C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_calc_rhs.F,v 1.36 2005/06/22 00:27:47 jmc Exp $
C $Name: $
#include "GAD_OPTIONS.h"
CBOP
C !ROUTINE: GAD_CALC_RHS
C !INTERFACE: ==========================================================
SUBROUTINE GAD_CALC_RHS(
I bi,bj,iMin,iMax,jMin,jMax,k,kM1,kUp,kDown,
I xA,yA,uTrans,vTrans,rTrans,rTransKp1,maskUp,
I uVel, vVel, wVel,
I diffKh, diffK4, KappaR, Tracer,
I tracerIdentity, advectionScheme, vertAdvecScheme,
I calcAdvection, implicitAdvection,
U fVerT, gTracer,
I myTime, myIter, myThid )
C !DESCRIPTION:
C Calculates the tendancy of a tracer due to advection and diffusion.
C It calculates the fluxes in each direction indepentently and then
C sets the tendancy to the divergence of these fluxes. The advective
C fluxes are only calculated here when using the linear advection schemes
C otherwise only the diffusive and parameterized fluxes are calculated.
C
C Contributions to the flux are calculated and added:
C \begin{equation*}
C {\bf F} = {\bf F}_{adv} + {\bf F}_{diff} +{\bf F}_{GM} + {\bf F}_{KPP}
C \end{equation*}
C
C The tendancy is the divergence of the fluxes:
C \begin{equation*}
C G_\theta = G_\theta + \nabla \cdot {\bf F}
C \end{equation*}
C
C The tendancy is assumed to contain data on entry.
C !USES: ===============================================================
IMPLICIT NONE
#include "SIZE.h"
#include "EEPARAMS.h"
#include "PARAMS.h"
#include "GRID.h"
#include "SURFACE.h"
#include "GAD.h"
#ifdef ALLOW_AUTODIFF_TAMC
#include "tamc.h"
#include "tamc_keys.h"
#endif /* ALLOW_AUTODIFF_TAMC */
C !INPUT PARAMETERS: ===================================================
C bi,bj :: tile indices
C iMin,iMax :: loop range for called routines
C jMin,jMax :: loop range for called routines
C kup :: index into 2 1/2D array, toggles between 1|2
C kdown :: index into 2 1/2D array, toggles between 2|1
C kp1 :: =k+1 for k
C xA,yA :: areas of X and Y face of tracer cells
C uTrans,vTrans :: 2-D arrays of volume transports at U,V points
C rTrans :: 2-D arrays of volume transports at W points
C rTransKp1 :: 2-D array of volume trans at W pts, interf k+1
C maskUp :: 2-D array for mask at W points
C uVel,vVel,wVel :: 3 components of the velcity field (3-D array)
C diffKh :: horizontal diffusion coefficient
C diffK4 :: bi-harmonic diffusion coefficient
C KappaR :: 2-D array for vertical diffusion coefficient, interf k
C Tracer :: tracer field
C tracerIdentity :: tracer identifier (required for KPP,GM)
C advectionScheme :: advection scheme to use (Horizontal plane)
C vertAdvecScheme :: advection scheme to use (Vertical direction)
C calcAdvection :: =False if Advec computed with multiDim scheme
C implicitAdvection:: =True if vertical Advec computed implicitly
C myTime :: current time
C myIter :: iteration number
C myThid :: thread number
INTEGER bi,bj,iMin,iMax,jMin,jMax
INTEGER k,kUp,kDown,kM1
_RS xA (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RS yA (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL uTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL rTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL rTransKp1(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RS maskUp(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL uVel (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
_RL vVel (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
_RL wVel (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
_RL diffKh, diffK4
_RL KappaR(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL Tracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
INTEGER tracerIdentity
INTEGER advectionScheme, vertAdvecScheme
LOGICAL calcAdvection
LOGICAL implicitAdvection
_RL myTime
INTEGER myIter, myThid
C !OUTPUT PARAMETERS: ==================================================
C gTracer :: tendancy array
C fVerT :: 2 1/2D arrays for vertical advective flux
_RL gTracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
_RL fVerT (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
C !LOCAL VARIABLES: ====================================================
C i,j :: loop indices
C df4 :: used for storing del^2 T for bi-harmonic term
C fZon :: zonal flux
C fMer :: meridional flux
C af :: advective flux
C df :: diffusive flux
C localT :: local copy of tracer field
#ifdef ALLOW_DIAGNOSTICS
CHARACTER*8 diagName
CHARACTER*4 GAD_DIAG_SUFX, diagSufx
EXTERNAL
#endif
INTEGER i,j
_RL df4 (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL fZon (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL fMer (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL af (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL df (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL localT(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL advFac, rAdvFac
CEOP
#ifdef ALLOW_AUTODIFF_TAMC
C-- only the kUp part of fverT is set in this subroutine
C-- the kDown is still required
fVerT(1,1,kDown) = fVerT(1,1,kDown)
#endif
#ifdef ALLOW_DIAGNOSTICS
C-- Set diagnostic suffix for the current tracer
IF ( useDiagnostics ) THEN
diagSufx = GAD_DIAG_SUFX( tracerIdentity, myThid )
ENDIF
#endif
advFac = 0. _d 0
IF (calcAdvection) advFac = 1. _d 0
rAdvFac = rkSign*advFac
IF (implicitAdvection) rAdvFac = 0. _d 0
DO j=1-OLy,sNy+OLy
DO i=1-OLx,sNx+OLx
fZon(i,j) = 0. _d 0
fMer(i,j) = 0. _d 0
fVerT(i,j,kUp) = 0. _d 0
df(i,j) = 0. _d 0
df4(i,j) = 0. _d 0
ENDDO
ENDDO
C-- Make local copy of tracer array
DO j=1-OLy,sNy+OLy
DO i=1-OLx,sNx+OLx
localT(i,j)=tracer(i,j,k,bi,bj)
ENDDO
ENDDO
C-- Unless we have already calculated the advection terms we initialize
C the tendency to zero.
C <== now done earlier at the beginning of thermodynamics.
c IF (calcAdvection) THEN
c DO j=1-Oly,sNy+Oly
c DO i=1-Olx,sNx+Olx
c gTracer(i,j,k,bi,bj)=0. _d 0
c ENDDO
c ENDDO
c ENDIF
C-- Pre-calculate del^2 T if bi-harmonic coefficient is non-zero
IF (diffK4 .NE. 0.) THEN
CALL GAD_GRAD_X(bi,bj,k,xA,localT,fZon,myThid)
CALL GAD_GRAD_Y(bi,bj,k,yA,localT,fMer,myThid)
CALL GAD_DEL2(bi,bj,k,fZon,fMer,df4,myThid)
ENDIF
C-- Initialize net flux in X direction
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
fZon(i,j) = 0. _d 0
ENDDO
ENDDO
C- Advective flux in X
IF (calcAdvection) THEN
IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN
CALL GAD_C2_ADV_X(bi,bj,k,uTrans,localT,af,myThid)
ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
CALL GAD_FLUXLIMIT_ADV_X( bi,bj,k, dTtracerLev(k),
I uTrans, uVel, maskW(1-Olx,1-Oly,k,bi,bj), localT,
O af, myThid )
ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN
CALL GAD_U3_ADV_X(bi,bj,k,uTrans,localT,af,myThid)
ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN
CALL GAD_C4_ADV_X(bi,bj,k,uTrans,localT,af,myThid)
ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
CALL GAD_DST3_ADV_X( bi,bj,k, dTtracerLev(k),
I uTrans, uVel, maskW(1-Olx,1-Oly,k,bi,bj), localT,
O af, myThid )
ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
IF ( inAdMode ) THEN
cph This block is to trick the adjoint:
cph IF inAdExact=.FALSE., we want to use DST3
cph with limiters in forward, but without limiters in reverse.
CALL GAD_DST3_ADV_X( bi,bj,k, dTtracerLev(k),
I uTrans, uVel, maskW(1-Olx,1-Oly,k,bi,bj), localT,
O af, myThid )
ELSE
CALL GAD_DST3FL_ADV_X( bi,bj,k, dTtracerLev(k),
I uTrans, uVel, maskW(1-Olx,1-Oly,k,bi,bj), localT,
O af, myThid )
ENDIF
ELSE
STOP 'GAD_CALC_RHS: Bad advectionScheme (X)'
ENDIF
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
fZon(i,j) = fZon(i,j) + af(i,j)
ENDDO
ENDDO
#ifdef ALLOW_DIAGNOSTICS
IF ( useDiagnostics ) THEN
diagName = 'ADVx'//diagSufx
CALL DIAGNOSTICS_FILL(af,diagName, k,1, 2,bi,bj, myThid)
ENDIF
#endif
ENDIF
C- Diffusive flux in X
IF (diffKh.NE.0.) THEN
CALL GAD_DIFF_X(bi,bj,k,xA,diffKh,localT,df,myThid)
ELSE
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
df(i,j) = 0. _d 0
ENDDO
ENDDO
ENDIF
C- Add bi-harmonic diffusive flux in X
IF (diffK4 .NE. 0.) THEN
CALL GAD_BIHARM_X(bi,bj,k,xA,df4,diffK4,df,myThid)
ENDIF
#ifdef ALLOW_GMREDI
C- GM/Redi flux in X
IF (useGMRedi) THEN
C *note* should update GMREDI_XTRANSPORT to use localT and set df *aja*
CALL GMREDI_XTRANSPORT(
I iMin,iMax,jMin,jMax,bi,bj,K,
I xA,Tracer,tracerIdentity,
U df,
I myThid)
ENDIF
#endif
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
fZon(i,j) = fZon(i,j) + df(i,j)
ENDDO
ENDDO
#ifdef ALLOW_DIAGNOSTICS
C- Diagnostics of Tracer flux in X dir (mainly Diffusive term),
C excluding advective terms:
IF ( useDiagnostics .AND.
& (diffKh.NE.0. .OR. diffK4 .NE.0. .OR. useGMRedi) ) THEN
diagName = 'DIFx'//diagSufx
CALL DIAGNOSTICS_FILL(df,diagName, k,1, 2,bi,bj, myThid)
ENDIF
#endif
C-- Initialize net flux in Y direction
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
fMer(i,j) = 0. _d 0
ENDDO
ENDDO
C- Advective flux in Y
IF (calcAdvection) THEN
IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN
CALL GAD_C2_ADV_Y(bi,bj,k,vTrans,localT,af,myThid)
ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
CALL GAD_FLUXLIMIT_ADV_Y( bi,bj,k, dTtracerLev(k),
I vTrans, vVel, maskS(1-Olx,1-Oly,k,bi,bj), localT,
O af, myThid )
ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN
CALL GAD_U3_ADV_Y(bi,bj,k,vTrans,localT,af,myThid)
ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN
CALL GAD_C4_ADV_Y(bi,bj,k,vTrans,localT,af,myThid)
ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
CALL GAD_DST3_ADV_Y( bi,bj,k, dTtracerLev(k),
I vTrans, vVel, maskS(1-Olx,1-Oly,k,bi,bj), localT,
O af, myThid )
ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
IF ( inAdMode ) THEN
cph This block is to trick the adjoint:
cph IF inAdExact=.FALSE., we want to use DST3
cph with limiters in forward, but without limiters in reverse.
CALL GAD_DST3_ADV_Y( bi,bj,k, dTtracerLev(k),
I vTrans, vVel, maskS(1-Olx,1-Oly,k,bi,bj), localT,
O af, myThid )
ELSE
CALL GAD_DST3FL_ADV_Y( bi,bj,k, dTtracerLev(k),
I vTrans, vVel, maskS(1-Olx,1-Oly,k,bi,bj), localT,
O af, myThid )
ENDIF
ELSE
STOP 'GAD_CALC_RHS: Bad advectionScheme (Y)'
ENDIF
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
fMer(i,j) = fMer(i,j) + af(i,j)
ENDDO
ENDDO
#ifdef ALLOW_DIAGNOSTICS
IF ( useDiagnostics ) THEN
diagName = 'ADVy'//diagSufx
CALL DIAGNOSTICS_FILL(af,diagName, k,1, 2,bi,bj, myThid)
ENDIF
#endif
ENDIF
C- Diffusive flux in Y
IF (diffKh.NE.0.) THEN
CALL GAD_DIFF_Y(bi,bj,k,yA,diffKh,localT,df,myThid)
ELSE
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
df(i,j) = 0. _d 0
ENDDO
ENDDO
ENDIF
C- Add bi-harmonic flux in Y
IF (diffK4 .NE. 0.) THEN
CALL GAD_BIHARM_Y(bi,bj,k,yA,df4,diffK4,df,myThid)
ENDIF
#ifdef ALLOW_GMREDI
C- GM/Redi flux in Y
IF (useGMRedi) THEN
C *note* should update GMREDI_YTRANSPORT to use localT and set df *aja*
CALL GMREDI_YTRANSPORT(
I iMin,iMax,jMin,jMax,bi,bj,K,
I yA,Tracer,tracerIdentity,
U df,
I myThid)
ENDIF
#endif
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
fMer(i,j) = fMer(i,j) + df(i,j)
ENDDO
ENDDO
#ifdef ALLOW_DIAGNOSTICS
C- Diagnostics of Tracer flux in Y dir (mainly Diffusive terms),
C excluding advective terms:
IF ( useDiagnostics .AND.
& (diffKh.NE.0. .OR. diffK4 .NE.0. .OR. useGMRedi) ) THEN
diagName = 'DIFy'//diagSufx
CALL DIAGNOSTICS_FILL(df,diagName, k,1, 2,bi,bj, myThid)
ENDIF
#endif
C-- Compute vertical flux fVerT(kUp) at interface k (between k-1 & k):
C- Advective flux in R
#ifdef ALLOW_AIM
C- a hack to prevent Water-Vapor vert.transport into the stratospheric level Nr
IF (calcAdvection .AND. .NOT.implicitAdvection .AND. K.GE.2 .AND.
& (.NOT.useAIM .OR.tracerIdentity.NE.GAD_SALINITY .OR.K.LT.Nr)
& ) THEN
#else
IF (calcAdvection .AND. .NOT.implicitAdvection .AND. K.GE.2) THEN
#endif
C- Compute vertical advective flux in the interior:
IF (vertAdvecScheme.EQ.ENUM_CENTERED_2ND) THEN
CALL GAD_C2_ADV_R(bi,bj,k,rTrans,tracer,af,myThid)
ELSEIF (vertAdvecScheme.EQ.ENUM_FLUX_LIMIT) THEN
CALL GAD_FLUXLIMIT_ADV_R(
& bi,bj,k,dTtracerLev(k),rTrans,wVel,tracer,af,myThid)
ELSEIF (vertAdvecScheme.EQ.ENUM_UPWIND_3RD ) THEN
CALL GAD_U3_ADV_R(bi,bj,k,rTrans,tracer,af,myThid)
ELSEIF (vertAdvecScheme.EQ.ENUM_CENTERED_4TH) THEN
CALL GAD_C4_ADV_R(bi,bj,k,rTrans,tracer,af,myThid)
ELSEIF (vertAdvecScheme.EQ.ENUM_DST3 ) THEN
CALL GAD_DST3_ADV_R(
& bi,bj,k,dTtracerLev(k),rTrans,wVel,tracer,af,myThid)
ELSEIF (vertAdvecScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
cph This block is to trick the adjoint:
cph IF inAdExact=.FALSE., we want to use DST3
cph with limiters in forward, but without limiters in reverse.
IF ( inAdMode ) THEN
CALL GAD_DST3_ADV_R(
& bi,bj,k,dTtracerLev(k),rTrans,wVel,tracer,af,myThid)
ELSE
CALL GAD_DST3FL_ADV_R(
& bi,bj,k,dTtracerLev(k),rTrans,wVel,tracer,af,myThid)
ENDIF
ELSE
STOP 'GAD_CALC_RHS: Bad vertAdvecScheme (R)'
ENDIF
C- add the advective flux to fVerT
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
fVerT(i,j,kUp) = fVerT(i,j,kUp) + af(i,j)
ENDDO
ENDDO
#ifdef ALLOW_DIAGNOSTICS
IF ( useDiagnostics ) THEN
diagName = 'ADVr'//diagSufx
CALL DIAGNOSTICS_FILL(af,diagName, k,1, 2,bi,bj, myThid)
C- note: needs to explicitly increment the counter since DIAGNOSTICS_FILL
C does it only if k=1 (never the case here)
IF ( k.EQ.2 ) CALL DIAGNOSTICS_COUNT(diagName,bi,bj,myThid)
ENDIF
#endif
ENDIF
C- Diffusive flux in R
C Note: For K=1 then KM1=1 and this gives a dT/dr = 0 upper
C boundary condition.
IF (implicitDiffusion) THEN
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
df(i,j) = 0. _d 0
ENDDO
ENDDO
ELSE
CALL GAD_DIFF_R(bi,bj,k,KappaR,tracer,df,myThid)
ENDIF
#ifdef ALLOW_GMREDI
C- GM/Redi flux in R
IF (useGMRedi) THEN
C *note* should update GMREDI_RTRANSPORT to set df *aja*
CALL GMREDI_RTRANSPORT(
I iMin,iMax,jMin,jMax,bi,bj,K,
I Tracer,tracerIdentity,
U df,
I myThid)
ENDIF
#endif
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j)
ENDDO
ENDDO
#ifdef ALLOW_DIAGNOSTICS
C- Diagnostics of Tracer flux in R dir (mainly Diffusive terms),
C Explicit terms only & excluding advective terms:
IF ( useDiagnostics .AND.
& (.NOT.implicitDiffusion .OR. useGMRedi) ) THEN
diagName = 'DFrE'//diagSufx
CALL DIAGNOSTICS_FILL(df,diagName, k,1, 2,bi,bj, myThid)
ENDIF
#endif
#ifdef ALLOW_KPP
C- Set non local KPP transport term (ghat):
IF ( useKPP .AND. k.GE.2 ) THEN
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
df(i,j) = 0. _d 0
ENDDO
ENDDO
IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN
CALL KPP_TRANSPORT_T(
I iMin,iMax,jMin,jMax,bi,bj,k,km1,
O df )
ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN
CALL KPP_TRANSPORT_S(
I iMin,iMax,jMin,jMax,bi,bj,k,km1,
O df )
#ifdef ALLOW_PTRACERS
ELSEIF (tracerIdentity .GE. GAD_TR1) THEN
CALL KPP_TRANSPORT_PTR(
I iMin,iMax,jMin,jMax,bi,bj,k,km1,
I tracerIdentity-GAD_TR1+1,
O df )
#endif
ELSE
PRINT*,'invalid tracer indentity: ', tracerIdentity
STOP 'GAD_CALC_RHS: Ooops'
ENDIF
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j)
ENDDO
ENDDO
ENDIF
#endif
C-- Divergence of fluxes
DO j=1-Oly,sNy+Oly-1
DO i=1-Olx,sNx+Olx-1
gTracer(i,j,k,bi,bj)=gTracer(i,j,k,bi,bj)
& -_recip_hFacC(i,j,k,bi,bj)*recip_drF(k)*recip_rA(i,j,bi,bj)
& *( (fZon(i+1,j)-fZon(i,j))
& +(fMer(i,j+1)-fMer(i,j))
& +(fVerT(i,j,kDown)-fVerT(i,j,kUp))*rkSign
& -localT(i,j)*( (uTrans(i+1,j)-uTrans(i,j))
& +(vTrans(i,j+1)-vTrans(i,j))
& +(rTransKp1(i,j)-rTrans(i,j))*rAdvFac
& )*advFac
& )
ENDDO
ENDDO
#ifdef ALLOW_DEBUG
IF ( debugLevel .GE. debLevB
& .AND. tracerIdentity.EQ.GAD_TEMPERATURE
& .AND. k.EQ.2 .AND. myIter.EQ.1+nIter0
& .AND. nPx.EQ.1 .AND. nPy.EQ.1
& .AND. useCubedSphereExchange ) THEN
CALL DEBUG_CS_CORNER_UV( ' fZon,fMer from GAD_CALC_RHS',
& fZon,fMer, k, standardMessageUnit,bi,bj,myThid )
ENDIF
#endif /* ALLOW_DEBUG */
RETURN
END