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C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_calc_rhs.F,v 1.18 2003/05/14 09:20:06 mlosch 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_CALC_RHS |
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|
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C !INTERFACE: ========================================================== |
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SUBROUTINE GAD_CALC_RHS( |
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I bi,bj,iMin,iMax,jMin,jMax,k,kM1,kUp,kDown, |
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I xA,yA,uTrans,vTrans,rTrans,maskUp, |
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I diffKh, diffK4, KappaRT, Tracer, |
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I tracerIdentity, advectionScheme, calcAdvection, |
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U fVerT, gTracer, |
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I myThid ) |
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|
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C !DESCRIPTION: |
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C Calculates the tendancy of a tracer due to advection and diffusion. |
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C It calculates the fluxes in each direction indepentently and then |
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C sets the tendancy to the divergence of these fluxes. The advective |
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C fluxes are only calculated here when using the linear advection schemes |
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C otherwise only the diffusive and parameterized fluxes are calculated. |
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C |
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C Contributions to the flux are calculated and added: |
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C \begin{equation*} |
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C {\bf F} = {\bf F}_{adv} + {\bf F}_{diff} +{\bf F}_{GM} + {\bf F}_{KPP} |
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C \end{equation*} |
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C |
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C The tendancy is the divergence of the fluxes: |
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C \begin{equation*} |
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C G_\theta = G_\theta + \nabla \cdot {\bf F} |
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C \end{equation*} |
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C |
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C The tendancy is assumed to contain data on entry. |
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|
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C !USES: =============================================================== |
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IMPLICIT NONE |
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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 "DYNVARS.h" |
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#include "SURFACE.h" |
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#include "GAD.h" |
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#ifdef ALLOW_PTRACERS |
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#include "PTRACERS_OPTIONS.h" |
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#include "PTRACERS.h" |
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#endif |
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|
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#ifdef ALLOW_AUTODIFF_TAMC |
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#include "tamc.h" |
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#include "tamc_keys.h" |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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|
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C !INPUT PARAMETERS: =================================================== |
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C bi,bj :: tile indices |
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C iMin,iMax,jMin,jMax :: loop range for called routines |
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C kup :: index into 2 1/2D array, toggles between 1 and 2 |
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C kdown :: index into 2 1/2D array, toggles between 2 and 1 |
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C kp1 :: =k+1 for k<Nr, =Nr for k=Nr |
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C xA,yA :: areas of X and Y face of tracer cells |
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C uTrans,vTrans,rTrans :: 2-D arrays of volume transports at U,V and W points |
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C maskUp :: 2-D array for mask at W points |
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C diffKh :: horizontal diffusion coefficient |
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C diffK4 :: bi-harmonic diffusion coefficient |
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C KappaRT :: 3-D array for vertical diffusion coefficient |
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C Tracer :: tracer field |
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C tracerIdentity :: identifier for the tracer (required for KPP and GM) |
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C advectionScheme :: advection scheme to use |
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C calcAdvection :: =False if Advec terms computed with multiDim scheme |
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C myThid :: thread number |
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INTEGER bi,bj,iMin,iMax,jMin,jMax |
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INTEGER k,kUp,kDown,kM1 |
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_RS xA (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RS yA (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL uTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL vTrans(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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_RS maskUp(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL diffKh, diffK4 |
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_RL KappaRT(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL Tracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy) |
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INTEGER tracerIdentity |
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INTEGER advectionScheme |
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LOGICAL calcAdvection |
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INTEGER myThid |
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|
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C !OUTPUT PARAMETERS: ================================================== |
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C gTracer :: tendancy array |
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C fVerT :: 2 1/2D arrays for vertical advective flux |
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_RL gTracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy) |
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_RL fVerT (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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|
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C !LOCAL VARIABLES: ==================================================== |
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C i,j :: loop indices |
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C df4 :: used for storing del^2 T for bi-harmonic term |
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C fZon :: zonal flux |
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C fmer :: meridional flux |
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C af :: advective flux |
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C df :: diffusive flux |
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C localT :: local copy of tracer field |
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INTEGER i,j |
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_RL df4 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fZon (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fMer (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 df (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL localT(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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CEOP |
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|
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#ifdef ALLOW_AUTODIFF_TAMC |
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C-- only the kUp part of fverT is set in this subroutine |
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C-- the kDown is still required |
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fVerT(1,1,kDown) = fVerT(1,1,kDown) |
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#endif |
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|
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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fZon(i,j) = 0. _d 0 |
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fMer(i,j) = 0. _d 0 |
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fVerT(i,j,kUp) = 0. _d 0 |
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df(i,j) = 0. _d 0 |
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df4(i,j) = 0. _d 0 |
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localT(i,j) = 0. _d 0 |
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ENDDO |
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ENDDO |
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|
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C-- Make local copy of tracer array |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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localT(i,j)=tracer(i,j,k,bi,bj) |
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ENDDO |
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ENDDO |
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|
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C-- Unless we have already calculated the advection terms we initialize |
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C the tendency to zero. |
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IF (calcAdvection) 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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gTracer(i,j,k,bi,bj)=0. _d 0 |
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ENDDO |
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ENDDO |
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ENDIF |
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|
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C-- Pre-calculate del^2 T if bi-harmonic coefficient is non-zero |
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IF (diffK4 .NE. 0.) THEN |
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CALL GAD_GRAD_X(bi,bj,k,xA,localT,fZon,myThid) |
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CALL GAD_GRAD_Y(bi,bj,k,yA,localT,fMer,myThid) |
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CALL GAD_DEL2(bi,bj,k,fZon,fMer,df4,myThid) |
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ENDIF |
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|
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C-- Initialize net flux in X direction |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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fZon(i,j) = 0. _d 0 |
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ENDDO |
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ENDDO |
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|
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C- Advective flux in X |
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IF (calcAdvection) THEN |
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IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN |
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CALL GAD_C2_ADV_X(bi,bj,k,uTrans,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN |
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CALL GAD_FLUXLIMIT_ADV_X( |
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& bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN |
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CALL GAD_U3_ADV_X(bi,bj,k,uTrans,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN |
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CALL GAD_C4_ADV_X(bi,bj,k,uTrans,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN |
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CALL GAD_DST3_ADV_X( |
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& bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
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CALL GAD_DST3FL_ADV_X( |
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& bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid) |
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ELSE |
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STOP 'GAD_CALC_RHS: Bad advectionScheme (X)' |
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ENDIF |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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fZon(i,j) = fZon(i,j) + af(i,j) |
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ENDDO |
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ENDDO |
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ENDIF |
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|
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C- Diffusive flux in X |
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IF (diffKh.NE.0.) THEN |
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CALL GAD_DIFF_X(bi,bj,k,xA,diffKh,localT,df,myThid) |
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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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|
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#ifdef ALLOW_GMREDI |
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C- GM/Redi flux in X |
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IF (useGMRedi) THEN |
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C *note* should update GMREDI_XTRANSPORT to use localT and set df *aja* |
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CALL GMREDI_XTRANSPORT( |
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I iMin,iMax,jMin,jMax,bi,bj,K, |
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I xA,Tracer,tracerIdentity, |
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U df, |
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I myThid) |
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ENDIF |
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#endif |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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fZon(i,j) = fZon(i,j) + df(i,j) |
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ENDDO |
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ENDDO |
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|
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C- Bi-harmonic duffusive flux in X |
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IF (diffK4 .NE. 0.) THEN |
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CALL GAD_BIHARM_X(bi,bj,k,xA,df4,diffK4,df,myThid) |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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fZon(i,j) = fZon(i,j) + df(i,j) |
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ENDDO |
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ENDDO |
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ENDIF |
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|
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C-- Initialize net flux in Y direction |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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fMer(i,j) = 0. _d 0 |
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ENDDO |
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ENDDO |
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|
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C- Advective flux in Y |
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IF (calcAdvection) THEN |
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IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN |
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CALL GAD_C2_ADV_Y(bi,bj,k,vTrans,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN |
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CALL GAD_FLUXLIMIT_ADV_Y( |
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& bi,bj,k,deltaTtracer,vTrans,vVel,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN |
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CALL GAD_U3_ADV_Y(bi,bj,k,vTrans,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN |
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CALL GAD_C4_ADV_Y(bi,bj,k,vTrans,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN |
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CALL GAD_DST3_ADV_Y( |
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& bi,bj,k,deltaTtracer,vTrans,vVel,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
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CALL GAD_DST3FL_ADV_Y( |
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& bi,bj,k,deltaTtracer,vTrans,vVel,localT,af,myThid) |
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ELSE |
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STOP 'GAD_CALC_RHS: Bad advectionScheme (Y)' |
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ENDIF |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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fMer(i,j) = fMer(i,j) + af(i,j) |
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ENDDO |
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ENDDO |
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ENDIF |
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|
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C- Diffusive flux in Y |
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IF (diffKh.NE.0.) THEN |
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CALL GAD_DIFF_Y(bi,bj,k,yA,diffKh,localT,df,myThid) |
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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 |
| 268 |
ENDIF |
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|
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#ifdef ALLOW_GMREDI |
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C- GM/Redi flux in Y |
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IF (useGMRedi) THEN |
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C *note* should update GMREDI_YTRANSPORT to use localT and set df *aja* |
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CALL GMREDI_YTRANSPORT( |
| 275 |
I iMin,iMax,jMin,jMax,bi,bj,K, |
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I yA,Tracer,tracerIdentity, |
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U df, |
| 278 |
I myThid) |
| 279 |
ENDIF |
| 280 |
#endif |
| 281 |
DO j=1-Oly,sNy+Oly |
| 282 |
DO i=1-Olx,sNx+Olx |
| 283 |
fMer(i,j) = fMer(i,j) + df(i,j) |
| 284 |
ENDDO |
| 285 |
ENDDO |
| 286 |
|
| 287 |
C- Bi-harmonic flux in Y |
| 288 |
IF (diffK4 .NE. 0.) THEN |
| 289 |
CALL GAD_BIHARM_Y(bi,bj,k,yA,df4,diffK4,df,myThid) |
| 290 |
DO j=1-Oly,sNy+Oly |
| 291 |
DO i=1-Olx,sNx+Olx |
| 292 |
fMer(i,j) = fMer(i,j) + df(i,j) |
| 293 |
ENDDO |
| 294 |
ENDDO |
| 295 |
ENDIF |
| 296 |
|
| 297 |
#ifdef NONLIN_FRSURF |
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C-- Compute vertical flux fVerT(kDown) at interface k+1 (between k & k+1): |
| 299 |
IF ( calcAdvection .AND. K.EQ.Nr .AND. |
| 300 |
& useRealFreshWaterFlux .AND. |
| 301 |
& buoyancyRelation .EQ. 'OCEANICP' ) THEN |
| 302 |
DO j=1-Oly,sNy+Oly |
| 303 |
DO i=1-Olx,sNx+Olx |
| 304 |
fVerT(i,j,kDown) = convertEmP2rUnit*PmEpR(i,j,bi,bj) |
| 305 |
& *rA(i,j,bi,bj)*maskC(i,j,k,bi,bj)*Tracer(i,j,k,bi,bj) |
| 306 |
ENDDO |
| 307 |
ENDDO |
| 308 |
ENDIF |
| 309 |
#endif /* NONLIN_FRSURF */ |
| 310 |
|
| 311 |
C-- Compute vertical flux fVerT(kUp) at interface k (between k-1 & k): |
| 312 |
C- Advective flux in R |
| 313 |
IF (calcAdvection) THEN |
| 314 |
C Note: wVel needs to be masked |
| 315 |
IF (K.GE.2) THEN |
| 316 |
C- Compute vertical advective flux in the interior: |
| 317 |
IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN |
| 318 |
CALL GAD_C2_ADV_R(bi,bj,k,rTrans,tracer,af,myThid) |
| 319 |
ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN |
| 320 |
CALL GAD_FLUXLIMIT_ADV_R( |
| 321 |
& bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid) |
| 322 |
ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN |
| 323 |
CALL GAD_U3_ADV_R(bi,bj,k,rTrans,tracer,af,myThid) |
| 324 |
ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN |
| 325 |
CALL GAD_C4_ADV_R(bi,bj,k,rTrans,tracer,af,myThid) |
| 326 |
ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN |
| 327 |
CALL GAD_DST3_ADV_R( |
| 328 |
& bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid) |
| 329 |
ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
| 330 |
CALL GAD_DST3FL_ADV_R( |
| 331 |
& bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid) |
| 332 |
ELSE |
| 333 |
STOP 'GAD_CALC_RHS: Bad advectionScheme (R)' |
| 334 |
ENDIF |
| 335 |
C- Surface "correction" term at k>1 : |
| 336 |
DO j=1-Oly,sNy+Oly |
| 337 |
DO i=1-Olx,sNx+Olx |
| 338 |
af(i,j) = af(i,j) |
| 339 |
& + (maskC(i,j,k,bi,bj)-maskC(i,j,k-1,bi,bj))* |
| 340 |
& rTrans(i,j)*Tracer(i,j,k,bi,bj) |
| 341 |
ENDDO |
| 342 |
ENDDO |
| 343 |
ELSE |
| 344 |
C- Surface "correction" term at k=1 : |
| 345 |
DO j=1-Oly,sNy+Oly |
| 346 |
DO i=1-Olx,sNx+Olx |
| 347 |
af(i,j) = rTrans(i,j)*Tracer(i,j,k,bi,bj) |
| 348 |
ENDDO |
| 349 |
ENDDO |
| 350 |
ENDIF |
| 351 |
C- add the advective flux to fVerT |
| 352 |
DO j=1-Oly,sNy+Oly |
| 353 |
DO i=1-Olx,sNx+Olx |
| 354 |
fVerT(i,j,kUp) = fVerT(i,j,kUp) + af(i,j) |
| 355 |
ENDDO |
| 356 |
ENDDO |
| 357 |
ENDIF |
| 358 |
|
| 359 |
C- Diffusive flux in R |
| 360 |
C Note: For K=1 then KM1=1 and this gives a dT/dr = 0 upper |
| 361 |
C boundary condition. |
| 362 |
IF (implicitDiffusion) THEN |
| 363 |
DO j=1-Oly,sNy+Oly |
| 364 |
DO i=1-Olx,sNx+Olx |
| 365 |
df(i,j) = 0. _d 0 |
| 366 |
ENDDO |
| 367 |
ENDDO |
| 368 |
ELSE |
| 369 |
CALL GAD_DIFF_R(bi,bj,k,KappaRT,tracer,df,myThid) |
| 370 |
ENDIF |
| 371 |
|
| 372 |
#ifdef ALLOW_GMREDI |
| 373 |
C- GM/Redi flux in R |
| 374 |
IF (useGMRedi) THEN |
| 375 |
C *note* should update GMREDI_RTRANSPORT to set df *aja* |
| 376 |
CALL GMREDI_RTRANSPORT( |
| 377 |
I iMin,iMax,jMin,jMax,bi,bj,K, |
| 378 |
I Tracer,tracerIdentity, |
| 379 |
U df, |
| 380 |
I myThid) |
| 381 |
ENDIF |
| 382 |
#endif |
| 383 |
|
| 384 |
DO j=1-Oly,sNy+Oly |
| 385 |
DO i=1-Olx,sNx+Olx |
| 386 |
fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j) |
| 387 |
ENDDO |
| 388 |
ENDDO |
| 389 |
|
| 390 |
#ifdef ALLOW_KPP |
| 391 |
C- Add non local KPP transport term (ghat) to diffusive T flux. |
| 392 |
IF (useKPP) THEN |
| 393 |
DO j=1-Oly,sNy+Oly |
| 394 |
DO i=1-Olx,sNx+Olx |
| 395 |
df(i,j) = 0. _d 0 |
| 396 |
ENDDO |
| 397 |
ENDDO |
| 398 |
IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN |
| 399 |
C *note* should update KPP_TRANSPORT_T to set df *aja* |
| 400 |
CALL KPP_TRANSPORT_T( |
| 401 |
I iMin,iMax,jMin,jMax,bi,bj,k,km1, |
| 402 |
I KappaRT, |
| 403 |
U df ) |
| 404 |
ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN |
| 405 |
CALL KPP_TRANSPORT_S( |
| 406 |
I iMin,iMax,jMin,jMax,bi,bj,k,km1, |
| 407 |
I KappaRT, |
| 408 |
U df ) |
| 409 |
#ifdef ALLOW_PTRACERS |
| 410 |
ELSEIF (tracerIdentity .GE. GAD_TR1 .AND. |
| 411 |
& tracerIdentity .LE. (GAD_TR1+PTRACERS_numInUse-1)) THEN |
| 412 |
CALL KPP_TRANSPORT_PTR( |
| 413 |
I iMin,iMax,jMin,jMax,bi,bj,k,km1, |
| 414 |
I tracerIdentity,KappaRT, |
| 415 |
U df ) |
| 416 |
#endif |
| 417 |
ELSE |
| 418 |
PRINT*,'invalid tracer indentity: ', tracerIdentity |
| 419 |
STOP 'GAD_CALC_RHS: Ooops' |
| 420 |
ENDIF |
| 421 |
DO j=1-Oly,sNy+Oly |
| 422 |
DO i=1-Olx,sNx+Olx |
| 423 |
fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j) |
| 424 |
ENDDO |
| 425 |
ENDDO |
| 426 |
ENDIF |
| 427 |
#endif |
| 428 |
|
| 429 |
C-- Divergence of fluxes |
| 430 |
DO j=1-Oly,sNy+Oly-1 |
| 431 |
DO i=1-Olx,sNx+Olx-1 |
| 432 |
gTracer(i,j,k,bi,bj)=gTracer(i,j,k,bi,bj) |
| 433 |
& -_recip_hFacC(i,j,k,bi,bj)*recip_drF(k) |
| 434 |
& *recip_rA(i,j,bi,bj) |
| 435 |
& *( |
| 436 |
& +( fZon(i+1,j)-fZon(i,j) ) |
| 437 |
& +( fMer(i,j+1)-fMer(i,j) ) |
| 438 |
& +( fVerT(i,j,kUp)-fVerT(i,j,kDown) )*rkFac |
| 439 |
& ) |
| 440 |
ENDDO |
| 441 |
ENDDO |
| 442 |
|
| 443 |
#ifdef NONLIN_FRSURF |
| 444 |
C-- account for 3.D divergence of the flow in rStar coordinate: |
| 445 |
IF (calcAdvection .AND. select_rStar.GT.0) THEN |
| 446 |
DO j=1-Oly,sNy+Oly-1 |
| 447 |
DO i=1-Olx,sNx+Olx-1 |
| 448 |
gTracer(i,j,k,bi,bj) = gTracer(i,j,k,bi,bj) |
| 449 |
& - (rStarExpC(i,j,bi,bj) - 1. _d 0)/deltaTfreesurf |
| 450 |
& *tracer(i,j,k,bi,bj)*maskC(i,j,k,bi,bj) |
| 451 |
ENDDO |
| 452 |
ENDDO |
| 453 |
ENDIF |
| 454 |
IF (calcAdvection .AND. select_rStar.LT.0) THEN |
| 455 |
DO j=1-Oly,sNy+Oly-1 |
| 456 |
DO i=1-Olx,sNx+Olx-1 |
| 457 |
gTracer(i,j,k,bi,bj) = gTracer(i,j,k,bi,bj) |
| 458 |
& - rStarDhCDt(i,j,bi,bj) |
| 459 |
& *tracer(i,j,k,bi,bj)*maskC(i,j,k,bi,bj) |
| 460 |
ENDDO |
| 461 |
ENDDO |
| 462 |
ENDIF |
| 463 |
#endif /* NONLIN_FRSURF */ |
| 464 |
|
| 465 |
|
| 466 |
RETURN |
| 467 |
END |
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