * (PSRC(:,IS,:) - PSRC(:,IS+2,:))**2
- ZBNEG3(:,IS,:) = 13./12 * (PSRC(:,IS-1,:) - 2.0*PSRC(:,IS,:) + &
- PSRC(:,IS+1,:))**2 + &
- 1./4 * ( PSRC(:,IS-1,:) - 4.0*PSRC(:,IS,:) + 3.0*PSRC(:,IS+1,:))**2
-!
- ZOMP1(:,IS,:) = ZGAMMA1 / (ZEPS + ZBPOS1(:,IS,:))**2
- ZOMP2(:,IS,:) = ZGAMMA2 / (ZEPS + ZBPOS2(:,IS,:))**2
- ZOMP3(:,IS,:) = ZGAMMA3 / (ZEPS + ZBPOS3(:,IS,:))**2
- ZOMN1(:,IS,:) = ZGAMMA1 / (ZEPS + ZBNEG1(:,IS,:))**2
- ZOMN2(:,IS,:) = ZGAMMA2 / (ZEPS + ZBNEG2(:,IS,:))**2
- ZOMN3(:,IS,:) = ZGAMMA3 / (ZEPS + ZBNEG3(:,IS,:))**2
-!
- PR(:,IS,:) = (ZOMP2(:,IS,:)/(ZOMP1(:,IS,:)+ZOMP2(:,IS,:)+ZOMP3(:,IS,:)) * &
- ZFPOS2(:,IS,:) &
- + ZOMP1(:,IS,:)/(ZOMP1(:,IS,:)+ZOMP2(:,IS,:)+ZOMP3(:,IS,:)) * ZFPOS1(:,IS,:)&
- + ZOMP3(:,IS,:)/(ZOMP1(:,IS,:)+ZOMP2(:,IS,:)+ZOMP3(:,IS,:)) * ZFPOS3(:,IS,:))&
- * (0.5+SIGN(0.5,PRVCT(:,IS,:))) &
- + (ZOMN2(:,IS,:)/(ZOMN1(:,IS,:)+ZOMN2(:,IS,:)+ZOMN3(:,IS,:)) * ZFNEG2(:,IS,:)&
- + ZOMN1(:,IS,:)/(ZOMN1(:,IS,:)+ZOMN2(:,IS,:)+ZOMN3(:,IS,:)) * ZFNEG1(:,IS,:)&
- + ZOMN3(:,IS,:)/(ZOMN1(:,IS,:)+ZOMN2(:,IS,:)+ZOMN3(:,IS,:)) * ZFNEG3(:,IS,:))&
- * (0.5-SIGN(0.5,PRVCT(:,IS,:)))
-!
- ENDIF
-!
- IF(LNORTH_ll()) THEN
- PR(:,IN,:) = PSRC(:,IN,:) * (0.5+SIGN(0.5,PRVCT(:,IN,:))) + PSRC(:,IN+1,:) *&
- (0.5-SIGN(0.5,PRVCT(:,IN,:)))
-!
- ZFPOS1(:,IN-1,:) = 0.5 * (3.0*PSRC(:,IN-1,:) - PSRC(:,IN-2,:))
- ZFPOS2(:,IN-1,:) = 0.5 * (PSRC(:,IN-1, :) + PSRC(:,IN, :))
- ZBPOS1(:,IN-1,:) = (PSRC(:,IN-1,:) - PSRC(:,IN-2,:))**2
- ZBPOS2(:,IN-1,:) = (PSRC(:,IN, :) - PSRC(:,IN-1,:))**2
-!
- ZFNEG1(:,IN-1,:) = 0.5 * (3.0*PSRC(:,IN,:) - PSRC(:,IN+1,:))
- ZFNEG2(:,IN-1,:) = 0.5 * (PSRC(:,IN-1, :) + PSRC(:,IN, :))
- ZBNEG1(:,IN-1,:) = (PSRC(:,IN,:) - PSRC(:,IN+1,:))**2
- ZBNEG2(:,IN-1,:) = (PSRC(:,IN-1,:) - PSRC(:,IN,:))**2
-!
- ZOMP1(:,IN-1,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,IN-1,:))**2
- ZOMN1(:,IN-1,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,IN-1,:))**2
- ZOMP2(:,IN-1,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,IN-1,:))**2
- ZOMN2(:,IN-1,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,IN-1,:))**2
-!
- PR(:,IN-1,:) = (ZOMP2(:,IN-1,:)/(ZOMP1(:,IN-1,:)+ZOMP2(:,IN-1,:)) * &
- ZFPOS2(:,IN-1,:) &
- + ZOMP1(:,IN-1,:)/(ZOMP1(:,IN-1,:)+ZOMP2(:,IN-1,:)) * &
- ZFPOS1(:,IN-1,:)) * (0.5+SIGN(0.5,PRVCT(:,IN-1,:))) &
- + (ZOMN2(:,IN-1,:)/(ZOMN1(:,IN-1,:)+ZOMN2(:,IN-1,:)) * &
- ZFNEG2(:,IN-1,:) &
- + ZOMN1(:,IN-1,:)/(ZOMN1(:,IN-1,:)+ZOMN2(:,IN-1,:)) * &
- ZFNEG1(:,IN-1,:)) * (0.5-SIGN(0.5,PRVCT(:,IN-1,:)))
-!
- ELSEIF(NHALO == 1) THEN
- ZFPOS1(:,IN,:) = 0.5 * (3.0*PSRC(:,IN,:) - PSRC(:,IN-1,:))
- ZFPOS2(:,IN,:) = 0.5 * (PSRC(:,IN, :) + PSRC(:,IN+1,:))
- ZBPOS1(:,IN,:) = (PSRC(:,IN, :) - PSRC(:,IN-1,:))**2
- ZBPOS2(:,IN,:) = (PSRC(:,IN+1,:) - PSRC(:,IN, :))**2
-!
- ZFNEG1(:,IN,:) = 0.5 * (3.0*PSRC(:,IN+1,:) - TPHALO2%NORTH(:,:))
- ZFNEG2(:,IN,:) = 0.5 * (PSRC(:,IN, :) + PSRC(:,IN+1,:))
- ZBNEG1(:,IN,:) = (PSRC(:,IN+1,:) - TPHALO2%NORTH(:,:))**2
- ZBNEG2(:,IN,:) = (PSRC(:,IN, :) - PSRC(:,IN+1,:))**2
- !
- ZOMP1(:,IN,:) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,IN,:))**2
- ZOMN1(:,IN,:) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,IN,:))**2
- ZOMP2(:,IN,:) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,IN,:))**2
- ZOMN2(:,IN,:) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,IN,:))**2
-!
- PR(:,IN,:) = (ZOMP2(:,IN,:)/(ZOMP1(:,IN,:)+ZOMP2(:,IN,:)) * ZFPOS2(:,IN,:) &
- + ZOMP1(:,IN,:)/(ZOMP1(:,IN,:)+ZOMP2(:,IN,:)) * ZFPOS1(:,IN,:)) *&
- (0.5+SIGN(0.5,PRVCT(:,IN,:))) &
- + (ZOMN2(:,IN,:)/(ZOMN1(:,IN,:)+ZOMN2(:,IN,:)) * ZFNEG2(:,IN,:) &
- + ZOMN1(:,IN,:)/(ZOMN1(:,IN,:)+ZOMN2(:,IN,:)) * ZFNEG1(:,IN,:)) *&
- (0.5-SIGN(0.5,PRVCT(:,IN,:)))
-!
- ZFPOS1(:,IN-1,:) = 1./6 * (2.0*PSRC(:,IN-3,:) - 7.0*PSRC(:,IN-2,:) + &
- 11.0*PSRC(:,IN-1,:))
- ZFPOS2(:,IN-1,:) = 1./6 * (-1.0*PSRC(:,IN-2,:) + 5.0*PSRC(:,IN-1,:) + &
- 2.0*PSRC(:,IN,:))
- ZFPOS3(:,IN-1,:) = 1./6 * (2.0*PSRC(:,IN-1,:) + 5.0*PSRC(:,IN,:) - &
- 1.0*PSRC(:,IN+1,:))
-!
- ZFNEG1(:,IN-1,:) = 1./6 * (11.0*PSRC(:,IN, :) - 7.0*PSRC(:,IN+1,:) + &
- 2.0*TPHALO2%NORTH(:,:))
- ZFNEG2(:,IN-1,:) = 1./6 * (2.0*PSRC(:,IN-1, :) + 5.0*PSRC(:,IN, :) - &
- 1.0*PSRC(:,IN+1,:))
- ZFNEG3(:,IN-1,:) = 1./6 * (-1.0*PSRC(:,IN-2,:) + 5.0*PSRC(:,IN-1,:) + &
- 2.0*PSRC(:,IN, :))
-!
- ZBPOS1(:,IN-1,:) = 13./12 * (PSRC(:,IN-3,:) - 2.0*PSRC(:,IN-2,:) + &
- PSRC(:,IN-1,:))**2 + &
- 1./4 * (PSRC(:,IN-3,:) - 4.0*PSRC(:,IN-2,:) + 3.0*PSRC(:,IN-1,:))**2
- ZBPOS2(:,IN-1,:) = 13./12 * (PSRC(:,IN-2,:) - 2.0*PSRC(:,IN-1,:) + &
- PSRC(:,IN,:))**2 + &
- 1./4 * (PSRC(:,IN-2,:) - PSRC(:,IN,:))**2
- ZBPOS3(:,IN-1,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + &
- PSRC(:,IN+1,:))**2 + &
- 1./4 * ( 3.0*PSRC(:,IN-1,:) - 4.0*PSRC(:,IN,:) + PSRC(:,IN+1,:))**2
-!
- ZBNEG1(:,IN-1,:) = 13./12 * (PSRC(:,IN,:) - 2.0*PSRC(:,IN+1,:) + &
- TPHALO2%NORTH(:,:))**2 + &
- 1./4 * ( 3.0*PSRC(:,IN,:) - 4.0*PSRC(:,IN+1,:) + TPHALO2%NORTH(:,:))**2
- ZBNEG2(:,IN-1,:) = 13./12 * (PSRC(:,IN-1,:) - 2.0*PSRC(:,IN,:) + &
- PSRC(:,IN+1,:))**2 + &
- 1./4 * (PSRC(:,IN-1,:) - PSRC(:,IN+1,:))**2
- ZBNEG3(:,IN-1,:) = 13./12 * (PSRC(:,IN-2,:) - 2.0*PSRC(:,IN-1,:) + &
- PSRC(:,IN,:))**2 + &
- 1./4 * ( PSRC(:,IN-2,:) - 4.0*PSRC(:,IN-1,:) + 3.0*PSRC(:,IN,:))**2
-!
- ZOMP1(:,IN-1,:) = ZGAMMA1 / (ZEPS + ZBPOS1(:,IN-1,:))**2
- ZOMP2(:,IN-1,:) = ZGAMMA2 / (ZEPS + ZBPOS2(:,IN-1,:))**2
- ZOMP3(:,IN-1,:) = ZGAMMA3 / (ZEPS + ZBPOS3(:,IN-1,:))**2
- ZOMN1(:,IN-1,:) = ZGAMMA1 / (ZEPS + ZBNEG1(:,IN-1,:))**2
- ZOMN2(:,IN-1,:) = ZGAMMA2 / (ZEPS + ZBNEG2(:,IN-1,:))**2
- ZOMN3(:,IN-1,:) = ZGAMMA3 / (ZEPS + ZBNEG3(:,IN-1,:))**2
-!
- PR(:,IN-1,:) = (ZOMP2(:,IN-1,:)/(ZOMP1(:,IN-1,:)+ZOMP2(:,IN-1,:)+ &
- ZOMP3(:,IN-1,:)) * ZFPOS2(:,IN-1,:) &
- + ZOMP1(:,IN-1,:)/(ZOMP1(:,IN-1,:)+ZOMP2(:,IN-1,:)+&
- ZOMP3(:,IN-1,:)) * ZFPOS1(:,IN-1,:) &
- + ZOMP3(:,IN-1,:)/(ZOMP1(:,IN-1,:)+ZOMP2(:,IN-1,:)+&
- ZOMP3(:,IN-1,:)) * ZFPOS3(:,IN-1,:)) &
- * (0.5+SIGN(0.5,PRVCT(:,IN-1,:))) &
- + (ZOMN2(:,IN-1,:)/(ZOMN1(:,IN-1,:)+ZOMN2(:,IN-1,:)+&
- ZOMN3(:,IN-1,:)) * ZFNEG2(:,IN-1,:) &
- + ZOMN1(:,IN-1,:)/(ZOMN1(:,IN-1,:)+ZOMN2(:,IN-1,:)+&
- ZOMN3(:,IN-1,:)) * ZFNEG1(:,IN-1,:) &
- + ZOMN3(:,IN-1,:)/(ZOMN1(:,IN-1,:)+ZOMN2(:,IN-1,:)+&
- ZOMN3(:,IN-1,:)) * ZFNEG3(:,IN-1,:)) &
- * (0.5-SIGN(0.5,PRVCT(:,IN-1,:)))
-!
- ENDIF
-!
- ZFPOS1(:,IS+1:IN-2,:) = 1./6 * (2.0*PSRC(:,IS-1:IN-4,:) - 7.0*PSRC(:,IS:IN-3,:) +&
- 11.0*PSRC(:,IS+1:IN-2,:))
- ZFPOS2(:,IS+1:IN-2,:) = 1./6 * (-1.0*PSRC(:,IS:IN-3,:) + 5.0*PSRC(:,IS+1:IN-2,:)+&
- 2.0*PSRC(:,IS+2:IN-1,:))
- ZFPOS3(:,IS+1:IN-2,:) = 1./6 * (2.0*PSRC(:,IS+1:IN-2,:) + 5.0*PSRC(:,IS+2:IN-1,:)&
- - 1.0*PSRC(:,IS+3:IN,:))
-!
- ZBPOS1(:,IS+1:IN-2,:) = 13./12 * (PSRC(:,IS-1:IN-4,:) - 2.0*PSRC(:,IS:IN-3,:) + &
- PSRC(:,IS+1:IN-2,:))**2 + &
- 1./4 * (PSRC(:,IS-1:IN-4,:) - 4.0*PSRC(:,IS:IN-3,:) + 3.0*PSRC(:,IS+1:IN-2,:))**2
- ZBPOS2(:,IS+1:IN-2,:) = 13./12 * (PSRC(:,IS:IN-3,:) - 2.0*PSRC(:,IS+1:IN-2,:) + &
- PSRC(:,IS+2:IN-1,:))**2 + &
- 1./4 * (PSRC(:,IS:IN-3,:) - PSRC(:,IS+2:IN-1,:))**2
- ZBPOS3(:,IS+1:IN-2,:) = 13./12 * (PSRC(:,IS+1:IN-2,:) - 2.0*PSRC(:,IS+2:IN-1,:) +&
- PSRC(:,IS+3:IN,:))**2 + &
- 1./4 * ( 3.0*PSRC(:,IS+1:IN-2,:) - 4.0*PSRC(:,IS+2:IN-1,:) + &
- PSRC(:,IS+3:IN,:))**2
-!
- ZFNEG1(:,IS+1:IN-2,:) = 1./6 * (11.0*PSRC(:,IS+2:IN-1,:) - &
- 7.0*PSRC(:,IS+3:IN,:) + 2.0*PSRC(:,IS+4:IN+1,:))
- ZFNEG2(:,IS+1:IN-2,:) = 1./6 * (2.0*PSRC(:,IS+1:IN-2,:) + &
- 5.0*PSRC(:,IS+2:IN-1,:) - 1.0*PSRC(:,IS+3:IN,:))
- ZFNEG3(:,IS+1:IN-2,:) = 1./6 * (-1.0*PSRC(:,IS:IN-3,:) + &
- 5.0*PSRC(:,IS+1:IN-2,:) + 2.0*PSRC(:,IS+2:IN-1,:))
-!
- ZBNEG1(:,IS+1:IN-2,:) = 13./12 * (PSRC(:,IS+2:IN-1,:) - &
- 2.0*PSRC(:,IS+3:IN,:) + PSRC(:,IS+4:IN+1,:))**2 + &
- 1./4 * ( 3.0*PSRC(:,IS+2:IN-1,:) - 4.0*PSRC(:,IS+3:IN,:) + &
- PSRC(:,IS+4:IN+1,:))**2
- ZBNEG2(:,IS+1:IN-2,:) = 13./12 * (PSRC(:,IS+1:IN-2,:) - &
- 2.0*PSRC(:,IS+2:IN-1,:) + PSRC(:,IS+3:IN,:))**2 + &
- 1./4 * (PSRC(:,IS+1:IN-2,:) - PSRC(:,IS+3:IN,:))**2
- ZBNEG3(:,IS+1:IN-2,:) = 13./12 * (PSRC(:,IS:IN-3,:) - &
- 2.0*PSRC(:,IS+1:IN-2,:) + PSRC(:,IS+2:IN-1,:))**2 + &
- 1./4 * ( PSRC(:,IS:IN-3,:) - 4.0*PSRC(:,IS+1:IN-2,:) + &
- 3.0*PSRC(:,IS+2:IN-1,:))**2
-!
- ZOMP1(:,IS+1:IN-2,:) = ZGAMMA1 / (ZEPS + ZBPOS1(:,IS+1:IN-2,:))**2
- ZOMP2(:,IS+1:IN-2,:) = ZGAMMA2 / (ZEPS + ZBPOS2(:,IS+1:IN-2,:))**2
- ZOMP3(:,IS+1:IN-2,:) = ZGAMMA3 / (ZEPS + ZBPOS3(:,IS+1:IN-2,:))**2
- ZOMN1(:,IS+1:IN-2,:) = ZGAMMA1 / (ZEPS + ZBNEG1(:,IS+1:IN-2,:))**2
- ZOMN2(:,IS+1:IN-2,:) = ZGAMMA2 / (ZEPS + ZBNEG2(:,IS+1:IN-2,:))**2
- ZOMN3(:,IS+1:IN-2,:) = ZGAMMA3 / (ZEPS + ZBNEG3(:,IS+1:IN-2,:))**2
-!
- PR(:,IS+1:IN-2,:) = (ZOMP2(:,IS+1:IN-2,:)/(ZOMP1(:,IS+1:IN-2,:)+ &
- ZOMP2(:,IS+1:IN-2,:)+ZOMP3(:,IS+1:IN-2,:)) * ZFPOS2(:,IS+1:IN-2,:) &
- + ZOMP1(:,IS+1:IN-2,:)/(ZOMP1(:,IS+1:IN-2,:)+ &
- ZOMP2(:,IS+1:IN-2,:)+ZOMP3(:,IS+1:IN-2,:)) * ZFPOS1(:,IS+1:IN-2,:) &
- + ZOMP3(:,IS+1:IN-2,:)/(ZOMP1(:,IS+1:IN-2,:)+ZOMP2(:,IS+1:IN-2,:)+ &
- ZOMP3(:,IS+1:IN-2,:)) * ZFPOS3(:,IS+1:IN-2,:)) &
- * (0.5+SIGN(0.5,PRVCT(:,IS+1:IN-2,:))) &
- + (ZOMN2(:,IS+1:IN-2,:)/(ZOMN1(:,IS+1:IN-2,:)+ZOMN2(:,IS+1:IN-2,:)+ &
- ZOMN3(:,IS+1:IN-2,:)) * ZFNEG2(:,IS+1:IN-2,:) &
- + ZOMN1(:,IS+1:IN-2,:)/(ZOMN1(:,IS+1:IN-2,:)+ZOMN2(:,IS+1:IN-2,:)+ &
- ZOMN3(:,IS+1:IN-2,:)) * ZFNEG1(:,IS+1:IN-2,:) &
- + ZOMN3(:,IS+1:IN-2,:)/(ZOMN1(:,IS+1:IN-2,:)+ZOMN2(:,IS+1:IN-2,:)+ &
- ZOMN3(:,IS+1:IN-2,:)) * ZFNEG3(:,IS+1:IN-2,:)) &
- * (0.5-SIGN(0.5,PRVCT(:,IS+1:IN-2,:)))
-!
-END SELECT
-!
-PR = PR * PRVCT
+PR = PR * PRVCT ! Add contravariant flux
!
END SUBROUTINE ADVEC_WENO_K_3_VY
!
@@ -2536,6 +2743,7 @@ END SUBROUTINE ADVEC_WENO_K_3_VY
!!
!! MODIFICATIONS
!! -------------
+!! T. Lunet 02/10/2014: Complete code documentation
!!
!-------------------------------------------------------------------------------
!
@@ -2567,7 +2775,6 @@ INTEGER :: IT ! End useful area in x,y,z directions
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZFPOS1, ZFPOS2, ZFPOS3
!
! intermediate reconstruction fluxes for negative wind case
-! we need only one since ZFNEG2 = ZFPOS2
!
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZFNEG1, ZFNEG2, ZFNEG3
!
@@ -2581,14 +2788,8 @@ REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZBNEG1, ZBNEG2, ZBNEG3
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZOMP1, ZOMP2, ZOMP3
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZOMN1, ZOMN2, ZOMN3
!
-! standard weights
-!
-REAL, PARAMETER :: ZGAMMA1 = 1./10.
-REAL, PARAMETER :: ZGAMMA2 = 3./5.
-REAL, PARAMETER :: ZGAMMA3 = 3./10.
-REAL, PARAMETER :: ZGAMMA1_PRIM = 1./3.
-REAL, PARAMETER :: ZGAMMA2_PRIM = 2./3.
-!
+! EPSILON for weno weights calculation
+!
REAL, PARAMETER :: ZEPS = 1.0E-15
!
!-------------------------------------------------------------------------------
@@ -2619,151 +2820,145 @@ ZOMP3 = 0.0
ZOMN1 = 0.0
ZOMN2 = 0.0
ZOMN3 = 0.0
-!
-! r: many left cells in regard to 'k' cell for each stencil
-!
-! intermediate fluxes at the mass point on Wgrid u(i,j,k+1/2) for positive wind
-! case (left to the right)
-! (r=2 for the first stencil ZFPOS1, r=1 for the second ZFPOS2 and
-! r=0 for the last ZFPOS3)
-!
-ZFPOS1(:,:,IB+1:IT-2) = 1./6 * (2.0*PSRC(:,:,IB-1:IT-4) - 7.0*PSRC(:,:,IB:IT-3) + &
- 11.0*PSRC(:,:,IB+1:IT-2))
-ZFPOS1(:,:,IB) = 0.5 * (3.0*PSRC(:,:,IB) - PSRC(:,:,IB-1))
-ZFPOS1(:,:,IT-1) = 0.5 * (3.0*PSRC(:,:,IT-1) - PSRC(:,:,IT-2))
-!
-!
-ZFPOS2(:,:,IB+1:IT-2) = 1./6 * (-1.0*PSRC(:,:,IB:IT-3) + 5.0*PSRC(:,:,IB+1:IT-2) +&
- 2.0*PSRC(:,:,IB+2:IT-1))
-ZFPOS2(:,:,IB) = 0.5 * (PSRC(:,:,IB) + PSRC(:,:,IB+1))
-ZFPOS2(:,:,IT-1) = 0.5 * (PSRC(:,:,IT) + PSRC(:,:,IT+1))
-!
-ZFPOS3(:,:,IB+1:IT-2) = 1./6 * (2.0*PSRC(:,:,IB+1:IT-2) + 5.0*PSRC(:,:,IB+2:IT-1) -&
- 1.0*PSRC(:,:,IB+3:IT))
-!
-! r: many left cells in regard to 'k+1' cell for each stencil
-!
-! intermediate flux at the mass point on Wgrid (i,j,k+1/2)=(i,j,(k+1)-1/2)
-! for negative wind case (right to the left)
-! (r=2 for the last stencil ZFNEG3=ZFPOS2, r=1 for the second ZFNEG2=ZFPOS3
-! and r=0 for the first ZFNEG1)
-!
-ZFNEG1(:,:,IB+1:IT-2) = 1./6 * (11.0*PSRC(:,:,IB+2:IT-1) - 7.0*PSRC(:,:,IB+3:IT) +&
- 2.0*PSRC(:,:,IB+4:IT+1))
-ZFNEG1(:,:,IT-1) = 0.5 * (3.0*PSRC(:,:,IT) - PSRC(:,:,IT+1))
-ZFNEG1(:,:,IB) = 0.5 * (3.0*PSRC(:,:,IB+1) - PSRC(:,:,IB+2))
-!
-!
-ZFNEG2(:,:,IB+1:IT-2) = 1./6 * (2.0*PSRC(:,:,IB+1:IT-2) + 5.0*PSRC(:,:,IB+2:IT-1) -&
- 1.0*PSRC(:,:,IB+3:IT))
-ZFNEG2(:,:,IB) = 0.5 * (PSRC(:,:,IB) + PSRC(:,:,IB+1))
-ZFNEG2(:,:,IT-1) = 0.5 * (PSRC(:,:,IT-1) + PSRC(:,:,IT))
-!
-!
-ZFNEG3(:,:,IB+1:IT-2) = 1./6 * (-1.0*PSRC(:,:,IB:IT-3) + 5.0*PSRC(:,:,IB+1:IT-2) + &
- 2.0*PSRC(:,:,IB+2:IT-1))
-!
-! smoothness indicators for positive wind case
-!
-ZBPOS1(:,:,IB+1:IT-2) = 13./12 * (PSRC(:,:,IB-1:IT-4) - 2.0*PSRC(:,:,IB:IT-3) + &
- PSRC(:,:,IB+1:IT-2))**2 + &
- 1./4 * (PSRC(:,:,IB-1:IT-4) - 4.0*PSRC(:,:,IB:IT-3) + 3.0*PSRC(:,:,IB+1:IT-2))**2
-ZBPOS1(:,:,IB) = (PSRC(:,:,IB) - PSRC(:,:,IB-1))**2
-ZBPOS1(:,:,IT-1) = (PSRC(:,:,IT-1) - PSRC(:,:,IT-2))**2
-!
-!
-ZBPOS2(:,:,IB+1:IT-2) = 13./12 * (PSRC(:,:,IB:IT-3) - 2.0*PSRC(:,:,IB+1:IT-2) + &
- PSRC(:,:,IB+2:IT-1))**2 + &
- 1./4 * (PSRC(:,:,IB:IT-3) - PSRC(:,:,IB+2:IT-1))**2
-ZBPOS2(:,:,IB) = (PSRC(:,:,IB+1) - PSRC(:,:,IB))**2
-ZBPOS2(:,:,IT-1) = (PSRC(:,:,IT) - PSRC(:,:,IT-1))**2
-!
-!
-ZBPOS3(:,:,IB+1:IT-2) = 13./12 * (PSRC(:,:,IB+1:IT-2) - 2.0*PSRC(:,:,IB+2:IT-1) + &
- PSRC(:,:,IB+3:IT))**2 + &
- 1./4 * ( 3.0*PSRC(:,:,IB+1:IT-2) - 4.0*PSRC(:,:,IB+2:IT-1) + PSRC(:,:,IB+3:IT))**2
-!
-! smoothness indicators for negative wind case
-!
-ZBNEG1(:,:,IB+1:IT-2) = 13./12 * (PSRC(:,:,IB+2:IT-1) - 2.0*PSRC(:,:,IB+3:IT) + &
- PSRC(:,:,IB+4:IT+1))**2 + &
- 1./4 * ( 3.0*PSRC(:,:,IB+2:IT-1) - 4.0*PSRC(:,:,IB+3:IT) + PSRC(:,:,IB+4:IT+1))**2
-ZBNEG1(:,:,IB) = (PSRC(:,:,IB+1) - PSRC(:,:,IB+2))**2
-ZBNEG1(:,:,IT-1) = (PSRC(:,:,IT) - PSRC(:,:,IT+1))**2
-!
-ZBNEG2(:,:,IB+1:IT-2) = 13./12 * (PSRC(:,:,IB+1:IT-2) - 2.0*PSRC(:,:,IB+2:IT-1) + &
- PSRC(:,:,IB+3:IT))**2 + &
- 1./4 * (PSRC(:,:,IB+1:IT-2) - PSRC(:,:,IB+3:IT))**2
-ZBNEG2(:,:,IB) = (PSRC(:,:,IB) - PSRC(:,:,IB+1))**2
-ZBNEG2(:,:,IT-1) = (PSRC(:,:,IT-1) - PSRC(:,:,IT))**2
!
+!-------------------------------------------------------------------------------
+!* 1.1. Interior Fluxes
+! ---------------------
!
-ZBNEG3(:,:,IB+1:IT-2) = 13./12 * (PSRC(:,:,IB:IT-3) - 2.0*PSRC(:,:,IB+1:IT-2) + &
- PSRC(:,:,IB+2:IT-1))**2 + &
- 1./4 * ( PSRC(:,:,IB:IT-3) - 4.0*PSRC(:,:,IB+1:IT-2) + 3.0*PSRC(:,:,IB+2:IT-1))**2
+!-------------------------------------------------------------------------------
+! Flux calculation in the physical domain far enough from the boundary
+! WENO scheme order 5, IB+1 -> IT-2
+! Computation at the mass point on Wgrid v(i+1/2,j,k)
+!-------------------------------------------------------------------------------
!
-! WENO weights
+! ----- Positive fluxes -----
+!
+! First positive stencil, needs indices i-2, i-1, i
+ZFPOS1(:,:,IB+1:IT-2) = 1./6. * (2.0*PSRC(:,:,IB-1:IT-4) - 7.0*PSRC(:,:,IB:IT-3) + 11.0*PSRC(:,:,IB+1:IT-2)) ! Flux
+ZBPOS1(:,:,IB+1:IT-2) = 13./12. * ( PSRC(:,:,IB-1:IT-4) - 2.0*PSRC(:,:,IB:IT-3) + PSRC(:,:,IB+1:IT-2))**2 &
+ + 1./4 * ( PSRC(:,:,IB-1:IT-4) - 4.0*PSRC(:,:,IB:IT-3) + 3.0* PSRC(:,:,IB+1:IT-2))**2 ! Smoothness indicator
+ZOMP1(:,:,IB+1:IT-2) = 1./10. / (ZEPS + ZBPOS1(:,:,IB+1:IT-2))**2 ! Non-normalized weight
+!
+! Second positive stencil, needs indices i-1, i, i+1
+ZFPOS2(:,:,IB+1:IT-2) = 1./6. * (-1.0*PSRC(:,:,IB:IT-3) + 5.0*PSRC(:,:,IB+1:IT-2) + 2.0*PSRC(:,:,IB+2:IT-1)) ! Flux
+ZBPOS2(:,:,IB+1:IT-2) = 13./12 * ( PSRC(:,:,IB:IT-3) - 2.0*PSRC(:,:,IB+1:IT-2) + PSRC(:,:,IB+2:IT-1))**2 &
+ + 1./4 * ( PSRC(:,:,IB:IT-3) - PSRC(:,:,IB+2:IT-1))**2 ! Smoothness indicator
+ZOMP2(:,:,IB+1:IT-2) = 3./5. / (ZEPS + ZBPOS2(:,:,IB+1:IT-2))**2 ! Non-normalized weight
+!
+! Third positive stencil, needs indices i, i+1, i+2
+ZFPOS3(:,:,IB+1:IT-2) = 1./6 * (2.0*PSRC(:,:,IB+1:IT-2) + 5.0*PSRC(:,:,IB+2:IT-1) - PSRC(:,:,IB+3:IT)) ! Flux
+ZBPOS3(:,:,IB+1:IT-2) = 13./12 * ( PSRC(:,:,IB+1:IT-2) - 2.0*PSRC(:,:,IB+2:IT-1) + PSRC(:,:,IB+3:IT))**2 &
+ + 1./4 * (3.0*PSRC(:,:,IB+1:IT-2) - 4.0*PSRC(:,:,IB+2:IT-1) + PSRC(:,:,IB+3:IT))**2 ! Smoothness indicator
+ZOMP3(:,:,IB+1:IT-2) = 3./10. / (ZEPS + ZBPOS3(:,:,IB+1:IT-2))**2 ! Non-normalized weight
+!
+! ----- Negative fluxes -----
+!
+! First negative stencil, needs indices i+1, i+2, i+3
+ZFNEG1(:,:,IB+1:IT-2) = 1./6. * (11.0*PSRC(:,:,IB+2:IT-1) - 7.0*PSRC(:,:,IB+3:IT) + 2.0*PSRC(:,:,IB+4:IT+1)) ! Flux
+ZBNEG1(:,:,IB+1:IT-2) = 13./12. * ( PSRC(:,:,IB+2:IT-1) - 2.0*PSRC(:,:,IB+3:IT) + PSRC(:,:,IB+4:IT+1))**2 &
+ + 1./4 * (3.0* PSRC(:,:,IB+2:IT-1) - 4.0*PSRC(:,:,IB+3:IT) + PSRC(:,:,IB+4:IT+1))**2 ! Smoothness indicator
+ZOMN1(:,:,IB+1:IT-2) = 1./10. / (ZEPS + ZBNEG1(:,:,IB+1:IT-2))**2 ! Non-normalized weight
+!
+! Second negative stencil, needs indices i, i+1, i+2
+ZFNEG2(:,:,IB+1:IT-2) = 1./6. * (2.0*PSRC(:,:,IB+1:IT-2) + 5.0*PSRC(:,:,IB+2:IT-1) - 1.0*PSRC(:,:,IB+3:IT)) ! Flux
+ZBNEG2(:,:,IB+1:IT-2) = 13./12 * ( PSRC(:,:,IB+1:IT-2) - 2.0*PSRC(:,:,IB+2:IT-1) + PSRC(:,:,IB+3:IT))**2 &
+ + 1./4 * ( PSRC(:,:,IB+1:IT-2) - PSRC(:,:,IB+3:IT))**2 ! Smoothness indicator
+ZOMN2(:,:,IB+1:IT-2) = 3./5. / (ZEPS + ZBNEG2(:,:,IB+1:IT-2))**2 ! Non-normalized weight
+!
+! Third negative stencil, needs indices i-1, i, i+1
+ZFNEG3(:,:,IB+1:IT-2) = 1./6 * (-1.0*PSRC(:,:,IB:IT-3) + 5.0*PSRC(:,:,IB+1:IT-2) + 2.0*PSRC(:,:,IB+2:IT-1)) ! Flux
+ZBNEG3(:,:,IB+1:IT-2) = 13./12 * ( PSRC(:,:,IB:IT-3) - 2.0*PSRC(:,:,IB+1:IT-2) + PSRC(:,:,IB+2:IT-1))**2 &
+ + 1./4 * ( PSRC(:,:,IB:IT-3) - 4.0*PSRC(:,:,IB+1:IT-2) + 3.0*PSRC(:,:,IB+2:IT-1))**2 ! Smoothness indicator
+ZOMN3(:,:,IB+1:IT-2) = 3./10. / (ZEPS + ZBNEG3(:,:,IB+1:IT-2))**2 ! Non-normalized weight
+!
+!
+! ----- Total flux -----
+!
+PR(:,:,IB+1:IT-2) = (ZOMP1(:,:,IB+1:IT-2)/(ZOMP1(:,:,IB+1:IT-2)+ZOMP2(:,:,IB+1:IT-2)+ZOMP3(:,:,IB+1:IT-2)) &
+ * ZFPOS1(:,:,IB+1:IT-2) + &
+ ZOMP2(:,:,IB+1:IT-2)/(ZOMP1(:,:,IB+1:IT-2)+ZOMP2(:,:,IB+1:IT-2)+ZOMP3(:,:,IB+1:IT-2)) &
+ * ZFPOS2(:,:,IB+1:IT-2) + &
+ ZOMP3(:,:,IB+1:IT-2)/(ZOMP1(:,:,IB+1:IT-2)+ZOMP2(:,:,IB+1:IT-2)+ZOMP3(:,:,IB+1:IT-2)) &
+ * ZFPOS3(:,:,IB+1:IT-2)) &
+ * (0.5+SIGN(0.5,PRWCT(:,:,IB+1:IT-2))) &
+ + (ZOMN1(:,:,IB+1:IT-2)/(ZOMN1(:,:,IB+1:IT-2)+ZOMN2(:,:,IB+1:IT-2)+ZOMN3(:,:,IB+1:IT-2)) &
+ * ZFNEG1(:,:,IB+1:IT-2) &
+ + ZOMN2(:,:,IB+1:IT-2)/(ZOMN1(:,:,IB+1:IT-2)+ZOMN2(:,:,IB+1:IT-2)+ZOMN3(:,:,IB+1:IT-2)) &
+ * ZFNEG2(:,:,IB+1:IT-2) &
+ + ZOMN3(:,:,IB+1:IT-2)/(ZOMN1(:,:,IB+1:IT-2)+ZOMN2(:,:,IB+1:IT-2)+ZOMN3(:,:,IB+1:IT-2)) &
+ * ZFNEG3(:,:,IB+1:IT-2)) &
+ * (0.5-SIGN(0.5,PRWCT(:,:,IB+1:IT-2)))
!
-ZOMP1(:,:,IB+1:IT-2) = ZGAMMA1 / (ZEPS + ZBPOS1(:,:,IB+1:IT-2))**2
-ZOMP2(:,:,IB+1:IT-2) = ZGAMMA2 / (ZEPS + ZBPOS2(:,:,IB+1:IT-2))**2
-ZOMP3(:,:,IB+1:IT-2) = ZGAMMA3 / (ZEPS + ZBPOS3(:,:,IB+1:IT-2))**2
-ZOMN1(:,:,IB+1:IT-2) = ZGAMMA1 / (ZEPS + ZBNEG1(:,:,IB+1:IT-2))**2
-ZOMN2(:,:,IB+1:IT-2) = ZGAMMA2 / (ZEPS + ZBNEG2(:,:,IB+1:IT-2))**2
-ZOMN3(:,:,IB+1:IT-2) = ZGAMMA3 / (ZEPS + ZBNEG3(:,:,IB+1:IT-2))**2
-!
-ZOMP1(:,:, IB) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,:, IB))**2
-ZOMP2(:,:, IB) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,:, IB))**2
-ZOMN1(:,:, IB) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,:, IB))**2
-ZOMN2(:,:, IB) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,:, IB))**2
-ZOMP1(:,:,IT-1) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,:,IT-1))**2
-ZOMP2(:,:,IT-1) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,:,IT-1))**2
-ZOMN1(:,:,IT-1) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,:,IT-1))**2
-ZOMN2(:,:,IT-1) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,:,IT-1))**2
-!
-! WENO fluxes (5th order)
-!
-PR(:,:,IB+1:IT-2) = (ZOMP2(:,:,IB+1:IT-2)/(ZOMP1(:,:,IB+1:IT-2)+&
- ZOMP2(:,:,IB+1:IT-2)+ZOMP3(:,:,IB+1:IT-2)) * ZFPOS2(:,:,IB+1:IT-2) &
- + ZOMP1(:,:,IB+1:IT-2)/(ZOMP1(:,:,IB+1:IT-2)+ZOMP2(:,:,IB+1:IT-2)+ &
- ZOMP3(:,:,IB+1:IT-2)) * ZFPOS1(:,:,IB+1:IT-2) &
- + ZOMP3(:,:,IB+1:IT-2)/(ZOMP1(:,:,IB+1:IT-2)+ZOMP2(:,:,IB+1:IT-2)+ &
- ZOMP3(:,:,IB+1:IT-2)) * ZFPOS3(:,:,IB+1:IT-2)) &
- * (0.5+SIGN(0.5,PRWCT(:,:,IB+1:IT-2))) &
- + (ZOMN2(:,:,IB+1:IT-2)/(ZOMN1(:,:,IB+1:IT-2)+ZOMN2(:,:,IB+1:IT-2)+&
- ZOMN3(:,:,IB+1:IT-2)) * ZFNEG2(:,:,IB+1:IT-2) &
- + ZOMN1(:,:,IB+1:IT-2)/(ZOMN1(:,:,IB+1:IT-2)+ZOMN2(:,:,IB+1:IT-2)+ &
- ZOMN3(:,:,IB+1:IT-2)) * ZFNEG1(:,:,IB+1:IT-2) &
- + ZOMN3(:,:,IB+1:IT-2)/(ZOMN1(:,:,IB+1:IT-2)+ZOMN2(:,:,IB+1:IT-2)+ &
- ZOMN3(:,:,IB+1:IT-2)) * ZFNEG3(:,:,IB+1:IT-2)) &
- * (0.5-SIGN(0.5,PRWCT(:,:,IB+1:IT-2)))
-!
-! WENO fluxes (3rd order)
-!
-PR(:,:,IB) = (ZOMP2(:,:,IB)/(ZOMP1(:,:,IB)+ZOMP2(:,:,IB)) * ZFPOS2(:,:,IB) &
- + ZOMP1(:,:,IB)/(ZOMP1(:,:,IB)+ZOMP2(:,:,IB)) * ZFPOS1(:,:,IB)) * &
- (0.5+SIGN(0.5,PRWCT(:,:,IB) )) &
- + (ZOMN2(:,:,IB)/(ZOMN1(:,:,IB)+ZOMN2(:,:,IB)) * ZFNEG2(:,:,IB) &
- + ZOMN1(:,:,IB)/(ZOMN1(:,:,IB)+ZOMN2(:,:,IB)) * ZFNEG1(:,:,IB)) * &
- (0.5-SIGN(0.5,PRWCT(:,:,IB) ))
-!
-PR(:,:,IT-1) = (ZOMP2(:,:,IT-1)/(ZOMP1(:,:,IT-1)+ZOMP2(:,:,IT-1)) * &
- ZFPOS2(:,:,IT-1) &
- + ZOMP1(:,:,IT-1)/(ZOMP1(:,:,IT-1)+ZOMP2(:,:,IT-1)) * &
- ZFPOS1(:,:,IT-1)) * (0.5+SIGN(0.5,PRWCT(:,:,IT-1) ))&
- + (ZOMN2(:,:,IT-1)/(ZOMN1(:,:,IT-1)+ZOMN2(:,:,IT-1)) * &
- ZFNEG2(:,:,IT-1) &
- + ZOMN1(:,:,IT-1)/(ZOMN1(:,:,IT-1)+ZOMN2(:,:,IT-1)) * &
- ZFNEG1(:,:,IT-1)) * (0.5-SIGN(0.5,PRWCT(:,:,IT-1) ))
+!-------------------------------------------------------------------------------
+!* 1.2. Bottom border
+! ---------------------
+!---------------------------------------------------------------------------
+! WENO order reduction
+!---------------------------------------------------------------------------
!
+! WENO scheme order 1, IB-1
PR(:,:,IB-1) = PSRC(:,:,IB-1) * (0.5+SIGN(0.5,PRWCT(:,:,IB-1) )) &
+ PSRC(:,:,IB ) * (0.5-SIGN(0.5,PRWCT(:,:,IB-1) ))
!
+! ! WENO scheme order 3, IB
+ZFPOS1(:,:,IB) = 0.5 * (3.0*PSRC(:,:,IB) - PSRC(:,:,IB-1)) ! First positive flux
+ZFPOS2(:,:,IB) = 0.5 * ( PSRC(:,:,IB) + PSRC(:,:,IB+1)) ! Second positive flux
+ZBPOS1(:,:,IB) = (PSRC(:,:,IB) - PSRC(:,:,IB-1))**2 ! First positive smoothness indicator
+ZBPOS2(:,:,IB) = (PSRC(:,:,IB+1) - PSRC(:,:,IB))**2 ! Second positive smoothness indicator
+!
+ZFNEG1(:,:,IB) = 0.5 * (3.0*PSRC(:,:,IB+1) - PSRC(:,:,IB+2)) ! First negative flux
+ZFNEG2(:,:,IB) = 0.5 * ( PSRC(:,:,IB) + PSRC(:,:,IB+1)) ! Second negative flux
+ZBNEG1(:,:,IB) = (PSRC(:,:,IB+1) - PSRC(:,:,IB+2))**2 ! First negative smoothness indicator
+ZBNEG2(:,:,IB) = (PSRC(:,:,IB) - PSRC(:,:,IB+1))**2 ! Second negative smoothness indicator
+!
+ZOMP1(:,:,IB) = 1./3. / (ZEPS + ZBPOS1(:,:,IB))**2 ! First positive non-normalized weight
+ZOMP2(:,:,IB) = 2./3. / (ZEPS + ZBPOS2(:,:,IB))**2 ! Second positive non-normalized weight
+ZOMN1(:,:,IB) = 1./3. / (ZEPS + ZBNEG1(:,:,IB))**2 ! First negative non-normalized weight
+ZOMN2(:,:,IB) = 2./3. / (ZEPS + ZBNEG2(:,:,IB))**2 ! Second negative non-normalized weight
+!
+PR(:,:,IB) = (ZOMN2(:,:,IB)/(ZOMN1(:,:,IB)+ZOMN2(:,:,IB)) * ZFNEG2(:,:,IB) + &
+ (ZOMN1(:,:,IB)/(ZOMN1(:,:,IB)+ZOMN2(:,:,IB)) * ZFNEG1(:,:,IB))) &
+ *(0.5-SIGN(0.5,PRWCT(:,:,IB))) + &
+ (ZOMP2(:,:,IB)/(ZOMP1(:,:,IB)+ZOMP2(:,:,IB)) * ZFPOS2(:,:,IB) + &
+ (ZOMP1(:,:,IB)/(ZOMP1(:,:,IB)+ZOMP2(:,:,IB)) * ZFPOS1(:,:,IB))) &
+ *(0.5+SIGN(0.5,PRWCT(:,:,IB))) ! Total flux
+!
+!-------------------------------------------------------------------------------
+!* 1.3. Top border
+! ---------------------
+!
+!---------------------------------------------------------------------------
+! Open, or Wall, or Nest boundary condition => WENO order reduction
+!---------------------------------------------------------------------------
+!
+! WENO scheme order 1, IT
PR(:,:,IT) = PSRC(:,:,IT ) * (0.5+SIGN(0.5,PRWCT(:,:,IT) )) &
+ PSRC(:,:,IT+1) * (0.5-SIGN(0.5,PRWCT(:,:,IT) ))
!
-PR(:,:,IT+1) = -999.
+! ! WENO scheme order 3, IT-1
+ZFPOS1(:,:,IT-1) = 0.5 * (3.0*PSRC(:,:,IT-1) - PSRC(:,:,IT-2)) ! First positive flux
+ZFPOS2(:,:,IT-1) = 0.5 * ( PSRC(:,:,IT-1) + PSRC(:,:,IT)) ! Second positive flux
+ZBPOS1(:,:,IT-1) = (PSRC(:,:,IT-1) - PSRC(:,:,IT-2))**2 ! First positive smoothness indicator
+ZBPOS2(:,:,IT-1) = (PSRC(:,:,IT) - PSRC(:,:,IT-1))**2 ! Second positive smoothness indicator
+!
+ZFNEG1(:,:,IT-1) = 0.5 * (3.0*PSRC(:,:,IT) - PSRC(:,:,IT+1)) ! First negative flux
+ZFNEG2(:,:,IT-1) = 0.5 * ( PSRC(:,:,IT-1) + PSRC(:,:,IT)) ! Second negative flux
+ZBNEG1(:,:,IT-1) = (PSRC(:,:,IT) - PSRC(:,:,IT+1))**2 ! First negative smoothness indicator
+ZBNEG2(:,:,IT-1) = (PSRC(:,:,IT-1) - PSRC(:,:,IT))**2 ! Second negative smoothness indicator
+!
+ZOMP1(:,:,IT-1) = 1./3. / (ZEPS + ZBPOS1(:,:,IT-1))**2 ! First positive non-normalized weight
+ZOMP2(:,:,IT-1) = 2./3. / (ZEPS + ZBPOS2(:,:,IT-1))**2 ! Second positive non-normalized weight
+ZOMN1(:,:,IT-1) = 1./3. / (ZEPS + ZBNEG1(:,:,IT-1))**2 ! First negative non-normalized weight
+ZOMN2(:,:,IT-1) = 2./3. / (ZEPS + ZBNEG2(:,:,IT-1))**2 ! Second negative non-normalized weight
+!
+PR(:,:,IT-1) = (ZOMN2(:,:,IT-1)/(ZOMN1(:,:,IT-1)+ZOMN2(:,:,IT-1))*ZFNEG2(:,:,IT-1) + &
+ (ZOMN1(:,:,IT-1)/(ZOMN1(:,:,IT-1)+ZOMN2(:,:,IT-1))*ZFNEG1(:,:,IT-1))) &
+ *(0.5-SIGN(0.5,PRWCT(:,:,IT-1))) + &
+ (ZOMP2(:,:,IT-1)/(ZOMP1(:,:,IT-1)+ZOMP2(:,:,IT-1))*ZFPOS2(:,:,IT-1) + &
+ (ZOMP1(:,:,IT-1)/(ZOMP1(:,:,IT-1)+ZOMP2(:,:,IT-1))*ZFPOS1(:,:,IT-1))) &
+ * (0.5+SIGN(0.5,PRWCT(:,:,IT-1))) ! Total flux
!
-PR = PR * PRWCT
+PR = PR * PRWCT ! Add contravariant flux
!
END FUNCTION WENO_K_3_WZ
!
@@ -2784,6 +2979,7 @@ END FUNCTION WENO_K_3_WZ
!!
!! MODIFICATIONS
!! -------------
+!! T. Lunet 02/10/2014: Complete code documentation
!!
!-------------------------------------------------------------------------------
!
@@ -2815,7 +3011,6 @@ INTEGER :: IT ! End useful area in x,y,z directions
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZFPOS1, ZFPOS2, ZFPOS3
!
! intermediate reconstruction fluxes for negative wind case
-! we need only one since ZFNEG2 = ZFPOS2
!
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZFNEG1, ZFNEG2, ZFNEG3
!
@@ -2829,14 +3024,8 @@ REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZBNEG1, ZBNEG2, ZBNEG3
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZOMP1, ZOMP2, ZOMP3
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZOMN1, ZOMN2, ZOMN3
!
-! standard weights
-!
-REAL, PARAMETER :: ZGAMMA1 = 1./10.
-REAL, PARAMETER :: ZGAMMA2 = 3./5.
-REAL, PARAMETER :: ZGAMMA3 = 3./10.
-REAL, PARAMETER :: ZGAMMA1_PRIM = 1./3.
-REAL, PARAMETER :: ZGAMMA2_PRIM = 2./3.
-!
+! EPSILON for weno weights calculation
+!
REAL, PARAMETER :: ZEPS = 1.0E-15
!
!-------------------------------------------------------------------------------
@@ -2853,166 +3042,158 @@ ZFPOS1 = 0.0
ZFPOS2 = 0.0
ZFPOS3 = 0.0
ZFNEG1 = 0.0
-ZFNEG2 = 0.0
+ZFNEG2 = 0.0
ZFNEG3 = 0.0
ZBPOS1 = 0.0
ZBPOS2 = 0.0
ZBPOS3 = 0.0
ZBNEG1 = 0.0
ZBNEG2 = 0.0
-ZBNEG3 = 0.0
+ZBNEG3 = 0.0
ZOMP1 = 0.0
ZOMP2 = 0.0
ZOMP3 = 0.0
ZOMN1 = 0.0
ZOMN2 = 0.0
-ZOMN3 = 0.0
-!
-! r: many left cells in regard to 'k-1' cell for each stencil
-!
-! intermediate fluxes at the mass point on Wgrid u(i,j,k-1/2)=(i,j,(k-1)-1/2)
-! for positive wind case (left to the right)
-! (r=2 for the first stencil ZFPOS1, r=1 for the second ZFPOS2 and
-! r=0 for the last ZFPOS3)
-!
-ZFPOS1(:,:,IB+2:IT-1) = 1./6 * (2.0*PSRC(:,:,IB-1:IT-4) - 7.0*PSRC(:,:,IB:IT-3) + &
- 11.0*PSRC(:,:,IB+1:IT-2))
-ZFPOS1(:,:,IB+1) = 0.5 * (3.0*PSRC(:,:, IB) - PSRC(:,:,IB-1))
-ZFPOS1(:,:, IT) = 0.5 * (3.0*PSRC(:,:,IT-1) - PSRC(:,:,IT-2))
-!
-!
-ZFPOS2(:,:,IB+2:IT-1) = 1./6 * (-1.0*PSRC(:,:,IB:IT-3) + 5.0*PSRC(:,:,IB+1:IT-2) + &
- 2.0*PSRC(:,:,IB+2:IT-1))
-ZFPOS2(:,:,IB+1) = 0.5 * (PSRC(:,:, IB) + PSRC(:,:,IB+1))
-ZFPOS2(:,:, IT) = 0.5 * (PSRC(:,:,IT-1) + PSRC(:,:, IT))
-!
-!
-ZFPOS3(:,:,IB+2:IT-1) = 1./6 * (2.0*PSRC(:,:,IB+1:IT-2) + 5.0*PSRC(:,:,IB+2:IT-1) -&
- 1.0*PSRC(:,:,IB+3:IT))
-!
-! r: many left cells in regard to 'k' cell for each stencil
-!
-! intermediate fluxes at the mass point on Ugrid u(i,j,k-1/2) for negative wind
-! case (R. to the L.)
-! (r=2 for the third stencil ZFNEG3=ZFPOS2, r=1 for the second ZFNEG2=ZFPOS3
-! and r=0 for the first ZFNEG1)
-!
-ZFNEG1(:,:,IB+2:IT-1) = 1./6 * (11.0*PSRC(:,:,IB+2:IT-1) - 7.0*PSRC(:,:,IB+3:IT) + &
- 2.0*PSRC(:,:,IB+4:IT+1))
-ZFNEG1(:,:,IB+1) = 0.5 * (3.0*PSRC(:,:,IB+1) - PSRC(:,:,IB+2))
-ZFNEG1(:,:, IT) = 0.5 * (3.0*PSRC(:,:, IT) - PSRC(:,:,IT+1))
-!
-ZFNEG2(:,:,IB+2:IT-1) = 1./6 * (2.0*PSRC(:,:,IB+1:IT-2) + 5.0*PSRC(:,:,IB+2:IT-1) -&
- 1.0*PSRC(:,:,IB+3:IT))
-ZFNEG2(:,:,IB+1) = 0.5 * (PSRC(:,:, IB) + PSRC(:,:,IB+1))
-ZFNEG2(:,:, IT) = 0.5 * (PSRC(:,:,IT-1) + PSRC(:,:, IT))
-!
-!
-ZFNEG3(:,:,IB+2:IT-1) = 1./6 * (-1.0*PSRC(:,:,IB:IT-3) + 5.0*PSRC(:,:,IB+1:IT-2) + &
- 2.0*PSRC(:,:,IB+2:IT-1))
-!
-! smoothness indicators for positive wind case
-!
-ZBPOS1(:,:,IB+2:IT-1) = 13./12 * (PSRC(:,:,IB-1:IT-4) - 2.0*PSRC(:,:,IB:IT-3) + &
- PSRC(:,:,IB+1:IT-2))**2 + &
- 1./4 * (PSRC(:,:,IB-1:IT-4) - 4.0*PSRC(:,:,IB:IT-3) + 3.0*PSRC(:,:,IB+1:IT-2))**2
-ZBPOS1(:,:,IB+1) = (PSRC(:,:, IB) - PSRC(:,:,IB-1))**2
-ZBPOS1(:,:, IT) = (PSRC(:,:,IT-1) - PSRC(:,:,IT-2))**2
-!
-!
-ZBPOS2(:,:,IB+2:IT-1) = 13./12 * (PSRC(:,:,IB:IT-3) - 2.0*PSRC(:,:,IB+1:IT-2) + &
- PSRC(:,:,IB+2:IT-1))**2 + &
- 1./4 * (PSRC(:,:,IB:IT-3) - PSRC(:,:,IB+2:IT-1))**2
-ZBPOS2(:,:,IB+1) = (PSRC(:,:,IB+1) - PSRC(:,:, IB))**2
-ZBPOS2(:,:, IT) = (PSRC(:,:, IT) - PSRC(:,:,IT-1))**2
-!
+ZOMN3 = 0.0
!
-ZBPOS3(:,:,IB+2:IT-1) = 13./12 * (PSRC(:,:,IB+1:IT-2) - 2.0*PSRC(:,:,IB+2:IT-1) + &
- PSRC(:,:,IB+3:IT))**2 + &
- 1./4 * ( 3.0*PSRC(:,:,IB+1:IT-2) - 4.0*PSRC(:,:,IB+2:IT-1) + PSRC(:,:,IB+3:IT))**2
+!-------------------------------------------------------------------------------
+!* 1.1. Interior Fluxes
+! ---------------------
!
-! smoothness indicators for negative wind case
+!-------------------------------------------------------------------------------
+! Flux calculation in the physical domain far enough from the boundary
+! WENO scheme order 5, IB+2 -> IT-1
+! Computation at the mass point on Wgrid v(i-1/2,j,k)
+!-------------------------------------------------------------------------------
!
-ZBNEG1(:,:,IB+2:IT-1) = 13./12 * (PSRC(:,:,IB+2:IT-1) - 2.0*PSRC(:,:,IB+3:IT) + &
- PSRC(:,:,IB+4:IT+1))**2 + &
- 1./4 * ( 3.0*PSRC(:,:,IB+2:IT-1) - 4.0*PSRC(:,:,IB+3:IT) + PSRC(:,:,IB+4:IT+1))**2
-ZBNEG1(:,:,IB+1) = (PSRC(:,:,IB+1) - PSRC(:,:,IB+2))**2
-ZBNEG1(:,:, IT) = (PSRC(:,:, IT) - PSRC(:,:,IT+1))**2
+! ----- Positive fluxes -----
+!
+! First positive stencil, needs indices i-3, i-2, i-1
+ZFPOS1(:,:,IB+2:IT-1) = 1./6. * (2.0*PSRC(:,:,IB-1:IT-4) - 7.0*PSRC(:,:,IB:IT-3) + 11.0*PSRC(:,:,IB+1:IT-2)) ! Flux
+ZBPOS1(:,:,IB+2:IT-1) = 13./12. * ( PSRC(:,:,IB-1:IT-4) - 2.0*PSRC(:,:,IB:IT-3) + PSRC(:,:,IB+1:IT-2))**2 &
+ + 1./4 * ( PSRC(:,:,IB-1:IT-4) - 4.0*PSRC(:,:,IB:IT-3) + 3.0* PSRC(:,:,IB+1:IT-2))**2 ! Smoothness indicator
+ZOMP1(:,:,IB+2:IT-1) = 1./10. / (ZEPS + ZBPOS1(:,:,IB+2:IT-1))**2 ! Non-normalized weight
+!
+! Second positive stencil, needs indices i-2, i-1, i
+ZFPOS2(:,:,IB+2:IT-1) = 1./6. * (-1.0*PSRC(:,:,IB:IT-3) + 5.0*PSRC(:,:,IB+1:IT-2) + 2.0*PSRC(:,:,IB+2:IT-1)) ! Flux
+ZBPOS2(:,:,IB+2:IT-1) = 13./12 * ( PSRC(:,:,IB:IT-3) - 2.0*PSRC(:,:,IB+1:IT-2) + PSRC(:,:,IB+2:IT-1))**2 &
+ + 1./4 * ( PSRC(:,:,IB:IT-3) - PSRC(:,:,IB+2:IT-1))**2 ! Smoothness indicator
+ZOMP2(:,:,IB+2:IT-1) = 3./5. / (ZEPS + ZBPOS2(:,:,IB+2:IT-1))**2 ! Non-normalized weight
+!
+! Third positive stencil, needs indices i-1, i, i+1
+ZFPOS3(:,:,IB+2:IT-1) = 1./6 * (2.0*PSRC(:,:,IB+1:IT-2) + 5.0*PSRC(:,:,IB+2:IT-1) - PSRC(:,:,IB+3:IT)) ! Flux
+ZBPOS3(:,:,IB+2:IT-1) = 13./12 * ( PSRC(:,:,IB+1:IT-2) - 2.0*PSRC(:,:,IB+2:IT-1) + PSRC(:,:,IB+3:IT))**2 &
+ + 1./4 * (3.0*PSRC(:,:,IB+1:IT-2) - 4.0*PSRC(:,:,IB+2:IT-1) + PSRC(:,:,IB+3:IT))**2 ! Smoothness indicator
+ZOMP3(:,:,IB+2:IT-1) = 3./10. / (ZEPS + ZBPOS3(:,:,IB+2:IT-1))**2 ! Non-normalized weight
+!
+! ----- Negative fluxes -----
+!
+! First negative stencil, needs indices i, i+1, i+2
+ZFNEG1(:,:,IB+2:IT-1) = 1./6. * (11.0*PSRC(:,:,IB+2:IT-1) - 7.0*PSRC(:,:,IB+3:IT) + 2.0*PSRC(:,:,IB+4:IT+1)) ! Flux
+ZBNEG1(:,:,IB+2:IT-1) = 13./12. * ( PSRC(:,:,IB+2:IT-1) - 2.0*PSRC(:,:,IB+3:IT) + PSRC(:,:,IB+4:IT+1))**2 &
+ + 1./4 * (3.0* PSRC(:,:,IB+2:IT-1) - 4.0*PSRC(:,:,IB+3:IT) + PSRC(:,:,IB+4:IT+1))**2 ! Smoothness indicator
+ZOMN1(:,:,IB+2:IT-1) = 1./10. / (ZEPS + ZBNEG1(:,:,IB+2:IT-1))**2 ! Non-normalized weight
+!
+! Second negative stencil, needs indices i-1, i, i+1
+ZFNEG2(:,:,IB+2:IT-1) = 1./6. * (2.0*PSRC(:,:,IB+1:IT-2) + 5.0*PSRC(:,:,IB+2:IT-1) - 1.0*PSRC(:,:,IB+3:IT)) ! Flux
+ZBNEG2(:,:,IB+2:IT-1) = 13./12 * ( PSRC(:,:,IB+1:IT-2) - 2.0*PSRC(:,:,IB+2:IT-1) + PSRC(:,:,IB+3:IT))**2 &
+ + 1./4 * ( PSRC(:,:,IB+1:IT-2) - PSRC(:,:,IB+3:IT))**2 ! Smoothness indicator
+ZOMN2(:,:,IB+2:IT-1) = 3./5. / (ZEPS + ZBNEG2(:,:,IB+2:IT-1))**2 ! Non-normalized weight
+!
+! Third negative stencil, needs indices i-2, i-1, i
+ZFNEG3(:,:,IB+2:IT-1) = 1./6 * (-1.0*PSRC(:,:,IB:IT-3) + 5.0*PSRC(:,:,IB+1:IT-2) + 2.0*PSRC(:,:,IB+2:IT-1)) ! Flux
+ZBNEG3(:,:,IB+2:IT-1) = 13./12 * ( PSRC(:,:,IB:IT-3) - 2.0*PSRC(:,:,IB+1:IT-2) + PSRC(:,:,IB+2:IT-1))**2 &
+ + 1./4 * ( PSRC(:,:,IB:IT-3) - 4.0*PSRC(:,:,IB+1:IT-2) + 3.0*PSRC(:,:,IB+2:IT-1))**2 ! Smoothness indicator
+ZOMN3(:,:,IB+2:IT-1) = 3./10. / (ZEPS + ZBNEG3(:,:,IB+2:IT-1))**2 ! Non-normalized weight
+!
+!
+! ----- Total flux -----
+!
+PR(:,:,IB+2:IT-1) = (ZOMP1(:,:,IB+2:IT-1)/(ZOMP1(:,:,IB+2:IT-1)+ZOMP2(:,:,IB+2:IT-1)+ZOMP3(:,:,IB+2:IT-1)) &
+ * ZFPOS1(:,:,IB+2:IT-1) + &
+ ZOMP2(:,:,IB+2:IT-1)/(ZOMP1(:,:,IB+2:IT-1)+ZOMP2(:,:,IB+2:IT-1)+ZOMP3(:,:,IB+2:IT-1)) &
+ * ZFPOS2(:,:,IB+2:IT-1) + &
+ ZOMP3(:,:,IB+2:IT-1)/(ZOMP1(:,:,IB+2:IT-1)+ZOMP2(:,:,IB+2:IT-1)+ZOMP3(:,:,IB+2:IT-1)) &
+ * ZFPOS3(:,:,IB+2:IT-1)) &
+ * (0.5+SIGN(0.5,PRWCT(:,:,IB+2:IT-1))) &
+ + (ZOMN1(:,:,IB+2:IT-1)/(ZOMN1(:,:,IB+2:IT-1)+ZOMN2(:,:,IB+2:IT-1)+ZOMN3(:,:,IB+2:IT-1)) &
+ * ZFNEG1(:,:,IB+2:IT-1) &
+ + ZOMN2(:,:,IB+2:IT-1)/(ZOMN1(:,:,IB+2:IT-1)+ZOMN2(:,:,IB+2:IT-1)+ZOMN3(:,:,IB+2:IT-1)) &
+ * ZFNEG2(:,:,IB+2:IT-1) &
+ + ZOMN3(:,:,IB+2:IT-1)/(ZOMN1(:,:,IB+2:IT-1)+ZOMN2(:,:,IB+2:IT-1)+ZOMN3(:,:,IB+2:IT-1)) &
+ * ZFNEG3(:,:,IB+2:IT-1)) &
+ * (0.5-SIGN(0.5,PRWCT(:,:,IB+2:IT-1)))
!
-ZBNEG2(:,:,IB+2:IT-1) = 13./12 * (PSRC(:,:,IB+1:IT-2) - 2.0*PSRC(:,:,IB+2:IT-1) + &
- PSRC(:,:,IB+3:IT))**2 + &
- 1./4 * (PSRC(:,:,IB+1:IT-2) - PSRC(:,:,IB+3:IT))**2
-ZBNEG2(:,:,IB+1) = (PSRC(:,:, IB) - PSRC(:,:,IB+1))**2
-ZBNEG2(:,:, IT) = (PSRC(:,:,IT-1) - PSRC(:,:, IT))**2
+!-------------------------------------------------------------------------------
+!* 1.2. Bottom border
+! ---------------------
+!---------------------------------------------------------------------------
+! WENO order reduction
+!---------------------------------------------------------------------------
!
+! WENO scheme order 1, IB
+PR(:,:,IB) = PSRC(:,:,IB-1) * (0.5+SIGN(0.5,PRWCT(:,:,IB) )) &
+ + PSRC(:,:,IB ) * (0.5-SIGN(0.5,PRWCT(:,:,IB) ))
!
-ZBNEG3(:,:,IB+2:IT-1) = 13./12 * (PSRC(:,:,IB:IT-3) - 2.0*PSRC(:,:,IB+1:IT-2) + &
- PSRC(:,:,IB+2:IT-1))**2 + &
- 1./4 * ( PSRC(:,:,IB:IT-3) - 4.0*PSRC(:,:,IB+1:IT-2) + 3.0*PSRC(:,:,IB+2:IT-1))**2
+! WENO scheme order 3, IB+1
+ZFPOS1(:,:,IB+1) = 0.5 * (3.0*PSRC(:,:,IB) - PSRC(:,:,IB-1)) ! First positive flux
+ZFPOS2(:,:,IB+1) = 0.5 * ( PSRC(:,:,IB) + PSRC(:,:,IB+1)) ! Second positive flux
+ZBPOS1(:,:,IB+1) = (PSRC(:,:,IB) - PSRC(:,:,IB-1))**2 ! First positive smoothness indicator
+ZBPOS2(:,:,IB+1) = (PSRC(:,:,IB+1) - PSRC(:,:,IB))**2 ! Second positive smoothness indicator
+!
+ZFNEG1(:,:,IB+1) = 0.5 * (3.0*PSRC(:,:,IB+1) - PSRC(:,:,IB+2)) ! First negative flux
+ZFNEG2(:,:,IB+1) = 0.5 * ( PSRC(:,:,IB) + PSRC(:,:,IB+1)) ! Second negative flux
+ZBNEG1(:,:,IB+1) = (PSRC(:,:,IB+1) - PSRC(:,:,IB+2))**2 ! First negative smoothness indicator
+ZBNEG2(:,:,IB+1) = (PSRC(:,:,IB) - PSRC(:,:,IB+1))**2 ! Second negative smoothness indicator
+!
+ZOMP1(:,:,IB+1) = 1./3. / (ZEPS + ZBPOS1(:,:,IB+1))**2 ! First positive non-normalized weight
+ZOMP2(:,:,IB+1) = 2./3. / (ZEPS + ZBPOS2(:,:,IB+1))**2 ! Second positive non-normalized weight
+ZOMN1(:,:,IB+1) = 1./3. / (ZEPS + ZBNEG1(:,:,IB+1))**2 ! First negative non-normalized weight
+ZOMN2(:,:,IB+1) = 2./3. / (ZEPS + ZBNEG2(:,:,IB+1))**2 ! Second negative non-normalized weight
+!
+PR(:,:,IB+1) = (ZOMP2(:,:,IB+1)/(ZOMP1(:,:,IB+1)+ZOMP2(:,:,IB+1)) * ZFPOS2(:,:,IB+1) &
+ + ZOMP1(:,:,IB+1)/(ZOMP1(:,:,IB+1)+ZOMP2(:,:,IB+1)) * ZFPOS1(:,:,IB+1)) * &
+ (0.5+SIGN(0.5,PRWCT(:,:,IB+1) )) &
+ + (ZOMN2(:,:,IB+1)/(ZOMN1(:,:,IB+1)+ZOMN2(:,:,IB+1)) * ZFNEG2(:,:,IB+1) &
+ + ZOMN1(:,:,IB+1)/(ZOMN1(:,:,IB+1)+ZOMN2(:,:,IB+1)) * ZFNEG1(:,:,IB+1)) * &
+ (0.5-SIGN(0.5,PRWCT(:,:,IB+1) )) ! Total flux
+!
+!-------------------------------------------------------------------------------
+!* 1.3. Top border
+! ---------------------
!
-! WENO weights
+!---------------------------------------------------------------------------
+! Open, or Wall, or Nest boundary condition => WENO order reduction
+!---------------------------------------------------------------------------
!
-ZOMP1(:,:,IB+2:IT-1) = ZGAMMA1 / (ZEPS + ZBPOS1(:,:,IB+2:IT-1))**2
-ZOMP2(:,:,IB+2:IT-1) = ZGAMMA2 / (ZEPS + ZBPOS2(:,:,IB+2:IT-1))**2
-ZOMP3(:,:,IB+2:IT-1) = ZGAMMA3 / (ZEPS + ZBPOS3(:,:,IB+2:IT-1))**2
-ZOMN1(:,:,IB+2:IT-1) = ZGAMMA1 / (ZEPS + ZBNEG1(:,:,IB+2:IT-1))**2
-ZOMN2(:,:,IB+2:IT-1) = ZGAMMA2 / (ZEPS + ZBNEG2(:,:,IB+2:IT-1))**2
-ZOMN3(:,:,IB+2:IT-1) = ZGAMMA3 / (ZEPS + ZBNEG3(:,:,IB+2:IT-1))**2
-!
-ZOMP1(:,:,IB+1) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,:,IB+1))**2
-ZOMP2(:,:,IB+1) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,:,IB+1))**2
-ZOMN1(:,:,IB+1) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,:,IB+1))**2
-ZOMN2(:,:,IB+1) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,:,IB+1))**2
-ZOMP1(:,:, IT) = ZGAMMA1_PRIM / (ZEPS + ZBPOS1(:,:, IT))**2
-ZOMP2(:,:, IT) = ZGAMMA2_PRIM / (ZEPS + ZBPOS2(:,:, IT))**2
-ZOMN1(:,:, IT) = ZGAMMA1_PRIM / (ZEPS + ZBNEG1(:,:, IT))**2
-ZOMN2(:,:, IT) = ZGAMMA2_PRIM / (ZEPS + ZBNEG2(:,:, IT))**2
-!
-PR(:,:,IB+2:IT-1) = (ZOMP1(:,:,IB+2:IT-1)/(ZOMP1(:,:,IB+2:IT-1)+ &
- ZOMP2(:,:,IB+2:IT-1)+ZOMP3(:,:,IB+2:IT-1)) * &
- ZFPOS1(:,:,IB+2:IT-1) &
- + ZOMP2(:,:,IB+2:IT-1)/(ZOMP1(:,:,IB+2:IT-1)+ &
- ZOMP2(:,:,IB+2:IT-1)+ZOMP3(:,:,IB+2:IT-1)) * &
- ZFPOS2(:,:,IB+2:IT-1) &
- + ZOMP3(:,:,IB+2:IT-1)/(ZOMP1(:,:,IB+2:IT-1)+ &
- ZOMP2(:,:,IB+2:IT-1)+ZOMP3(:,:,IB+2:IT-1)) * &
- ZFPOS3(:,:,IB+2:IT-1)) &
- * (0.5+SIGN(0.5,PRWCT(:,:,IB+2:IT-1))) &
- + (ZOMN1(:,:,IB+2:IT-1)/(ZOMN1(:,:,IB+2:IT-1)+ &
- ZOMN2(:,:,IB+2:IT-1)+ZOMN3(:,:,IB+2:IT-1)) * &
- ZFNEG1(:,:,IB+2:IT-1) &
- + ZOMN2(:,:,IB+2:IT-1)/(ZOMN1(:,:,IB+2:IT-1)+ &
- ZOMN2(:,:,IB+2:IT-1)+ZOMN3(:,:,IB+2:IT-1)) * &
- ZFNEG2(:,:,IB+2:IT-1) &
- + ZOMN3(:,:,IB+2:IT-1)/(ZOMN1(:,:,IB+2:IT-1)+ &
- ZOMN2(:,:,IB+2:IT-1)+ZOMN3(:,:,IB+2:IT-1)) * &
- ZFNEG3(:,:,IB+2:IT-1)) &
- * (0.5-SIGN(0.5,PRWCT(:,:,IB+2:IT-1) ))
-!
-PR(:,:,IB+1) = (ZOMP2(:,:,IB+1)/(ZOMP1(:,:,IB+1)+ZOMP2(:,:,IB+1)) * &
- ZFPOS2(:,:,IB+1) &
- + ZOMP1(:,:,IB+1)/(ZOMP1(:,:,IB+1)+ZOMP2(:,:,IB+1)) * &
- ZFPOS1(:,:,IB+1)) * (0.5+SIGN(0.5,PRWCT(:,:,IB+1) ))&
- + (ZOMN2(:,:,IB+1)/(ZOMN1(:,:,IB+1)+ZOMN2(:,:,IB+1)) * &
- ZFNEG2(:,:,IB+1) &
- + ZOMN1(:,:,IB+1)/(ZOMN1(:,:,IB+1)+ZOMN2(:,:,IB+1)) * &
- ZFNEG1(:,:,IB+1)) * (0.5-SIGN(0.5,PRWCT(:,:,IB+1) ))
+! WENO scheme order 1, IT+1
+PR(:,:,IT+1) = PSRC(:,:,IT ) * (0.5+SIGN(0.5,PRWCT(:,:,IT+1) )) &
+ + PSRC(:,:,IT+1) * (0.5-SIGN(0.5,PRWCT(:,:,IT+1) ))
!
+! WENO scheme order 3, IT
+ZFPOS1(:,:,IT) = 0.5 * (3.0*PSRC(:,:,IT-1) - PSRC(:,:,IT-2)) ! First positive flux
+ZFPOS2(:,:,IT) = 0.5 * ( PSRC(:,:,IT-1) + PSRC(:,:,IT)) ! Second positive flux
+ZBPOS1(:,:,IT) = (PSRC(:,:,IT-1) - PSRC(:,:,IT-2))**2 ! First positive smoothness indicator
+ZBPOS2(:,:,IT) = (PSRC(:,:,IT) - PSRC(:,:,IT-1))**2 ! Second positive smoothness indicator
+!
+ZFNEG1(:,:,IT) = 0.5 * (3.0*PSRC(:,:,IT) - PSRC(:,:,IT+1)) ! First negative flux
+ZFNEG2(:,:,IT) = 0.5 * ( PSRC(:,:,IT-1) + PSRC(:,:,IT)) ! Second negative flux
+ZBNEG1(:,:,IT) = (PSRC(:,:,IT) - PSRC(:,:,IT+1))**2 ! First negative smoothness indicator
+ZBNEG2(:,:,IT) = (PSRC(:,:,IT-1) - PSRC(:,:,IT))**2 ! Second negative smoothness indicator
+!
+ZOMP1(:,:,IT) = 1./3. / (ZEPS + ZBPOS1(:,:,IT))**2 ! First positive non-normalized weight
+ZOMP2(:,:,IT) = 2./3. / (ZEPS + ZBPOS2(:,:,IT))**2 ! Second positive non-normalized weight
+ZOMN1(:,:,IT) = 1./3. / (ZEPS + ZBNEG1(:,:,IT))**2 ! First negative non-normalized weight
+ZOMN2(:,:,IT) = 2./3. / (ZEPS + ZBNEG2(:,:,IT))**2 ! Second negative non-normalized weight
+!
PR(:,:,IT) = (ZOMP2(:,:,IT)/(ZOMP1(:,:,IT)+ZOMP2(:,:,IT)) * ZFPOS2(:,:,IT) &
+ ZOMP1(:,:,IT)/(ZOMP1(:,:,IT)+ZOMP2(:,:,IT)) * ZFPOS1(:,:,IT)) * &
(0.5+SIGN(0.5,PRWCT(:,:,IT) )) &
+ (ZOMN2(:,:,IT)/(ZOMN1(:,:,IT)+ZOMN2(:,:,IT)) * ZFNEG2(:,:,IT) &
+ ZOMN1(:,:,IT)/(ZOMN1(:,:,IT)+ZOMN2(:,:,IT)) * ZFNEG1(:,:,IT)) * &
- (0.5-SIGN(0.5,PRWCT(:,:,IT) ))
-!
-PR(:,:,IB) = PSRC(:,:,IB-1) * (0.5+SIGN(0.5,PRWCT(:,:,IB) )) &
- + PSRC(:,:,IB ) * (0.5-SIGN(0.5,PRWCT(:,:,IB) ))
-!
-PR(:,:,IT+1) = PSRC(:,:,IT ) * (0.5+SIGN(0.5,PRWCT(:,:,IT+1) )) &
- + PSRC(:,:,IT+1) * (0.5-SIGN(0.5,PRWCT(:,:,IT+1) ))
-!
-!PR(:,:,IB-1) = - 999.
+ (0.5-SIGN(0.5,PRWCT(:,:,IT) )) ! Total flux
!
-PR = PR * PRWCT
+PR = PR * PRWCT ! Add contravariant flux
!
END FUNCTION WENO_K_3_MZ
--
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