C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_dst3fl_impl_r.F,v 1.5 2016/10/05 18:43:36 jmc Exp $ C $Name: $ #include "GAD_OPTIONS.h" CBOP C !ROUTINE: GAD_DST3FL_IMPL_R C !INTERFACE: SUBROUTINE GAD_DST3FL_IMPL_R( I bi,bj,k, iMin,iMax,jMin,jMax, I deltaTarg, rTrans, recip_hFac, tFld, O a5d, b5d, c5d, d5d, e5d, I myThid ) C !DESCRIPTION: C Compute matrix element to solve vertical advection implicitly C using 3rd order Direct Space and Time (DST) advection scheme C with Flux-Limiter. 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 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 a5d :: 2nd lower diag of pentadiagonal matrix C b5d :: 1rst lower diag of pentadiagonal matrix C c5d :: main diag of pentadiagonal matrix C d5d :: 1rst upper diag of pentadiagonal matrix C e5d :: 2nd upper diag of pentadiagonal 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 a5d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL b5d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL c5d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL d5d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL e5d (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 km2 :: =max( k-2 , 1 ) C wCFL :: Courant-Friedrich-Levy number C lowFac :: low order term factor C highFac :: high order term factor C rCenter :: centered contribution C rUpwind :: upwind contribution C rC4km, rC4kp :: high order contributions INTEGER i,j,kp1,km2 _RL wCFL, rCenter, rUpwind _RL lowFac (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL highFac(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL rC4km, rC4kp _RL mskM, mskP, maskM2, maskP1 _RL Rj, Rjh, cL1, cH3, cM2, th1, th2 _RL deltaTcfl CEOP C-- process interior interface only: IF ( k.GT.1 .AND. k.LE.Nr ) THEN km2=MAX(1,k-2) kp1=MIN(Nr,k+1) maskP1 = 1. _d 0 maskM2 = 1. _d 0 IF ( k.LE.2 ) maskM2 = 0. _d 0 IF ( k.GE.Nr) maskP1 = 0. _d 0 C-- Compute the low-order term & high-order term fractions : deltaTcfl = deltaTarg(k) C DST-3 Flux-Limiter Advection Scheme: C- Limiter: Psi=max(0,min(1,cL1+theta*cH1,theta*(1-cfl)/cfl) ) C with theta=Rjh/Rj ; C is linearize arround the current value of theta(tFld) & cfl: C lowFac & highFac are set such as Psi*Rj = lowFac*Rj + highFac*Rjh DO j=jMin,jMax DO i=iMin,iMax wCFL = deltaTcfl*ABS(rTrans(i,j)) & *recip_rA(i,j,bi,bj)*recip_drC(k) & *recip_deepFac2F(k)*recip_rhoFacF(k) cL1 = (2. _d 0 -wCFL)*(1. _d 0 -wCFL)*oneSixth cH3 = (1. _d 0 -wCFL*wCFL)*oneSixth c cM2 = (1. _d 0 - wCFL)/( wCFL +1. _d -20) cM2 = (1. _d 0 + wCFL)/( wCFL +1. _d -20) Rj =(tFld(i,j,k) -tFld(i,j,k-1)) IF ( rTrans(i,j).GT.0. _d 0 ) THEN Rjh = (tFld(i,j,k-1)-tFld(i,j,km2))*maskC(i,j,km2,bi,bj) ELSE Rjh = (tFld(i,j,kp1)-tFld(i,j,k) )*maskC(i,j,kp1,bi,bj) ENDIF IF ( Rj*Rjh.LE.0. _d 0 ) THEN C- 1rst case: theta < 0 (Rj & Rjh opposite sign) => Psi = 0 lowFac(i,j) = 0. _d 0 highFac(i,j)= 0. _d 0 ELSE Rj = ABS(Rj) Rjh = ABS(Rjh) th1 = cL1*Rj+cH3*Rjh th2 = cM2*Rjh IF ( th1.LE.th2 .AND. th1.LE.Rj ) THEN C- 2nd case: cL1+theta*cH3 = min of the three = Psi lowFac(i,j) = cL1 highFac(i,j)= cH3 ELSEIF ( th2.LT.th1 .AND. th2.LE.Rj ) THEN C- 3rd case: theta*cM2 = min of the three = Psi lowFac(i,j) = 0. _d 0 highFac(i,j)= cM2 ELSE C- 4th case (Rj < th1 & Rj < th2) : 1 = min of the three = Psi lowFac(i,j) = 1. _d 0 highFac(i,j)= 0. _d 0 ENDIF 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 mskM = maskC(i,j,km2,bi,bj)*maskM2 mskP = maskC(i,j,kp1,bi,bj)*maskP1 rUpwind= (0.5 _d 0 -lowFac(i,j))*ABS(rCenter)*2. _d 0 rC4km = highFac(i,j)*(rCenter+ABS(rCenter))*mskM rC4kp = highFac(i,j)*(rCenter-ABS(rCenter))*mskP a5d(i,j,k) = a5d(i,j,k) & + rC4km & *deltaTarg(k) & *recip_hFac(i,j,k)*recip_drF(k) & *recip_deepFac2C(k)*recip_rhoFacC(k) b5d(i,j,k) = b5d(i,j,k) & - ( (rCenter+rUpwind) + rC4km ) & *deltaTarg(k) & *recip_hFac(i,j,k)*recip_drF(k) & *recip_deepFac2C(k)*recip_rhoFacC(k) c5d(i,j,k) = c5d(i,j,k) & - ( (rCenter-rUpwind) + rC4kp ) & *deltaTarg(k) & *recip_hFac(i,j,k)*recip_drF(k) & *recip_deepFac2C(k)*recip_rhoFacC(k) d5d(i,j,k) = d5d(i,j,k) & + rC4kp & *deltaTarg(k) & *recip_hFac(i,j,k)*recip_drF(k) & *recip_deepFac2C(k)*recip_rhoFacC(k) b5d(i,j,k-1) = b5d(i,j,k-1) & - rC4km & *deltaTarg(k-1) & *recip_hFac(i,j,k-1)*recip_drF(k-1) & *recip_deepFac2C(k-1)*recip_rhoFacC(k-1) c5d(i,j,k-1) = c5d(i,j,k-1) & + ( (rCenter+rUpwind) + rC4km ) & *deltaTarg(k-1) & *recip_hFac(i,j,k-1)*recip_drF(k-1) & *recip_deepFac2C(k-1)*recip_rhoFacC(k-1) d5d(i,j,k-1) = d5d(i,j,k-1) & + ( (rCenter-rUpwind) + rC4kp ) & *deltaTarg(k-1) & *recip_hFac(i,j,k-1)*recip_drF(k-1) & *recip_deepFac2C(k-1)*recip_rhoFacC(k-1) e5d(i,j,k-1) = e5d(i,j,k-1) & - rC4kp & *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