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C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_os7mp_adv_r.F,v 1.4 2007/05/11 18:24:31 adcroft Exp $ |
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C $Name: $ |
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|
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#include "GAD_OPTIONS.h" |
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|
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SUBROUTINE GAD_OS7MP_ADV_R( |
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I bi,bj,k,deltaTloc, |
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I wTrans, wFld, |
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I Q, |
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O wT, |
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I myThid ) |
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C /==========================================================\ |
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C | SUBROUTINE GAD_OS7MP_ADV_R | |
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C | o Compute Vertical advective Flux of tracer Q using | |
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C | 7th Order DST Sceheme with monotone preserving limiter | |
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C |==========================================================| |
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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 "GRID.h" |
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#include "GAD.h" |
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|
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C == Routine arguments == |
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INTEGER bi,bj,k |
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_RL deltaTloc |
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_RL wTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL wFld (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL Q (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL wT (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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INTEGER myThid |
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|
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C == Local variables == |
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INTEGER i,j,kp3,kp2,kp1,km1,km2,km3,km4 |
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_RL cfl,Psi |
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_RL wLoc,Fac,DelIp,DelI,Phi,Eps,rp1h,rp1h_cfl |
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_RL Qippp,Qipp,Qip,Qi,Qim,Qimm,Qimmm |
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_RL MskIpp,MskIp,MskI,MskIm,MskImm,MskImmm |
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_RL d2,d2p1,d2m1,A,B,C,D |
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_RL dp1h,dm1h,qMD,qUL,qLC,PhiMD,PhiLC,PhiMin,PhiMax |
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_RL DelM,DelP,DelMM,DelPP,DelMMM,DelPPP |
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_RL Del2MM,Del2M,Del2,Del2P,Del2PP |
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_RL Del3MM,Del3M,Del3P,Del3PP |
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_RL Del4M,Del4,Del4P |
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_RL Del5M,Del5P |
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_RL Del6 |
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|
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Eps = 1. _d -20 |
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|
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km4=MAX(1,k-4) |
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km3=MAX(1,k-3) |
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km2=MAX(1,k-2) |
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km1=MAX(1,k-1) |
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kp1=MIN(Nr,k+1) |
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kp2=MIN(Nr,k+2) |
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kp3=MIN(Nr,k+3) |
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|
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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|
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wLoc = wFld(i,j) |
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cfl = abs(wLoc*deltaTloc*recip_drC(k)) |
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|
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IF (wTrans(i,j).lt.0.) THEN |
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Qippp = Q(i,j,kp2) |
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Qipp = Q(i,j,kp1) |
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Qip = Q(i,j,k) |
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Qi = Q(i,j,km1) |
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Qim = Q(i,j,km2) |
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Qimm = Q(i,j,km3) |
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Qimmm = Q(i,j,km4) |
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|
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MskIpp = maskC(i,j,kp2,bi,bj) * float(kp2-kp1) |
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MskIp = maskC(i,j,kp1,bi,bj) * float(kp1-k) |
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MskI = maskC(i,j,k,bi,bj) * float(k-km1) |
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MskIm = maskC(i,j,km1,bi,bj) * float(km1-km2) |
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MskImm = maskC(i,j,km2,bi,bj) * float(km2-km3) |
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MskImmm = maskC(i,j,km3,bi,bj) * float(km3-km4) |
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ELSEIF (wTrans(i,j).gt.0.) THEN |
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Qippp = Q(i,j,km3) |
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Qipp = Q(i,j,km2) |
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Qip = Q(i,j,km1) |
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Qi = Q(i,j,k) |
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Qim = Q(i,j,kp1) |
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Qimm = Q(i,j,kp2) |
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Qimmm = Q(i,j,kp3) |
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|
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MskIpp = maskC(i,j,km2,bi,bj) * float(km2-km3) |
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MskIp = maskC(i,j,km1,bi,bj) * float(km1-km2) |
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MskI = maskC(i,j,k,bi,bj) * float(k-km1) |
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MskIm = maskC(i,j,kp1,bi,bj) * float(kp1-k) |
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MskImm = maskC(i,j,kp2,bi,bj) * float(kp2-kp1) |
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MskImmm = maskC(i,j,kp3,bi,bj) * float(kp3-kp2) |
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ENDIF |
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|
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IF (wTrans(i,j).ne.0.) THEN |
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C 2nd order correction [i i-1] |
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Fac = 1. |
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DelP = (Qip-Qi)*MskI |
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Phi = Fac * DelP |
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C 3rd order correction [i i-1 i-2] |
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Fac = Fac * ( cfl + 1. )/3. |
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DelM = (Qi-Qim)*MskIm |
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Del2 = DelP - DelM |
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Phi = Phi - Fac * Del2 |
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C 4th order correction [i+1 i i-1 i-2] |
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Fac = Fac * ( cfl - 2. )/4. |
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DelPP = (Qipp-Qip)*MskIp*MskI |
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Del2P = DelPP - DelP |
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Del3P = Del2P - Del2 |
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Phi = Phi + Fac * Del3p |
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C 5th order correction [i+1 i i-1 i-2 i-3] |
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Fac = Fac * ( cfl - 3. )/5. |
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DelMM = (Qim-Qimm)*MskImm*MskIm |
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Del2M = DelM - DelMM |
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Del3M = Del2 - Del2M |
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Del4 = Del3P - Del3M |
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Phi = Phi + Fac * Del4 |
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C 6th order correction [i+2 i+1 i i-1 i-2 i-3] |
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Fac = Fac * ( cfl + 2. )/6. |
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DelPPP = (Qippp-Qipp)*MskIpp*MskIp*MskI |
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Del2PP = DelPP - DelP |
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Del3PP = Del2PP - Del2P |
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Del4P = Del3PP - Del3P |
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Del5P = Del4P - Del4 |
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Phi = Phi + Fac * Del5P |
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C 7th order correction [i+2 i+1 i i-1 i-2 i-3 i-4] |
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Fac = Fac * ( cfl + 2. )/7. |
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DelMMM = (Qimm-Qimmm)*MskImmm*MskImm*MskIm |
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Del2MM = DelMM - DelMMM |
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Del3MM = Del2M - Del2MM |
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Del4M = Del3M - Del3MM |
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Del5M = Del4 - Del4M |
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Del6 = Del5P - Del5M |
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Phi = Phi - Fac * Del6 |
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|
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DelIp = ( Qip - Qi ) * MskI |
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Phi = sign(1. _d 0,Phi)*sign(1. _d 0,DelIp) |
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& *abs(Phi+Eps)/abs(DelIp+Eps) |
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|
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DelI = ( Qi - Qim ) * MskIm |
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rp1h =sign(1. _d 0,DelI)*sign(1. _d 0,DelIp) |
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& *abs(DelI+Eps)/abs(DelIp+Eps) |
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rp1h_cfl = rp1h/(cfl+Eps) |
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|
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C TVD limiter |
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! Phi = max(0. _d 0, min( 2./(1-cfl), Phi, 2.*rp1h_cfl ) ) |
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|
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C MP limiter |
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d2 = Del2 !( ( Qip + Qim ) - 2.*Qi ) * MskI * MskIm |
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d2p1 = Del2P !( ( Qipp + Qi ) - 2.*Qip ) * MskIp * MskI |
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d2m1 = Del2M !( ( Qi + Qimm ) - 2.*Qim ) * MskIm * MskImm |
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A = 4.*d2 - d2p1 |
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B = 4.*d2p1 - d2 |
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C = d2 |
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D = d2p1 |
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dp1h = max(min(A,B,C,D),0. _d 0)+min(max(A,B,C,D),0. _d 0) |
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A = 4.*d2m1 - d2 |
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B = 4.*d2 - d2m1 |
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C = d2m1 |
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D = d2 |
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dm1h = max(min(A,B,C,D),0. _d 0)+min(max(A,B,C,D),0. _d 0) |
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!qMD = 0.5*( ( Qi + Qip ) - dp1h ) |
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qMD = 0.5*( ( 2.*Qi + DelIp ) - dp1h ) |
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qUL = Qi + (1.-cfl)/(cfl+Eps)*DelI |
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qLC = Qi + 0.5*( 1.+dm1h/(DelI+Eps) )*(qUL-Qi) |
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PhiMD = 2./(1.-cfl)*(qMD-Qi+Eps)/(DelIp+Eps) |
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PhiLC = 2.*rp1h_cfl*(qLC-Qi+Eps)/(qUL-Qi+Eps) |
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PhiMin = max(min(0. _d 0,PhiMD), |
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& min(0. _d 0,2.*rp1h_cfl,PhiLC)) |
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PhiMax = min(max(2. _d 0/(1.-cfl),PhiMD), |
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& max(0. _d 0,2.*rp1h_cfl,PhiLC)) |
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Phi = max(PhiMin,min(Phi,PhiMax)) |
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|
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Psi = Phi * 0.5 * (1. - cfl) |
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wT(i,j) = wTrans(i,j)*( Qi + Psi*DelIp ) |
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ELSE |
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wT(i,j) = 0. |
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ENDIF |
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|
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ENDDO |
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ENDDO |
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|
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RETURN |
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END |
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