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C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_implicit_r.F,v 1.16 2012/09/11 01:32:02 heimbach Exp $ |
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C $Name: $ |
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|
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#include "GAD_OPTIONS.h" |
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|
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CBOP |
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C !ROUTINE: GAD_IMPLICIT_R |
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C !INTERFACE: |
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SUBROUTINE GAD_IMPLICIT_R( |
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I implicitAdvection, advectionScheme, tracerIdentity, |
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I deltaTLev, |
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I kappaRX, recip_hFac, wVel, tracer, |
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U gTracer, |
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I bi, bj, myTime, myIter, myThid ) |
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C !DESCRIPTION: |
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C Solve implicitly vertical advection and diffusion for one tracer. |
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|
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C !USES: |
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IMPLICIT NONE |
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C == Global data == |
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#include "SIZE.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "GRID.h" |
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#include "SURFACE.h" |
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#include "GAD.h" |
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|
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C !INPUT/OUTPUT PARAMETERS: |
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C == Routine Arguments == |
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C implicitAdvection :: if True, treat vertical advection implicitly |
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C advectionScheme :: advection scheme to use |
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C tracerIdentity :: Identifier for the tracer |
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C kappaRX :: 3-D array for vertical diffusion coefficient |
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C recip_hFac :: inverse of cell open-depth factor |
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C wVel :: vertical component of the velcity field |
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C tracer :: tracer field at current time step |
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C gTracer :: future tracer field |
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C bi,bj :: tile indices |
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C myTime :: current time |
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C myIter :: current iteration number |
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C myThid :: thread number |
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LOGICAL implicitAdvection |
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INTEGER advectionScheme |
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INTEGER tracerIdentity |
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_RL deltaTLev(Nr) |
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_RL kappaRX (1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RS recip_hFac(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL wVel (1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy) |
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_RL tracer (1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy) |
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_RL gTracer(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy) |
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INTEGER bi, bj |
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_RL myTime |
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INTEGER myIter, myThid |
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|
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#ifdef ALLOW_DIAGNOSTICS |
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C !FUNCTIONS: |
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CHARACTER*4 GAD_DIAG_SUFX |
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EXTERNAL GAD_DIAG_SUFX |
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LOGICAL DIAGNOSTICS_IS_ON |
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EXTERNAL DIAGNOSTICS_IS_ON |
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#endif |
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|
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C !LOCAL VARIABLES: |
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C == Local variables == |
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C iMin,iMax,jMin,jMax :: computational domain |
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C i,j,k :: loop indices |
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C a5d :: 2nd lower diagonal of the pentadiagonal matrix |
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C b5d :: 1rst lower diagonal of the pentadiagonal matrix |
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C c5d :: main diagonal of the pentadiagonal matrix |
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C d5d :: 1rst upper diagonal of the pentadiagonal matrix |
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C e5d :: 2nd upper diagonal of the pentadiagonal matrix |
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C rTrans :: vertical volume transport at interface k |
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C localTijk :: local copy of tracer (for Non-Lin Adv.Scheme) |
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C diagonalNumber :: number of non-zero diagonals in the matrix |
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C errCode :: > 0 if singular matrix |
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INTEGER iMin,iMax,jMin,jMax |
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PARAMETER( iMin = 1, iMax = sNx ) |
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PARAMETER( jMin = 1, jMax = sNy ) |
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INTEGER i,j,k |
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INTEGER diagonalNumber, errCode |
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_RL a5d(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL b5d(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL c5d(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL d5d(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL e5d(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL wFld (1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL rTrans (1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL localTijk(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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#ifdef ALLOW_DIAGNOSTICS |
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CHARACTER*8 diagName |
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CHARACTER*4 diagSufx |
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LOGICAL diagDif, diagAdv |
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INTEGER km1, km2, kp1, kp2 |
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_RL df (1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL af (1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL div(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL flx(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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#endif |
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CEOP |
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|
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C-- no need to solve anything with only 1 level: |
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IF (Nr.GT.1) THEN |
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|
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C-- Initialise |
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DO k=1,Nr |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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a5d(i,j,k) = 0. _d 0 |
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b5d(i,j,k) = 0. _d 0 |
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c5d(i,j,k) = 1. _d 0 |
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d5d(i,j,k) = 0. _d 0 |
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e5d(i,j,k) = 0. _d 0 |
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ENDDO |
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ENDDO |
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ENDDO |
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diagonalNumber = 1 |
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|
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C-- Non-Linear Advection scheme: keep a local copy of tracer field |
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IF ( advectionScheme.EQ.ENUM_FLUX_LIMIT .OR. |
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& advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
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IF ( multiDimAdvection ) THEN |
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DO k=1,Nr |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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localTijk(i,j,k) = gTracer(i,j,k,bi,bj) |
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ENDDO |
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ENDDO |
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ENDDO |
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ELSE |
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DO k=1,Nr |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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localTijk(i,j,k) = tracer(i,j,k,bi,bj) |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDIF |
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ENDIF |
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|
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IF (implicitDiffusion) THEN |
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C-- set the tri-diagonal matrix to solve the implicit diffusion problem |
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diagonalNumber = 3 |
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C- 1rst lower diagonal : |
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DO k=2,Nr |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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b5d(i,j,k) = -deltaTLev(k)*maskC(i,j,k-1,bi,bj) |
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& *recip_hFac(i,j,k)*recip_drF(k) |
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& *kappaRX(i,j, k )*recip_drC( k ) |
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ENDDO |
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ENDDO |
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ENDDO |
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C- 1rst upper diagonal : |
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DO k=1,Nr-1 |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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d5d(i,j,k) = -deltaTLev(k)*maskC(i,j,k+1,bi,bj) |
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& *recip_hFac(i,j,k)*recip_drF(k) |
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& *KappaRX(i,j,k+1)*recip_drC(k+1) |
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ENDDO |
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ENDDO |
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ENDDO |
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C- Main diagonal : |
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DO k=1,Nr |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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c5d(i,j,k) = 1. _d 0 - b5d(i,j,k) - d5d(i,j,k) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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C-- end if implicitDiffusion |
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ENDIF |
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|
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IF (implicitAdvection) THEN |
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|
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DO k=Nr,1,-1 |
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|
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C-- Compute transport |
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IF (k.EQ.1) THEN |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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wFld(i,j) = 0. _d 0 |
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rTrans(i,j) = 0. _d 0 |
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ENDDO |
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ENDDO |
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ELSE |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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wFld(i,j) = wVel(i,j,k,bi,bj) |
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#ifdef ALLOW_AUTODIFF_OPENAD |
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rTrans(i,j) = wFld(i,j)*rA(i,j,bi,bj)%v*maskC(i,j,k-1,bi,bj) |
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#else |
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rTrans(i,j) = wFld(i,j)*rA(i,j,bi,bj)*maskC(i,j,k-1,bi,bj) |
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#endif |
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ENDDO |
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ENDDO |
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#ifdef ALLOW_GMREDI |
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C-- Residual transp = Bolus transp + Eulerian transp |
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IF (useGMRedi) |
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& CALL GMREDI_CALC_WFLOW( |
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U wFld, rTrans, |
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I k, bi, bj, myThid ) |
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#endif /* ALLOW_GMREDI */ |
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ENDIF |
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|
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#ifdef ALLOW_AIM |
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C- a hack to prevent Water-Vapor vert.transport into the stratospheric level Nr |
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IF ( k.GE.2 .AND. |
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& (.NOT.useAIM .OR.tracerIdentity.NE.GAD_SALINITY .OR.k.LT.Nr) |
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& ) THEN |
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#else |
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IF ( k.GE.2 ) THEN |
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#endif |
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|
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IF ( advectionScheme.EQ.ENUM_CENTERED_2ND ) THEN |
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diagonalNumber = 3 |
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CALL GAD_C2_IMPL_R( bi,bj,k, iMin,iMax,jMin,jMax, |
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I deltaTLev, rTrans, recip_hFac, |
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U b5d, c5d, d5d, |
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I myThid ) |
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ELSEIF ( advectionScheme.EQ.ENUM_UPWIND_1RST |
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& .OR. advectionScheme.EQ.ENUM_DST2 ) THEN |
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diagonalNumber = 3 |
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CALL GAD_DST2U1_IMPL_R( bi,bj,k, iMin,iMax,jMin,jMax, |
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I advectionScheme, deltaTLev, |
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I rTrans, recip_hFac, |
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U b5d, c5d, d5d, |
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I myThid ) |
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ELSEIF ( advectionScheme.EQ.ENUM_FLUX_LIMIT ) THEN |
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diagonalNumber = 3 |
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CALL GAD_FLUXLIMIT_IMPL_R( bi,bj,k, iMin,iMax,jMin,jMax, |
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I deltaTLev, rTrans, recip_hFac, localTijk, |
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U b5d, c5d, d5d, |
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I myThid ) |
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ELSEIF ( advectionScheme.EQ.ENUM_UPWIND_3RD |
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& .OR. advectionScheme.EQ.ENUM_CENTERED_4TH |
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& .OR. advectionScheme.EQ.ENUM_DST3 ) THEN |
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diagonalNumber = 5 |
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CALL GAD_U3C4_IMPL_R( bi,bj,k, iMin,iMax,jMin,jMax, |
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I advectionScheme, deltaTLev, |
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I rTrans, recip_hFac, |
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U a5d, b5d, c5d, d5d, e5d, |
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I myThid ) |
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ELSEIF ( advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
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diagonalNumber = 5 |
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CALL GAD_DST3FL_IMPL_R( bi,bj,k, iMin,iMax,jMin,jMax, |
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I deltaTLev, rTrans, recip_hFac, localTijk, |
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U a5d, b5d, c5d, d5d, e5d, |
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I myThid ) |
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ELSE |
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STOP 'GAD_IMPLICIT_R: Adv.Scheme in Impl form not yet coded' |
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ENDIF |
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|
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ENDIF |
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|
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C-- end k loop |
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ENDDO |
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|
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C-- end if implicitAdvection |
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ENDIF |
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|
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IF ( diagonalNumber .EQ. 3 ) THEN |
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C-- Solve tri-diagonal system : |
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CALL SOLVE_TRIDIAGONAL( iMin,iMax, jMin,jMax, |
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I b5d, c5d, d5d, |
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U gTracer, |
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O errCode, |
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I bi, bj, myThid ) |
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IF (errCode.GE.1) THEN |
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STOP 'GAD_IMPLICIT_R: error when solving 3-Diag problem' |
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ENDIF |
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ELSEIF ( diagonalNumber .EQ. 5 ) THEN |
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C-- Solve penta-diagonal system : |
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CALL SOLVE_PENTADIAGONAL( iMin,iMax, jMin,jMax, |
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I a5d, b5d, c5d, d5d, e5d, |
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U gTracer, |
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O errCode, |
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I bi, bj, myThid ) |
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IF (errCode.GE.1) THEN |
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STOP 'GAD_IMPLICIT_R: error when solving 5-Diag problem' |
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ENDIF |
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ELSEIF ( diagonalNumber .NE. 1 ) THEN |
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STOP 'GAD_IMPLICIT_R: no solver available' |
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ENDIF |
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|
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#ifdef ALLOW_DIAGNOSTICS |
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C-- Set diagnostic suffix for the current tracer |
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IF ( useDiagnostics ) THEN |
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diagSufx = GAD_DIAG_SUFX( tracerIdentity, myThid ) |
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diagName = 'DFrI'//diagSufx |
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diagDif = implicitDiffusion |
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IF ( diagDif ) diagDif = DIAGNOSTICS_IS_ON(diagName,myThid) |
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diagName = 'ADVr'//diagSufx |
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diagAdv = implicitAdvection |
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IF ( diagAdv ) diagAdv = DIAGNOSTICS_IS_ON(diagName,myThid) |
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|
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IF ( diagDif .OR. diagAdv ) THEN |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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flx(i,j) = 0. _d 0 |
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ENDDO |
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ENDDO |
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DO k= Nr,1,-1 |
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IF ( implicitDiffusion .AND. k.GE.2 ) THEN |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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df(i,j) = |
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#ifdef ALLOW_AUTODIFF_OPENAD |
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& -rA(i,j,bi,bj)%v |
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#else |
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& -rA(i,j,bi,bj) |
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#endif |
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& * KappaRX(i,j,k)*recip_drC(k)*rkSign |
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& * (gTracer(i,j,k,bi,bj) - gTracer(i,j,k-1,bi,bj)) |
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& * maskC(i,j,k,bi,bj) |
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& * maskC(i,j,k-1,bi,bj) |
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ENDDO |
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ENDDO |
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ELSE |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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df(i,j) = 0. _d 0 |
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ENDDO |
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ENDDO |
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ENDIF |
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C- Note: Needs to explicitly increment counter (call DIAGNOSTICS_COUNT) |
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C since skipping k=1 DIAGNOSTICS_FILL call. |
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IF ( diagDif .AND. k.GE.2 ) THEN |
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diagName = 'DFrI'//diagSufx |
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CALL DIAGNOSTICS_FILL(df,diagName, k,1, 2,bi,bj, myThid) |
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IF ( k.EQ.2 ) CALL DIAGNOSTICS_COUNT(diagName,bi,bj,myThid) |
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ENDIF |
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IF ( diagAdv ) THEN |
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km1=MAX(1,k-1) |
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km2=MAX(1,k-2) |
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kp1=MIN(Nr,k+1) |
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kp2=MIN(Nr,k+2) |
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C-- Flux_divergence*deltaT = Tr^n - Tr^n+1 = [A-I](Tr^n+1) |
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C = deltaT*rkSign*[ Flx_k+1 - Flx_k ]/dz |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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div(i,j) = gTracer(i,j,k,bi,bj)*( c5d(i,j,k) - 1. _d 0 ) |
344 |
& + gTracer(i,j,km1,bi,bj)*b5d(i,j,k) |
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& + gTracer(i,j,kp1,bi,bj)*d5d(i,j,k) |
346 |
ENDDO |
347 |
ENDDO |
348 |
IF ( diagonalNumber .EQ. 5 ) THEN |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
351 |
div(i,j) = div(i,j) |
352 |
& + gTracer(i,j,km2,bi,bj)*a5d(i,j,k) |
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& + gTracer(i,j,kp2,bi,bj)*e5d(i,j,k) |
354 |
ENDDO |
355 |
ENDDO |
356 |
ENDIF |
357 |
#ifdef NONLIN_FRSURF |
358 |
IF ( nonlinFreeSurf.GT.0 ) THEN |
359 |
C-- use future hFac to stay consistent with solver matrix |
360 |
IF ( select_rStar.GT.0 ) THEN |
361 |
DO j=jMin,jMax |
362 |
DO i=iMin,iMax |
363 |
div(i,j) = div(i,j)*h0FacC(i,j,k,bi,bj)*drF(k) |
364 |
& *rStarFacC(i,j,bi,bj) |
365 |
ENDDO |
366 |
ENDDO |
367 |
ELSEIF ( selectSigmaCoord.NE.0 ) THEN |
368 |
DO j=jMin,jMax |
369 |
DO i=iMin,iMax |
370 |
div(i,j) = div(i,j)*( |
371 |
& _hFacC(i,j,k,bi,bj)*drF(k) |
372 |
& + dBHybSigF(k)*dEtaHdt(i,j,bi,bj)*deltaTfreesurf |
373 |
& ) |
374 |
ENDDO |
375 |
ENDDO |
376 |
ELSE |
377 |
DO j=jMin,jMax |
378 |
DO i=iMin,iMax |
379 |
IF ( k.EQ.kSurfC(i,j,bi,bj) ) THEN |
380 |
div(i,j) = div(i,j)*hFac_surfC(i,j,bi,bj)*drF(k) |
381 |
ELSE |
382 |
div(i,j) = div(i,j)*_hFacC(i,j,k,bi,bj)*drF(k) |
383 |
ENDIF |
384 |
ENDDO |
385 |
ENDDO |
386 |
ENDIF |
387 |
ELSE |
388 |
#else /* NONLIN_FRSURF */ |
389 |
IF ( .TRUE. ) THEN |
390 |
#endif /* NONLIN_FRSURF */ |
391 |
C-- use current hFac (consistent with solver matrix) |
392 |
DO j=jMin,jMax |
393 |
DO i=iMin,iMax |
394 |
div(i,j) = div(i,j)*_hFacC(i,j,k,bi,bj)*drF(k) |
395 |
ENDDO |
396 |
ENDDO |
397 |
ENDIF |
398 |
DO j=jMin,jMax |
399 |
DO i=iMin,iMax |
400 |
flx(i,j) = flx(i,j) |
401 |
#ifdef ALLOW_AUTODIFF_OPENAD |
402 |
& - rkSign*div(i,j)*rA(i,j,bi,bj)%v/deltaTLev(k) |
403 |
#else |
404 |
& - rkSign*div(i,j)*rA(i,j,bi,bj)/deltaTLev(k) |
405 |
#endif |
406 |
af(i,j) = flx(i,j) - df(i,j) |
407 |
ENDDO |
408 |
ENDDO |
409 |
diagName = 'ADVr'//diagSufx |
410 |
CALL DIAGNOSTICS_FILL(af,diagName, k,1, 2,bi,bj, myThid) |
411 |
ENDIF |
412 |
ENDDO |
413 |
ENDIF |
414 |
ENDIF |
415 |
#endif /* ALLOW_DIAGNOSTICS */ |
416 |
|
417 |
C-- end if Nr > 1 |
418 |
ENDIF |
419 |
|
420 |
RETURN |
421 |
END |