| 1 |
jmc |
1.4 |
C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_dst3fl_impl_r.F,v 1.3 2006/06/07 01:55:14 heimbach Exp $ |
| 2 |
jmc |
1.1 |
C $Name: $ |
| 3 |
|
|
|
| 4 |
|
|
#include "GAD_OPTIONS.h" |
| 5 |
|
|
|
| 6 |
|
|
CBOP |
| 7 |
|
|
C !ROUTINE: GAD_DST3FL_IMPL_R |
| 8 |
|
|
C !INTERFACE: |
| 9 |
|
|
SUBROUTINE GAD_DST3FL_IMPL_R( |
| 10 |
|
|
I bi,bj,k, iMin,iMax,jMin,jMax, |
| 11 |
jmc |
1.4 |
I deltaTarg, rTrans, recip_hFac, tFld, |
| 12 |
jmc |
1.1 |
O a5d, b5d, c5d, d5d, e5d, |
| 13 |
|
|
I myThid ) |
| 14 |
|
|
|
| 15 |
|
|
C !DESCRIPTION: |
| 16 |
|
|
|
| 17 |
|
|
C Compute matrix element to solve vertical advection implicitly |
| 18 |
|
|
C using 3rd order Direct Space and Time (DST) advection scheme |
| 19 |
|
|
C with Flux-Limiter. |
| 20 |
|
|
C Method: |
| 21 |
|
|
C contribution of vertical transport at interface k is added |
| 22 |
|
|
C to matrix lines k and k-1 |
| 23 |
|
|
|
| 24 |
|
|
C !USES: |
| 25 |
|
|
IMPLICIT NONE |
| 26 |
|
|
|
| 27 |
|
|
C == Global variables === |
| 28 |
|
|
#include "SIZE.h" |
| 29 |
|
|
#include "GRID.h" |
| 30 |
|
|
#include "EEPARAMS.h" |
| 31 |
|
|
#include "PARAMS.h" |
| 32 |
|
|
#include "GAD.h" |
| 33 |
|
|
|
| 34 |
|
|
C !INPUT/OUTPUT PARAMETERS: |
| 35 |
|
|
C == Routine Arguments == |
| 36 |
jmc |
1.4 |
C bi,bj :: tile indices |
| 37 |
|
|
C k :: vertical level |
| 38 |
|
|
C iMin,iMax :: computation domain |
| 39 |
|
|
C jMin,jMax :: computation domain |
| 40 |
|
|
C deltaTarg :: time step |
| 41 |
|
|
C rTrans :: vertical volume transport |
| 42 |
|
|
C recip_hFac :: inverse of cell open-depth factor |
| 43 |
|
|
C tFld :: tracer field |
| 44 |
|
|
C a5d :: 2nd lower diag of pentadiagonal matrix |
| 45 |
|
|
C b5d :: 1rst lower diag of pentadiagonal matrix |
| 46 |
|
|
C c5d :: main diag of pentadiagonal matrix |
| 47 |
|
|
C d5d :: 1rst upper diag of pentadiagonal matrix |
| 48 |
|
|
C e5d :: 2nd upper diag of pentadiagonal matrix |
| 49 |
|
|
C myThid :: thread number |
| 50 |
jmc |
1.1 |
INTEGER bi,bj,k |
| 51 |
|
|
INTEGER iMin,iMax,jMin,jMax |
| 52 |
jmc |
1.4 |
_RL deltaTarg(Nr) |
| 53 |
|
|
_RL rTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 54 |
|
|
_RS recip_hFac(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
| 55 |
|
|
_RL tFld (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
| 56 |
|
|
_RL a5d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
| 57 |
|
|
_RL b5d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
| 58 |
|
|
_RL c5d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
| 59 |
|
|
_RL d5d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
| 60 |
|
|
_RL e5d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
| 61 |
jmc |
1.1 |
INTEGER myThid |
| 62 |
|
|
|
| 63 |
|
|
C == Local Variables == |
| 64 |
jmc |
1.4 |
C i,j :: loop indices |
| 65 |
|
|
C kp1 :: =min( k+1 , Nr ) |
| 66 |
|
|
C km2 :: =max( k-2 , 1 ) |
| 67 |
|
|
C wCFL :: Courant-Friedrich-Levy number |
| 68 |
|
|
C lowFac :: low order term factor |
| 69 |
|
|
C highFac :: high order term factor |
| 70 |
|
|
C rCenter :: centered contribution |
| 71 |
|
|
C rUpwind :: upwind contribution |
| 72 |
|
|
C rC4km, rC4kp :: high order contributions |
| 73 |
jmc |
1.1 |
INTEGER i,j,kp1,km2 |
| 74 |
|
|
_RL wCFL, rCenter, rUpwind |
| 75 |
|
|
_RL lowFac (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 76 |
|
|
_RL highFac(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 77 |
|
|
_RL rC4km, rC4kp |
| 78 |
|
|
_RL mskM, mskP, maskM2, maskP1 |
| 79 |
|
|
_RL Rj, Rjh, cL1, cH3, cM2, th1, th2 |
| 80 |
|
|
_RL deltaTcfl |
| 81 |
|
|
CEOP |
| 82 |
|
|
|
| 83 |
|
|
C-- process interior interface only: |
| 84 |
|
|
IF ( k.GT.1 .AND. k.LE.Nr ) THEN |
| 85 |
|
|
|
| 86 |
|
|
km2=MAX(1,k-2) |
| 87 |
|
|
kp1=MIN(Nr,k+1) |
| 88 |
|
|
maskP1 = 1. _d 0 |
| 89 |
|
|
maskM2 = 1. _d 0 |
| 90 |
|
|
IF ( k.LE.2 ) maskM2 = 0. _d 0 |
| 91 |
|
|
IF ( k.GE.Nr) maskP1 = 0. _d 0 |
| 92 |
|
|
|
| 93 |
|
|
C-- Compute the low-order term & high-order term fractions : |
| 94 |
|
|
deltaTcfl = deltaTarg(k) |
| 95 |
|
|
C DST-3 Flux-Limiter Advection Scheme: |
| 96 |
|
|
C- Limiter: Psi=max(0,min(1,cL1+theta*cH1,theta*(1-cfl)/cfl) ) |
| 97 |
|
|
C with theta=Rjh/Rj ; |
| 98 |
|
|
C is linearize arround the current value of theta(tFld) & cfl: |
| 99 |
|
|
C lowFac & highFac are set such as Psi*Rj = lowFac*Rj + highFac*Rjh |
| 100 |
|
|
DO j=jMin,jMax |
| 101 |
|
|
DO i=iMin,iMax |
| 102 |
|
|
wCFL = deltaTcfl*ABS(rTrans(i,j)) |
| 103 |
|
|
& *recip_rA(i,j,bi,bj)*recip_drC(k) |
| 104 |
|
|
cL1 = (2. _d 0 -wCFL)*(1. _d 0 -wCFL)*oneSixth |
| 105 |
|
|
cH3 = (1. _d 0 -wCFL*wCFL)*oneSixth |
| 106 |
|
|
c cM2 = (1. _d 0 - wCFL)/( wCFL +1. _d -20) |
| 107 |
|
|
cM2 = (1. _d 0 + wCFL)/( wCFL +1. _d -20) |
| 108 |
|
|
|
| 109 |
|
|
Rj =(tFld(i,j,k) -tFld(i,j,k-1)) |
| 110 |
|
|
IF ( rTrans(i,j).GT.0. _d 0 ) THEN |
| 111 |
|
|
Rjh = (tFld(i,j,k-1)-tFld(i,j,km2))*maskC(i,j,km2,bi,bj) |
| 112 |
|
|
ELSE |
| 113 |
|
|
Rjh = (tFld(i,j,kp1)-tFld(i,j,k) )*maskC(i,j,kp1,bi,bj) |
| 114 |
|
|
ENDIF |
| 115 |
|
|
IF ( Rj*Rjh.LE.0. _d 0 ) THEN |
| 116 |
|
|
C- 1rst case: theta < 0 (Rj & Rjh opposite sign) => Psi = 0 |
| 117 |
|
|
lowFac(i,j) = 0. _d 0 |
| 118 |
|
|
highFac(i,j)= 0. _d 0 |
| 119 |
|
|
ELSE |
| 120 |
|
|
Rj = ABS(Rj) |
| 121 |
|
|
Rjh = ABS(Rjh) |
| 122 |
|
|
th1 = cL1*Rj+cH3*Rjh |
| 123 |
|
|
th2 = cM2*Rjh |
| 124 |
|
|
IF ( th1.LE.th2 .AND. th1.LE.Rj ) THEN |
| 125 |
|
|
C- 2nd case: cL1+theta*cH3 = min of the three = Psi |
| 126 |
|
|
lowFac(i,j) = cL1 |
| 127 |
|
|
highFac(i,j)= cH3 |
| 128 |
|
|
ELSEIF ( th2.LT.th1 .AND. th2.LE.Rj ) THEN |
| 129 |
|
|
C- 3rd case: theta*cM2 = min of the three = Psi |
| 130 |
|
|
lowFac(i,j) = 0. _d 0 |
| 131 |
|
|
highFac(i,j)= cM2 |
| 132 |
|
|
ELSE |
| 133 |
|
|
C- 4th case (Rj < th1 & Rj < th2) : 1 = min of the three = Psi |
| 134 |
|
|
lowFac(i,j) = 1. _d 0 |
| 135 |
|
|
highFac(i,j)= 0. _d 0 |
| 136 |
|
|
ENDIF |
| 137 |
|
|
ENDIF |
| 138 |
|
|
ENDDO |
| 139 |
|
|
ENDDO |
| 140 |
|
|
|
| 141 |
|
|
C-- Add centered & upwind contributions |
| 142 |
|
|
DO j=jMin,jMax |
| 143 |
|
|
DO i=iMin,iMax |
| 144 |
|
|
rCenter= 0.5 _d 0 *rTrans(i,j)*recip_rA(i,j,bi,bj)*rkSign |
| 145 |
|
|
mskM = maskC(i,j,km2,bi,bj)*maskM2 |
| 146 |
|
|
mskP = maskC(i,j,kp1,bi,bj)*maskP1 |
| 147 |
|
|
rUpwind= (0.5 _d 0 -lowFac(i,j))*ABS(rCenter)*2. _d 0 |
| 148 |
|
|
rC4km = highFac(i,j)*(rCenter+ABS(rCenter))*mskM |
| 149 |
|
|
rC4kp = highFac(i,j)*(rCenter-ABS(rCenter))*mskP |
| 150 |
|
|
|
| 151 |
|
|
a5d(i,j,k) = a5d(i,j,k) |
| 152 |
|
|
& + rC4km |
| 153 |
|
|
& *deltaTarg(k) |
| 154 |
jmc |
1.4 |
& *recip_hFac(i,j,k)*recip_drF(k) |
| 155 |
jmc |
1.1 |
b5d(i,j,k) = b5d(i,j,k) |
| 156 |
|
|
& - ( (rCenter+rUpwind) + rC4km ) |
| 157 |
|
|
& *deltaTarg(k) |
| 158 |
jmc |
1.4 |
& *recip_hFac(i,j,k)*recip_drF(k) |
| 159 |
jmc |
1.1 |
c5d(i,j,k) = c5d(i,j,k) |
| 160 |
|
|
& - ( (rCenter-rUpwind) + rC4kp ) |
| 161 |
|
|
& *deltaTarg(k) |
| 162 |
jmc |
1.4 |
& *recip_hFac(i,j,k)*recip_drF(k) |
| 163 |
jmc |
1.1 |
d5d(i,j,k) = d5d(i,j,k) |
| 164 |
|
|
& + rC4kp |
| 165 |
|
|
& *deltaTarg(k) |
| 166 |
jmc |
1.4 |
& *recip_hFac(i,j,k)*recip_drF(k) |
| 167 |
jmc |
1.1 |
b5d(i,j,k-1) = b5d(i,j,k-1) |
| 168 |
|
|
& - rC4km |
| 169 |
|
|
& *deltaTarg(k-1) |
| 170 |
jmc |
1.4 |
& *recip_hFac(i,j,k-1)*recip_drF(k-1) |
| 171 |
jmc |
1.1 |
c5d(i,j,k-1) = c5d(i,j,k-1) |
| 172 |
|
|
& + ( (rCenter+rUpwind) + rC4km ) |
| 173 |
|
|
& *deltaTarg(k-1) |
| 174 |
jmc |
1.4 |
& *recip_hFac(i,j,k-1)*recip_drF(k-1) |
| 175 |
jmc |
1.1 |
d5d(i,j,k-1) = d5d(i,j,k-1) |
| 176 |
|
|
& + ( (rCenter-rUpwind) + rC4kp ) |
| 177 |
|
|
& *deltaTarg(k-1) |
| 178 |
jmc |
1.4 |
& *recip_hFac(i,j,k-1)*recip_drF(k-1) |
| 179 |
jmc |
1.1 |
e5d(i,j,k-1) = e5d(i,j,k-1) |
| 180 |
|
|
& - rC4kp |
| 181 |
|
|
& *deltaTarg(k-1) |
| 182 |
jmc |
1.4 |
& *recip_hFacC(i,j,k-1,bi,bj)*recip_drF(k-1) |
| 183 |
jmc |
1.1 |
ENDDO |
| 184 |
|
|
ENDDO |
| 185 |
|
|
|
| 186 |
|
|
C-- process interior interface only: end |
| 187 |
|
|
ENDIF |
| 188 |
|
|
|
| 189 |
|
|
RETURN |
| 190 |
|
|
END |
Parent Directory
| 
Revision Log
| 
Revision Graph