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