C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_u3c4_impl_r.F,v 1.12 2016/10/05 18:43:36 jmc Exp $ C $Name: $ #include "GAD_OPTIONS.h" CBOP C !ROUTINE: GAD_U3C4_IMPL_R C !INTERFACE: SUBROUTINE GAD_U3C4_IMPL_R( I bi,bj,k, iMin,iMax,jMin,jMax, I advectionScheme, deltaTarg, rTrans, recip_hFac, O a5d, b5d, c5d, d5d, e5d, I myThid ) C !DESCRIPTION: C Compute matrix element to solve vertical advection implicitly C using 3rd order upwind advection scheme, C or 3rd order Direct Space and Time advection scheme, C or 4th order Centered advection scheme. C Method: C contribution of vertical transport at interface k is added C to matrix lines k and k-1 C !USES: IMPLICIT NONE C == Global variables === #include "SIZE.h" #include "GRID.h" #include "EEPARAMS.h" #include "PARAMS.h" #include "GAD.h" C !INPUT/OUTPUT PARAMETERS: C == Routine Arguments == C bi,bj :: tile indices C k :: vertical level C iMin,iMax :: computation domain C jMin,jMax :: computation domain C advectionScheme :: advection scheme to use C deltaTarg :: time step C rTrans :: vertical volume transport C recip_hFac :: inverse of cell open-depth factor C a5d :: 2nd lower diag of pentadiagonal matrix C b5d :: 1rst lower diag of pentadiagonal matrix C c5d :: main diag of pentadiagonal matrix C d5d :: 1rst upper diag of pentadiagonal matrix C e5d :: 2nd upper diag of pentadiagonal matrix C myThid :: thread number INTEGER bi,bj,k INTEGER iMin,iMax,jMin,jMax INTEGER advectionScheme _RL deltaTarg(Nr) _RL rTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RS recip_hFac(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL a5d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL b5d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL c5d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL d5d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL e5d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) INTEGER myThid C == Local Variables == C i,j :: loop indices C kp1 :: =min( k+1 , Nr ) C km2 :: =max( k-2 , 1 ) C rCenter :: centered contribution C rUpwind :: upwind contribution C rC4km, rC4kp :: high order contribution C rHigh :: high order term factor LOGICAL flagC4 INTEGER i,j,kp1,km2 #if (defined ALLOW_AUTODIFF defined TARGET_NEC_SX) _RL rC4km2D (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL rC4kp2D (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL rCenter2D(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL rUpwind2D(1-OLx:sNx+OLx,1-OLy:sNy+OLy) #endif _RL wCFL, rCenter, rUpwind _RL rC4km, rC4kp, rHigh _RL mskM, mskP, maskM2, maskP1 _RL deltaTcfl CEOP C-- process interior interface only: IF ( k.GT.1 .AND. k.LE.Nr ) THEN km2=MAX(1,k-2) kp1=MIN(Nr,k+1) maskP1 = 1. _d 0 maskM2 = 1. _d 0 IF ( k.LE.2 ) maskM2 = 0. _d 0 IF ( k.GE.Nr) maskP1 = 0. _d 0 flagC4 = advectionScheme.EQ.ENUM_CENTERED_4TH & .AND. k.GT.2 .AND. k.LT.Nr C-- Add centered, upwind and high-order contributions deltaTcfl = deltaTarg(k) #if (defined ALLOW_AUTODIFF defined TARGET_NEC_SX) DO j=jMin,jMax DO i=iMin,iMax rCenter2D(i,j) = & 0.5 _d 0 *rTrans(i,j)*recip_rA(i,j,bi,bj)*rkSign mskM = maskC(i,j,km2,bi,bj)*maskM2 mskP = maskC(i,j,kp1,bi,bj)*maskP1 IF ( flagC4 .AND. mskM*mskP.GT.0. _d 0 ) THEN rUpwind2D(i,j) = 0. _d 0 rC4km2D (i,j) = oneSixth*rCenter*mskM rC4kp2D (i,j) = oneSixth*rCenter*mskP ELSEIF ( advectionScheme.EQ.ENUM_DST3 ) THEN wCFL = deltaTcfl*ABS(rTrans(i,j)) & *recip_rA(i,j,bi,bj)*recip_drC(k) & *recip_deepFac2F(k)*recip_rhoFacF(k) rHigh = (1. _d 0 -wCFL*wCFL)*oneSixth c rUpwind2D(i,j) = (2. _d 0*rHigh - wCFL)*ABS(rCenter) rUpwind2D(i,j) = (2. _d 0*rHigh )*ABS(rCenter) rC4km2D (i,j) = rHigh * (rCenter+ABS(rCenter))*mskM rC4kp2D (i,j) = rHigh * (rCenter-ABS(rCenter))*mskP ELSE rUpwind2D(i,j) = 2. _d 0*oneSixth*ABS(rCenter) rC4km2D (i,j) = oneSixth*(rCenter+ABS(rCenter))*mskM rC4kp2D (i,j) = oneSixth*(rCenter-ABS(rCenter))*mskP ENDIF ENDDO ENDDO #endif /* ALLOW_AUTODIFF and TARGET_NEC_SX */ DO j=jMin,jMax DO i=iMin,iMax #if (defined ALLOW_AUTODIFF defined TARGET_NEC_SX) rC4km = rC4km2D (i,j) rC4kp = rC4kp2D (i,j) rCenter = rCenter2D(i,j) rUpwind = rUpwind2D(i,j) #else rCenter= 0.5 _d 0 *rTrans(i,j)*recip_rA(i,j,bi,bj)*rkSign mskM = maskC(i,j,km2,bi,bj)*maskM2 mskP = maskC(i,j,kp1,bi,bj)*maskP1 IF ( flagC4 .AND. mskM*mskP.GT.0. _d 0 ) THEN rUpwind= 0. _d 0 rC4km = oneSixth*rCenter*mskM rC4kp = oneSixth*rCenter*mskP ELSEIF ( advectionScheme.EQ.ENUM_DST3 ) THEN wCFL = deltaTcfl*ABS(rTrans(i,j)) & *recip_rA(i,j,bi,bj)*recip_drC(k) & *recip_deepFac2F(k)*recip_rhoFacF(k) rHigh = (1. _d 0 -wCFL*wCFL)*oneSixth c rUpwind= (2. _d 0*rHigh - wCFL)*ABS(rCenter) rUpwind= (2. _d 0*rHigh )*ABS(rCenter) rC4km = rHigh * (rCenter+ABS(rCenter))*mskM rC4kp = rHigh * (rCenter-ABS(rCenter))*mskP ELSE rUpwind= 2. _d 0*oneSixth*ABS(rCenter) rC4km = oneSixth*(rCenter+ABS(rCenter))*mskM rC4kp = oneSixth*(rCenter-ABS(rCenter))*mskP ENDIF #endif /* ALLOW_AUTODIFF and TARGET_NEC_SX */ a5d(i,j,k) = a5d(i,j,k) & + rC4km & *deltaTarg(k) & *recip_hFac(i,j,k)*recip_drF(k) & *recip_deepFac2C(k)*recip_rhoFacC(k) b5d(i,j,k) = b5d(i,j,k) & - ( (rCenter+rUpwind) + rC4km ) & *deltaTarg(k) & *recip_hFac(i,j,k)*recip_drF(k) & *recip_deepFac2C(k)*recip_rhoFacC(k) c5d(i,j,k) = c5d(i,j,k) & - ( (rCenter-rUpwind) + rC4kp ) & *deltaTarg(k) & *recip_hFac(i,j,k)*recip_drF(k) & *recip_deepFac2C(k)*recip_rhoFacC(k) d5d(i,j,k) = d5d(i,j,k) & + rC4kp & *deltaTarg(k) & *recip_hFac(i,j,k)*recip_drF(k) & *recip_deepFac2C(k)*recip_rhoFacC(k) b5d(i,j,k-1) = b5d(i,j,k-1) & - rC4km & *deltaTarg(k-1) & *recip_hFac(i,j,k-1)*recip_drF(k-1) & *recip_deepFac2C(k-1)*recip_rhoFacC(k-1) c5d(i,j,k-1) = c5d(i,j,k-1) & + ( (rCenter+rUpwind) + rC4km ) & *deltaTarg(k-1) & *recip_hFac(i,j,k-1)*recip_drF(k-1) & *recip_deepFac2C(k-1)*recip_rhoFacC(k-1) d5d(i,j,k-1) = d5d(i,j,k-1) & + ( (rCenter-rUpwind) + rC4kp ) & *deltaTarg(k-1) & *recip_hFac(i,j,k-1)*recip_drF(k-1) & *recip_deepFac2C(k-1)*recip_rhoFacC(k-1) e5d(i,j,k-1) = e5d(i,j,k-1) & - rC4kp & *deltaTarg(k-1) & *recip_hFac(i,j,k-1)*recip_drF(k-1) & *recip_deepFac2C(k-1)*recip_rhoFacC(k-1) ENDDO ENDDO C-- process interior interface only: end ENDIF RETURN END