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C $Header: /u/gcmpack/MITgcm/pkg/gmredi/gmredi_calc_psi_bvp.F,v 1.1 2011/02/10 21:24:19 jmc Exp $ |
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C $Name: $ |
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|
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#include "GMREDI_OPTIONS.h" |
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|
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CBOP |
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C !ROUTINE: GMREDI_CALC_PSI_BVP |
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C !INTERFACE: |
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SUBROUTINE GMREDI_CALC_PSI_BVP( |
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I bi, bj, iMin, iMax, jMin, jMax, |
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I sigmaX, sigmaY, sigmaR, |
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I myThid ) |
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|
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | SUBROUTINE GMREDI_CALC_PSI_BVP |
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C | o Calculate stream-functions for GM bolus velocity using |
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C | the BVP in Ferrari et al. (OM, 2010) |
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C *==========================================================* |
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C \ev |
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|
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C !USES: |
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IMPLICIT NONE |
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|
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C == Global variables == |
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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 "GMREDI.h" |
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|
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C !INPUT/OUTPUT PARAMETERS: |
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C bi,bj :: Tile indices |
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C iMin,iMax :: computation domain 1rst index bounds |
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C jMin,jMax :: computation domain 2nd index bounds |
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C sigmaX :: Zonal gradient of density |
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C sigmaY :: Meridional gradient of density |
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C sigmaR :: Vertical gradient of Pot.density (locally referenced) |
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C myThid :: My Thread Id number |
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INTEGER bi,bj,iMin,iMax,jMin,jMax |
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_RL sigmaX(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL sigmaY(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL sigmaR(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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INTEGER myThid |
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CEOP |
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|
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#ifdef ALLOW_GMREDI |
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#ifdef GM_BOLUS_BVP |
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|
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C !LOCAL VARIABLES: |
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INTEGER i,j,k, km1 |
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INTEGER errCode |
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_RL half_K |
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_RL sigmaX_W |
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_RL sigmaY_W |
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_RL dSigmaDrW |
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_RL dSigmaDrS |
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_RL wkb_cW(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL wkb_cS(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL rPI, c2 |
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#ifdef ALLOW_DIAGNOSTICS |
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_RL tmpFac |
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#endif |
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CHARACTER*(MAX_LEN_MBUF) msgBuf |
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|
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PARAMETER ( rPI = 0.318309886183791 _d 0 ) |
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|
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C- Matrix elements for tri-diagonal solver |
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_RL GM_a3d(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL GM_b3d(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL GM_c3d(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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|
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C- Initialization : <= done in S/R gmredi_init |
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IF (GM_UseBVP) THEN |
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|
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C Initialize the WKB wave speeds to zero |
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C We use c = int_{-H}^0 N dz/(GM_BVP_ModeNumber*PI) and have absorbed |
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C a factor of g/rhoConst |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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wkb_cW(i,j) = 0. _d 0 |
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wkb_cS(i,j) = 0. _d 0 |
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ENDDO |
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ENDDO |
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|
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C Surface BC : set to zero |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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GM_a3d(i,j,1) = 0. _d 0 |
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GM_b3d(i,j,1) = 1. _d 0 |
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GM_c3d(i,j,1) = 0. _d 0 |
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GM_PsiX(i,j,1,bi,bj) = 0. _d 0 |
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GM_PsiY(i,j,1,bi,bj) = 0. _d 0 |
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ENDDO |
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ENDDO |
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|
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DO k=2,Nr |
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km1 = k-1 |
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half_K = GM_background_K |
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& *(GM_bolFac1d(km1)+GM_bolFac1d(k))*op25 |
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C Gradient of Sigma below U and V points |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx+1,sNx+Olx |
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sigmaX_W = op5*( sigmaX(i,j,km1)+sigmaX(i,j,k) ) |
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& *maskW(i,j,k,bi,bj) |
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dSigmaDrW = op5*( sigmaR(i-1,j,k)+sigmaR(i,j,k) ) |
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& *maskW(i,j,k,bi,bj) |
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|
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wkb_cW(i,j) = wkb_cW(i,j) |
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& + SQRT(MAX( -dSigmaDrW, 0. _d 0 )) |
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& *drC(k)*GM_BVP_rModeNumber*rPI |
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|
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C Part of main diagonal coming from zeroth order derivative |
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GM_b3d(i,j,k) = MAX( -dSigmaDrW, GM_Small_Number ) |
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|
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C This is initially the RHS |
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GM_PsiX(i,j,k,bi,bj) = half_K*sigmaX_W |
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& *(GM_bolFac2d(i-1,j,bi,bj)+GM_bolFac2d(i,j,bi,bj)) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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C Note: Use Dirichlet BC @ Surface & Bottom (whereas we use Neumann BC for |
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C implicit diffusion/advection Pb). |
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C Surface BC implementation: => keep non zero coeff @ k=2 |
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C and set Psi=1 with Identity coeff @ k=1 |
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C Same for bottom, except if kBottom=Nr (solver only process k=1:Nr) |
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C should substract c3d(k=Nr)*Psi(k=Nr+1) to RHS @ k=Nr ; |
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C However in our case this term is zero since Psi(k=Nr+1)=0 |
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DO k=2,Nr |
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km1 = k-1 |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx+1,sNx+Olx |
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IF ( maskW(i,j,k,bi,bj).EQ.0. ) THEN |
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C- at Bottom and below, use identity matrix |
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GM_a3d(i,j,k) = 0. _d 0 |
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GM_b3d(i,j,k) = 1. _d 0 |
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GM_c3d(i,j,k) = 0. _d 0 |
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ELSE |
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c2 = MAX( wkb_cW(i,j)*wkb_cW(i,j), GM_BVP_cHat2Min ) |
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GM_a3d(i,j,k) = -c2*recip_drC(k) |
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& *recip_drF(km1)*recip_hFacW(i,j,km1,bi,bj) |
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GM_b3d(i,j,k) = GM_b3d(i,j,k) |
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& + c2*recip_drC(k) |
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& *(recip_drF(km1)*recip_hFacW(i,j,km1,bi,bj) |
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& +recip_drF(k)*recip_hFacW(i,j,k,bi,bj) ) |
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GM_c3d(i,j,k) = -c2*recip_drC(k) |
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& *recip_drF(k)*recip_hFacW(i,j,k,bi,bj) |
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ENDIF |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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CALL SOLVE_TRIDIAGONAL( iMin+1,iMax,jMin,jMax, |
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& GM_a3d,GM_b3d,GM_c3d, |
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& GM_PsiX, |
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& errCode,bi,bj,myThid) |
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|
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IF ( errCode .GT. 0 ) THEN |
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WRITE(msgBuf,'(A)') |
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& 'S/R GMREDI_CALC_PSI_BVP: matrix singular for PsiX' |
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CALL PRINT_ERROR( msgBuf, myThid ) |
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STOP 'ABNORMAL END: S/R GMREDI_CALC_PSI_BVP' |
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ENDIF |
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|
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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|
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DO k=2,Nr |
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km1 = k-1 |
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half_K = GM_background_K |
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& *(GM_bolFac1d(km1)+GM_bolFac1d(k))*op25 |
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DO j=1-Oly+1,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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sigmaY_W = op5*( sigmaY(i,j,km1)+sigmaY(i,j,k) ) |
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& *maskS(i,j,k,bi,bj) |
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dSigmaDrS = op5*( sigmaR(i,j-1,k)+sigmaR(i,j,k) ) |
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& *maskS(i,j,k,bi,bj) |
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|
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wkb_cS(i,j) = wkb_cS(i,j) |
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& + SQRT(MAX( -dSigmaDrS, 0. _d 0 )) |
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& *drC(k)*GM_BVP_rModeNumber*rPI |
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|
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C Part of main diagonal coming from zeroth order derivative |
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GM_b3d(i,j,k) = MAX( -dSigmaDrS, GM_Small_Number ) |
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|
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C This is initially the RHS |
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GM_PsiY(i,j,k,bi,bj) = half_K*sigmaY_W |
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& *(GM_bolFac2d(i,j-1,bi,bj)+GM_bolFac2d(i,j,bi,bj)) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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DO k=2,Nr |
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km1 = k-1 |
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DO j=1-Oly+1,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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IF ( maskS(i,j,k,bi,bj).EQ.0. ) THEN |
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C- at Bottom and below, use identity matrix |
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GM_a3d(i,j,k) = 0. _d 0 |
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GM_b3d(i,j,k) = 1. _d 0 |
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GM_c3d(i,j,k) = 0. _d 0 |
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ELSE |
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c2 = MAX( wkb_cS(i,j)*wkb_cS(i,j), GM_BVP_cHat2Min ) |
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GM_a3d(i,j,k) = -c2*recip_drC(k) |
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& *recip_drF(km1)*recip_hFacS(i,j,km1,bi,bj) |
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GM_b3d(i,j,k) = GM_b3d(i,j,k) |
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& + c2*recip_drC(k) |
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& *(recip_drF(km1)*recip_hFacS(i,j,km1,bi,bj) |
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& +recip_drF(k)*recip_hFacS(i,j,k,bi,bj) ) |
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GM_c3d(i,j,k) = -c2*recip_drC(k) |
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& *recip_drF(k)*recip_hFacS(i,j,k,bi,bj) |
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ENDIF |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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CALL SOLVE_TRIDIAGONAL( iMin,iMax,jMin+1,jMax, |
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& GM_a3d,GM_b3d,GM_c3d, |
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& GM_PsiY, |
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& errCode,bi,bj,myThid) |
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|
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IF ( errCode .GT. 0 ) THEN |
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WRITE(msgBuf,'(A)') |
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& 'S/R GMREDI_CALC_PSI_BVP: matrix singular for PsiY' |
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CALL PRINT_ERROR( msgBuf, myThid ) |
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STOP 'ABNORMAL END: S/R GMREDI_CALC_PSI_BVP' |
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ENDIF |
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|
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#ifdef ALLOW_DIAGNOSTICS |
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C Write some diagnostics |
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IF ( useDiagnostics ) THEN |
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tmpFac = SQRT(gravity/rhoConst) |
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CALL DIAGNOSTICS_SCALE_FILL( wkb_cW, tmpFac, 1, 'GM_BVPcW', |
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& 0, 1, 2, bi, bj, myThid ) |
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CALL DIAGNOSTICS_SCALE_FILL( wkb_cS, tmpFac, 1, 'GM_BVPcS', |
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& 0, 1, 2, bi, bj, myThid ) |
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ENDIF |
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#endif |
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|
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ENDIF |
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#endif /* GM_BOLUS_ADVEC */ |
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#endif /* ALLOW_GMREDI */ |
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|
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RETURN |
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END |
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