C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_fluxlimit_impl_r.F,v 1.10 2016/10/05 18:43:36 jmc Exp $ C $Name: $ #include "GAD_OPTIONS.h" CBOP C !ROUTINE: GAD_FLUXLIMIT_IMPL_R C !INTERFACE: SUBROUTINE GAD_FLUXLIMIT_IMPL_R( I bi,bj,k, iMin,iMax,jMin,jMax, I deltaTarg, rTrans, recip_hFac, tFld, O a3d, b3d, c3d, I myThid ) C !DESCRIPTION: C Compute matrix element to solve vertical advection implicitly C using flux--limiter advection scheme. C Method: C contribution of vertical transport at interface k is added C to matrix lines k and k-1. C !USES: IMPLICIT NONE C == Global variables === #include "SIZE.h" #include "GRID.h" #include "EEPARAMS.h" #include "PARAMS.h" C !INPUT/OUTPUT PARAMETERS: C == Routine Arguments == C bi,bj :: tile indices C k :: vertical level C iMin,iMax :: computation domain C jMin,jMax :: computation domain C deltaTarg :: time step C rTrans :: vertical volume transport C recip_hFac :: inverse of cell open-depth factor C tFld :: tracer field C a3d :: lower diagonal of the tridiagonal matrix C b3d :: main diagonal of the tridiagonal matrix C c3d :: upper diagonal of the tridiagonal matrix C myThid :: thread number INTEGER bi,bj,k INTEGER iMin,iMax,jMin,jMax _RL deltaTarg(Nr) _RL rTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RS recip_hFac(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL tFld (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL a3d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL b3d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL c3d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) INTEGER myThid C == Local Variables == C i,j :: loop indices C kp1 :: =min( k+1 , Nr ) C km1 :: =max( k-1 , 1 ) C km2 :: =max( k-2 , 1 ) C Cr :: slope ratio C Rjm,Rj,Rjp :: differences at i-1,i,i+1 C w_CFL :: Courant-Friedrich-Levy number C upwindFac :: upwind factor C rCenter :: centered contribution C rUpwind :: upwind contribution INTEGER i,j,kp1,km1,km2 _RL Cr,Rjm,Rj,Rjp, w_CFL _RL upwindFac(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL rCenter, rUpwind _RL deltaTcfl C Statement function provides Limiter(Cr) #include "GAD_FLUX_LIMITER.h" CEOP km2=MAX(1,k-2) km1=MAX(1,k-1) kp1=MIN(Nr,k+1) C-- process interior interface only: IF ( k.GT.1 .AND. k.LE.Nr ) THEN C-- Compute the upwind fraction: deltaTcfl = deltaTarg(k) DO j=jMin,jMax DO i=iMin,iMax w_CFL = deltaTcfl*rTrans(i,j)*recip_rA(i,j,bi,bj)*recip_drC(k) & *recip_deepFac2F(k)*recip_rhoFacF(k) Rjp=(tFld(i,j,kp1)-tFld(i,j,k) )*maskC(i,j,kp1,bi,bj) Rj =(tFld(i,j,k) -tFld(i,j,km1)) Rjm=(tFld(i,j,km1)-tFld(i,j,km2))*maskC(i,j,km2,bi,bj) IF ( Rj.NE.0. _d 0) THEN IF (rTrans(i,j).LT.0. _d 0) THEN Cr=Rjm/Rj ELSE Cr=Rjp/Rj ENDIF upwindFac(i,j) = 1. _d 0 & - Limiter(Cr) * ( 1. _d 0 + ABS(w_CFL) ) upwindFac(i,j) = MAX( -1. _d 0, upwindFac(i,j) ) ELSE upwindFac(i,j) = 0. _d 0 ENDIF ENDDO ENDDO C-- Add centered & upwind contributions DO j=jMin,jMax DO i=iMin,iMax rCenter = 0.5 _d 0 *rTrans(i,j)*recip_rA(i,j,bi,bj)*rkSign rUpwind = ABS(rCenter)*upwindFac(i,j) a3d(i,j,k) = a3d(i,j,k) & - (rCenter+rUpwind)*deltaTarg(k) & *recip_hFac(i,j,k)*recip_drF(k) & *recip_deepFac2C(k)*recip_rhoFacC(k) b3d(i,j,k) = b3d(i,j,k) & - (rCenter-rUpwind)*deltaTarg(k) & *recip_hFac(i,j,k)*recip_drF(k) & *recip_deepFac2C(k)*recip_rhoFacC(k) b3d(i,j,k-1) = b3d(i,j,k-1) & + (rCenter+rUpwind)*deltaTarg(k-1) & *recip_hFac(i,j,k-1)*recip_drF(k-1) & *recip_deepFac2C(k-1)*recip_rhoFacC(k-1) c3d(i,j,k-1) = c3d(i,j,k-1) & + (rCenter-rUpwind)*deltaTarg(k-1) & *recip_hFac(i,j,k-1)*recip_drF(k-1) & *recip_deepFac2C(k-1)*recip_rhoFacC(k-1) ENDDO ENDDO C-- process interior interface only: end ENDIF RETURN END