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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
call Print_msg(NVERB_FATAL,'GEN','ADVEC_WENO_K_3_MX','WENO5/CYCL fluxes calculation needs JPHEXT (&NHALO) >= 3 on west side')
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! 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
call Print_msg(NVERB_FATAL,'GEN','ADVEC_WENO_K_3_MX','WENO5/west-int not parallelisable with NHALO < 3')
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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,:,:)))
END IF ! NHALO
END IF ! IF(LWEST_ll())
!-------------------------------------------------------------------------------
!* 1.3. East border
! ---------------------
!! IF(LEAST_ll() .AND. .FALSE. ) THEN
IF(LEAST_ll() ) THEN
!-----------------------------------------------------------------------------
! East border is physical -- IE,IE+1
!-----------------------------------------------------------------------------
SELECT CASE (HLBCX(2)) ! X direction LBC type on right side
!
CASE ('CYCL')
!---------------------------------------------------------------------------
! Periodic boundary condition
!---------------------------------------------------------------------------
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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
call Print_msg(NVERB_FATAL,'GEN','ADVEC_WENO_K_3_MX','WENO5/CYCL fluxes calculation needs JPHEXT (&NHALO) >= 3 on east side')
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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,:,:)))
!
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! ! 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
call Print_msg(NVERB_FATAL,'GEN','ADVEC_WENO_K_3_MX','WENO5/east-int not parallelisable with NHALO < 3')
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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)
! ########################################################################
!!
!!**** Computes PRVCT * PUT (or PRVCT * PWT). Upstream fluxes of U (or W)
!! variables in Y direction.
!! Input PUT is on U Grid 'ie' (i,j,k) based on UGRID reference
!! Output PR is on mass Grid 'ie' (i,j-1/2,k) based on UGRID reference
!!
!! AUTHOR
!! ------
!! F. Visentin *CNRS/LA*
!!
!! 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 : 02/10/2015 : correction on CYCL/OPEN boundaries
!!
!-------------------------------------------------------------------------------
!
USE MODD_CONF
USE MODD_LUNIT
!
USE MODE_ll
use mode_msg
!
IMPLICIT NONE
!
!* 0.1 Declarations of dummy arguments :
!
CHARACTER (LEN=4), DIMENSION(2), INTENT(IN) :: HLBCY ! Y direction LBC type
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSRC ! variable on U grid at t
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRVCT ! contrav. comp. on MASS GRID
!
! output source term
!
REAL, DIMENSION(:,:,:), INTENT(OUT) :: PR
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!
!* 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:: 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
!
REAL, DIMENSION(SIZE(PSRC,1),SIZE(PSRC,2),SIZE(PSRC,3)):: ZFNEG1, ZFNEG2, ZFNEG3
!
! smoothness indicators for positive wind case
!
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
!
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
!
! EPSILON for weno weights calculation
!
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REAL, PARAMETER :: ZEPS = 1.0E-15
!
!-----------------------------------------------------------------------------
!
!* 0.3. COMPUTES THE DOMAIN DIMENSIONS
! ------------------------------
!
CALL GET_INDICE_ll(IIB,IJB,IIE,IJE)
!
!---------------------------------------------------------------------------
!
!* 0.4. INITIALIZE THE FIELD
! ---------------------
!
PR(:,:,:) = 0.0
!
ZFPOS1 = 0.0
ZFPOS2 = 0.0
ZFPOS3 = 0.0
ZFNEG1 = 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
ZOMP1 = 0.0
ZOMP2 = 0.0
ZOMP3 = 0.0
ZOMN1 = 0.0
ZOMN2 = 0.0
ZOMN3 = 0.0
!
!-------------------------------------------------------------------------------
!* 1.1. Interior Fluxes
! ---------------------
IS=IJB
IN=IJE
!-------------------------------------------------------------------------------
! 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)
!-------------------------------------------------------------------------------
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! ----- 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
! ---------------------
!! IF(LSOUTH_ll() .AND. .FALSE. ) THEN
IF(LSOUTH_ll()) THEN
!-----------------------------------------------------------------------------
! South border is physical -- IS+1,IS
!-----------------------------------------------------------------------------
SELECT CASE (HLBCY(1)) ! Y direction LBC type on south side
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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
call Print_msg(NVERB_FATAL,'GEN','ADVEC_WENO_K_3_MY','WENO5/CYCL fluxes calculation needs JPHEXT (&NHALO) >= 3 on south side')
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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
call Print_msg(NVERB_FATAL,'GEN','ADVEC_WENO_K_3_MY','WENO5/south-int not parallelisable with NHALO < 3')
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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,:)))
END IF ! NHALO
END IF ! IF(LSOUTH_ll())
!-------------------------------------------------------------------------------
!* 1.3. East border
! ---------------------
!! IF(LNORTH_ll() .AND. .FALSE. ) THEN
IF( LNORTH_ll() ) THEN
!-----------------------------------------------------------------------------
! North border is physical -- IN,IN+1
!-----------------------------------------------------------------------------
SELECT CASE (HLBCY(2)) ! Y direction LBC type on north side
!
CASE ('CYCL')
!---------------------------------------------------------------------------
! Periodic boundary condition
!---------------------------------------------------------------------------
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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
call Print_msg(NVERB_FATAL,'GEN','ADVEC_WENO_K_3_MY','WENO5/CYCL fluxes calculation needs JPHEXT (&NHALO) >= 3 on south side')
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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,:)))
!
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! ! 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
call Print_msg(NVERB_FATAL,'GEN','ADVEC_WENO_K_3_MY','WENO5/north-int not parallelisable with NHALO < 3')
ELSEIF (NHALO>=3) THEN
!---------------------------------------------------------------------------
! NHALO >= 3 => WENO5 for all boundary points
!---------------------------------------------------------------------------
!
! ----- Positive fluxes -----
!
! First positive stencil, needs indices i-3, i-2, i-1