C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_dst2u1_impl_r.F,v 1.4 2016/10/05 18:43:36 jmc Exp $ C $Name: $ #include "GAD_OPTIONS.h" CBOP C !ROUTINE: GAD_DST2U1_IMPL_R C !INTERFACE: SUBROUTINE GAD_DST2U1_IMPL_R( I bi,bj,k, iMin,iMax,jMin,jMax, I advectionScheme, deltaTarg, rTrans, recip_hFac, O a3d, b3d, c3d, I myThid ) C !DESCRIPTION: C Compute matrix element to solve vertical advection implicitly C using DST 2nd.Order (=Lax-Wendroff) or 1rst Order Upwind 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" #include "GAD.h" C !INPUT/OUTPUT PARAMETERS: C == Routine Arguments == C bi,bj :: tile indices C k :: vertical level C advectionScheme :: advection scheme to use: either 2nd Order DST C or 1rst Order Upwind 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 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 INTEGER advectionScheme _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 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 w_CFL :: Courant-Friedrich-Levy number C rLimit :: centered (vs upwind) fraction C rCenter :: centered contribution C rUpwind :: upwind contribution INTEGER i,j c _RL w_CFL _RL rLimit _RL rCenter, rUpwind _RL deltaTcfl CEOP rLimit = 0. _d 0 IF ( advectionScheme.EQ.ENUM_DST2 ) rLimit = 1. _d 0 C-- process interior interface only: IF ( k.GT.1 .AND. k.LE.Nr ) THEN C-- Add centered & upwind contributions deltaTcfl = deltaTarg(k) DO j=jMin,jMax DO i=iMin,iMax c w_CFL = deltaTcfl*ABS(rTrans(i,j)) c & *recip_rA(i,j,bi,bj)*recip_drC(k) c & *recip_deepFac2F(k)*recip_rhoFacF(k) rCenter = 0.5 _d 0 *rTrans(i,j)*recip_rA(i,j,bi,bj)*rkSign rUpwind = ABS(rCenter) & * ( 1. _d 0 - rLimit ) c & * ( 1. _d 0 - rLimit*( 1. _d 0 + w_CFL ) ) 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