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jmc |
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C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_u3c4_impl_r.F,v 1.5 2005/06/22 00:27:47 jmc Exp $ |
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C $Name: $ |
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#include "GAD_OPTIONS.h" |
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CBOP |
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C !ROUTINE: GAD_DST3FL_IMPL_R |
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C !INTERFACE: |
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SUBROUTINE GAD_DST3FL_IMPL_R( |
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I bi,bj,k, iMin,iMax,jMin,jMax, |
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I deltaTarg, rTrans, tFld, |
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O a5d, b5d, c5d, d5d, e5d, |
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I myThid ) |
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C !DESCRIPTION: |
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C Compute matrix element to solve vertical advection implicitly |
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C using 3rd order Direct Space and Time (DST) advection scheme |
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C with Flux-Limiter. |
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C Method: |
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C contribution of vertical transport at interface k is added |
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C to matrix lines k and k-1 |
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C !USES: |
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IMPLICIT NONE |
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C == Global variables === |
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#include "SIZE.h" |
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#include "GRID.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "GAD.h" |
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C !INPUT/OUTPUT PARAMETERS: |
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C == Routine Arguments == |
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C bi,bj :: tile indices |
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C k :: vertical level |
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C iMin,iMax :: computation domain |
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C jMin,jMax :: computation domain |
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C deltaTarg :: time step |
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C rTrans :: vertical volume transport |
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C tFld :: tracer field |
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C a5d :: 2nd lower diag of pentadiagonal matrix |
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C b5d :: 1rst lower diag of pentadiagonal matrix |
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C c5d :: main diag of pentadiagonal matrix |
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C d5d :: 1rst upper diag of pentadiagonal matrix |
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C e5d :: 2nd upper diag of pentadiagonal matrix |
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C myThid :: thread number |
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INTEGER bi,bj,k |
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INTEGER iMin,iMax,jMin,jMax |
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_RL deltaTarg(Nr) |
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_RL rTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL tFld (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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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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INTEGER myThid |
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C == Local Variables == |
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C i,j :: loop indices |
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C kp1 :: =min( k+1 , Nr ) |
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C km2 :: =max( k-2 , 1 ) |
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C wCFL :: Courant-Friedrich-Levy number |
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C lowFac :: low order term factor |
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C highFac :: high order term factor |
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C rCenter :: centered contribution |
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C rUpwind :: upwind contribution |
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C rC4km, rC4kp :: high order contributions |
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LOGICAL flagC4 |
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INTEGER i,j,kp1,km2 |
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_RL wCFL, rCenter, rUpwind |
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_RL lowFac (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL highFac(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL rC4km, rC4kp |
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_RL mskM, mskP, maskM2, maskP1 |
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_RL Rj, Rjh, cL1, cH3, cM2, th1, th2 |
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_RL deltaTcfl |
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CEOP |
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C-- process interior interface only: |
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IF ( k.GT.1 .AND. k.LE.Nr ) THEN |
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km2=MAX(1,k-2) |
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kp1=MIN(Nr,k+1) |
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maskP1 = 1. _d 0 |
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maskM2 = 1. _d 0 |
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IF ( k.LE.2 ) maskM2 = 0. _d 0 |
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IF ( k.GE.Nr) maskP1 = 0. _d 0 |
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C-- Compute the low-order term & high-order term fractions : |
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deltaTcfl = deltaTarg(k) |
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C DST-3 Flux-Limiter Advection Scheme: |
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C- Limiter: Psi=max(0,min(1,cL1+theta*cH1,theta*(1-cfl)/cfl) ) |
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C with theta=Rjh/Rj ; |
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C is linearize arround the current value of theta(tFld) & cfl: |
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C lowFac & highFac are set such as Psi*Rj = lowFac*Rj + highFac*Rjh |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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wCFL = deltaTcfl*ABS(rTrans(i,j)) |
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& *recip_rA(i,j,bi,bj)*recip_drC(k) |
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cL1 = (2. _d 0 -wCFL)*(1. _d 0 -wCFL)*oneSixth |
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cH3 = (1. _d 0 -wCFL*wCFL)*oneSixth |
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c cM2 = (1. _d 0 - wCFL)/( wCFL +1. _d -20) |
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cM2 = (1. _d 0 + wCFL)/( wCFL +1. _d -20) |
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Rj =(tFld(i,j,k) -tFld(i,j,k-1)) |
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IF ( rTrans(i,j).GT.0. _d 0 ) THEN |
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Rjh = (tFld(i,j,k-1)-tFld(i,j,km2))*maskC(i,j,km2,bi,bj) |
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ELSE |
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Rjh = (tFld(i,j,kp1)-tFld(i,j,k) )*maskC(i,j,kp1,bi,bj) |
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ENDIF |
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IF ( Rj*Rjh.LE.0. _d 0 ) THEN |
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C- 1rst case: theta < 0 (Rj & Rjh opposite sign) => Psi = 0 |
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lowFac(i,j) = 0. _d 0 |
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highFac(i,j)= 0. _d 0 |
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ELSE |
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Rj = ABS(Rj) |
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Rjh = ABS(Rjh) |
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th1 = cL1*Rj+cH3*Rjh |
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th2 = cM2*Rjh |
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IF ( th1.LE.th2 .AND. th1.LE.Rj ) THEN |
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C- 2nd case: cL1+theta*cH3 = min of the three = Psi |
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lowFac(i,j) = cL1 |
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highFac(i,j)= cH3 |
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ELSEIF ( th2.LT.th1 .AND. th2.LE.Rj ) THEN |
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C- 3rd case: theta*cM2 = min of the three = Psi |
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lowFac(i,j) = 0. _d 0 |
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highFac(i,j)= cM2 |
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ELSE |
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C- 4th case (Rj < th1 & Rj < th2) : 1 = min of the three = Psi |
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lowFac(i,j) = 1. _d 0 |
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highFac(i,j)= 0. _d 0 |
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ENDIF |
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ENDIF |
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ENDDO |
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ENDDO |
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C-- Add centered & upwind contributions |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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rCenter= 0.5 _d 0 *rTrans(i,j)*recip_rA(i,j,bi,bj)*rkSign |
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mskM = maskC(i,j,km2,bi,bj)*maskM2 |
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mskP = maskC(i,j,kp1,bi,bj)*maskP1 |
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rUpwind= (0.5 _d 0 -lowFac(i,j))*ABS(rCenter)*2. _d 0 |
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rC4km = highFac(i,j)*(rCenter+ABS(rCenter))*mskM |
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rC4kp = highFac(i,j)*(rCenter-ABS(rCenter))*mskP |
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a5d(i,j,k) = a5d(i,j,k) |
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& + rC4km |
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& *deltaTarg(k) |
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& *recip_hFacC(i,j,k,bi,bj)*recip_drF(k) |
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b5d(i,j,k) = b5d(i,j,k) |
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& - ( (rCenter+rUpwind) + rC4km ) |
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& *deltaTarg(k) |
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& *recip_hFacC(i,j,k,bi,bj)*recip_drF(k) |
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c5d(i,j,k) = c5d(i,j,k) |
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& - ( (rCenter-rUpwind) + rC4kp ) |
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& *deltaTarg(k) |
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& *recip_hFacC(i,j,k,bi,bj)*recip_drF(k) |
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d5d(i,j,k) = d5d(i,j,k) |
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& + rC4kp |
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& *deltaTarg(k) |
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& *recip_hFacC(i,j,k,bi,bj)*recip_drF(k) |
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b5d(i,j,k-1) = b5d(i,j,k-1) |
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& - rC4km |
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& *deltaTarg(k-1) |
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& *recip_hFacC(i,j,k-1,bi,bj)*recip_drF(k-1) |
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c5d(i,j,k-1) = c5d(i,j,k-1) |
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& + ( (rCenter+rUpwind) + rC4km ) |
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& *deltaTarg(k-1) |
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& *recip_hFacC(i,j,k-1,bi,bj)*recip_drF(k-1) |
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d5d(i,j,k-1) = d5d(i,j,k-1) |
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& + ( (rCenter-rUpwind) + rC4kp ) |
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& *deltaTarg(k-1) |
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& *recip_hFacC(i,j,k-1,bi,bj)*recip_drF(k-1) |
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e5d(i,j,k-1) = e5d(i,j,k-1) |
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& - rC4kp |
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& *deltaTarg(k-1) |
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& *recip_hFacC(i,j,k-1,bi,bj)*recip_drF(k-1) |
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ENDDO |
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ENDDO |
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C-- process interior interface only: end |
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ENDIF |
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RETURN |
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END |
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