1 |
jmc |
1.9 |
C $Header: /u/gcmpack/MITgcm/pkg/mom_common/mom_v_implicit_r.F,v 1.8 2016/11/28 23:09:12 jmc Exp $ |
2 |
jmc |
1.1 |
C $Name: $ |
3 |
|
|
|
4 |
|
|
#include "MOM_COMMON_OPTIONS.h" |
5 |
|
|
|
6 |
|
|
CBOP |
7 |
|
|
C !ROUTINE: MOM_V_IMPLICIT_R |
8 |
|
|
C !INTERFACE: |
9 |
|
|
SUBROUTINE MOM_V_IMPLICIT_R( |
10 |
|
|
I kappaRV, |
11 |
|
|
I bi, bj, myTime, myIter, myThid ) |
12 |
|
|
C !DESCRIPTION: \bv |
13 |
|
|
C *==========================================================* |
14 |
|
|
C | S/R MOM_V_IMPLICIT_R |
15 |
|
|
C | o Solve implicitly vertical advection & diffusion |
16 |
|
|
C | of momentum, meridional component |
17 |
|
|
C *==========================================================* |
18 |
|
|
C *==========================================================* |
19 |
|
|
C \ev |
20 |
|
|
|
21 |
|
|
C !USES: |
22 |
|
|
IMPLICIT NONE |
23 |
|
|
C == Global data == |
24 |
|
|
#include "SIZE.h" |
25 |
|
|
#include "EEPARAMS.h" |
26 |
|
|
#include "PARAMS.h" |
27 |
|
|
#include "GRID.h" |
28 |
|
|
#include "DYNVARS.h" |
29 |
|
|
|
30 |
|
|
C !INPUT/OUTPUT PARAMETERS: |
31 |
|
|
C == Routine Arguments == |
32 |
jmc |
1.9 |
_RL kappaRV(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr+1) |
33 |
jmc |
1.1 |
INTEGER bi, bj |
34 |
|
|
_RL myTime |
35 |
|
|
INTEGER myIter, myThid |
36 |
|
|
|
37 |
|
|
C !LOCAL VARIABLES: |
38 |
|
|
C == Local variables == |
39 |
jmc |
1.6 |
C iMin,iMax,jMin,jMax :: computational domain |
40 |
|
|
C i,j,k :: loop indices |
41 |
|
|
C a5d :: 2nd lower diagonal of the pentadiagonal matrix |
42 |
|
|
C b5d :: 1rst lower diagonal of the pentadiagonal matrix |
43 |
|
|
C c5d :: main diagonal of the pentadiagonal matrix |
44 |
|
|
C d5d :: 1rst upper diagonal of the pentadiagonal matrix |
45 |
|
|
C e5d :: 2nd upper diagonal of the pentadiagonal matrix |
46 |
|
|
C rTrans :: vertical volume transport at interface k |
47 |
|
|
C diagonalNumber :: number of non-zero diagonals in the matrix |
48 |
|
|
C errCode :: > 0 if singular matrix |
49 |
jmc |
1.1 |
INTEGER iMin,iMax,jMin,jMax |
50 |
jmc |
1.6 |
PARAMETER( iMin = 1, iMax = sNx ) |
51 |
|
|
PARAMETER( jMin = 1, jMax = sNy+1 ) |
52 |
jmc |
1.1 |
INTEGER i,j,k |
53 |
|
|
INTEGER diagonalNumber, errCode |
54 |
jmc |
1.5 |
c _RL a5d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
55 |
|
|
_RL b5d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
56 |
|
|
_RL c5d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
57 |
|
|
_RL d5d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
58 |
|
|
c _RL e5d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
59 |
|
|
_RL rTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
60 |
jmc |
1.2 |
_RL rCenter, rUpwind, upwindFac |
61 |
jmc |
1.3 |
#ifdef ALLOW_DIAGNOSTICS |
62 |
|
|
CHARACTER*8 diagName |
63 |
|
|
LOGICAL DIAGNOSTICS_IS_ON |
64 |
|
|
EXTERNAL DIAGNOSTICS_IS_ON |
65 |
jmc |
1.5 |
_RL vf (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
66 |
jmc |
1.3 |
#endif |
67 |
jmc |
1.1 |
CEOP |
68 |
|
|
|
69 |
|
|
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
70 |
|
|
C Solve for V-component : |
71 |
|
|
C---------------------------- |
72 |
|
|
|
73 |
|
|
C-- Initialise |
74 |
|
|
DO k=1,Nr |
75 |
jmc |
1.5 |
DO j=1-OLy,sNy+OLy |
76 |
|
|
DO i=1-OLx,sNx+OLx |
77 |
jmc |
1.1 |
c a5d(i,j,k) = 0. _d 0 |
78 |
|
|
b5d(i,j,k) = 0. _d 0 |
79 |
|
|
c5d(i,j,k) = 1. _d 0 |
80 |
|
|
d5d(i,j,k) = 0. _d 0 |
81 |
|
|
c e5d(i,j,k) = 0. _d 0 |
82 |
|
|
ENDDO |
83 |
|
|
ENDDO |
84 |
|
|
ENDDO |
85 |
|
|
diagonalNumber = 1 |
86 |
|
|
|
87 |
|
|
IF ( implicitViscosity .AND. Nr.GT.1 ) THEN |
88 |
|
|
|
89 |
|
|
C-- set the tri-diagonal matrix to solve the implicit viscosity |
90 |
|
|
diagonalNumber = 3 |
91 |
|
|
C- 1rst lower diagonal : |
92 |
|
|
DO k=2,Nr |
93 |
|
|
DO j=jMin,jMax |
94 |
|
|
DO i=iMin,iMax |
95 |
jmc |
1.6 |
IF (maskS(i,j,k-1,bi,bj).EQ.oneRS) |
96 |
jmc |
1.5 |
& b5d(i,j,k) = -deltaTMom |
97 |
heimbach |
1.4 |
& *_recip_hFacS(i,j,k,bi,bj)*recip_drF(k) |
98 |
jmc |
1.6 |
& *recip_deepFac2C(k)*recip_rhoFacC(k) |
99 |
jmc |
1.1 |
& *kappaRV(i,j, k )*recip_drC( k ) |
100 |
jmc |
1.6 |
& *deepFac2F( k )*rhoFacF( k ) |
101 |
jmc |
1.1 |
ENDDO |
102 |
|
|
ENDDO |
103 |
|
|
ENDDO |
104 |
|
|
C- 1rst upper diagonal : |
105 |
|
|
DO k=1,Nr-1 |
106 |
|
|
DO j=jMin,jMax |
107 |
|
|
DO i=iMin,iMax |
108 |
jmc |
1.6 |
IF (maskS(i,j,k+1,bi,bj).EQ.oneRS) |
109 |
jmc |
1.5 |
& d5d(i,j,k) = -deltaTMom |
110 |
jmc |
1.6 |
& *_recip_hFacS(i,j,k,bi,bj)*recip_drF(k) |
111 |
|
|
& *recip_deepFac2C(k)*recip_rhoFacC(k) |
112 |
|
|
& *kappaRV(i,j,k+1)*recip_drC(k+1) |
113 |
|
|
& *deepFac2F(k+1)*rhoFacF(k+1) |
114 |
jmc |
1.1 |
ENDDO |
115 |
|
|
ENDDO |
116 |
|
|
ENDDO |
117 |
|
|
C- Main diagonal : |
118 |
|
|
DO k=1,Nr |
119 |
|
|
DO j=jMin,jMax |
120 |
|
|
DO i=iMin,iMax |
121 |
jmc |
1.6 |
c5d(i,j,k) = 1. _d 0 - ( b5d(i,j,k) + d5d(i,j,k) ) |
122 |
jmc |
1.1 |
ENDDO |
123 |
|
|
ENDDO |
124 |
|
|
ENDDO |
125 |
|
|
|
126 |
|
|
C-- end if implicitDiffusion |
127 |
|
|
ENDIF |
128 |
|
|
|
129 |
jmc |
1.8 |
IF ( selectImplicitDrag.GE.1 ) THEN |
130 |
|
|
IF ( no_slip_bottom .OR. selectBotDragQuadr.GE.0 |
131 |
|
|
& .OR. bottomDragLinear.NE.0. ) THEN |
132 |
|
|
CALL MOM_V_BOTDRAG_IMPL( |
133 |
|
|
I uVel(1-OLx,1-OLy,1,bi,bj), |
134 |
|
|
I vVel(1-OLx,1-OLy,1,bi,bj), |
135 |
|
|
I kappaRV, |
136 |
|
|
U c5d, |
137 |
|
|
I bi, bj, myIter, myThid ) |
138 |
|
|
ENDIF |
139 |
|
|
ENDIF |
140 |
|
|
|
141 |
jmc |
1.1 |
IF ( momImplVertAdv .AND. Nr.GT.1 ) THEN |
142 |
|
|
|
143 |
|
|
diagonalNumber = 3 |
144 |
|
|
DO k=2,Nr |
145 |
|
|
|
146 |
|
|
DO j=jMin,jMax |
147 |
|
|
DO i=iMin,iMax |
148 |
|
|
rTrans(i,j) = 0.5 _d 0 * ( |
149 |
|
|
& wVel(i, j ,k,bi,bj)*rA(i, j ,bi,bj) |
150 |
|
|
& *maskC(i, j ,k-1,bi,bj) |
151 |
|
|
& + wVel(i,j-1,k,bi,bj)*rA(i,j-1,bi,bj) |
152 |
|
|
& *maskC(i,j-1,k-1,bi,bj) |
153 |
jmc |
1.6 |
& )*deepFac2F(k)*rhoFacF(k) |
154 |
jmc |
1.1 |
ENDDO |
155 |
|
|
ENDDO |
156 |
|
|
|
157 |
|
|
IF ( vectorInvariantMomentum ) THEN |
158 |
jmc |
1.2 |
C- space Centered/Upwind advection scheme, Advective form: |
159 |
|
|
IF ( upwindShear ) THEN |
160 |
|
|
upwindFac = 1. _d 0 |
161 |
|
|
ELSE |
162 |
|
|
upwindFac = 0. _d 0 |
163 |
|
|
ENDIF |
164 |
jmc |
1.1 |
DO j=jMin,jMax |
165 |
|
|
DO i=iMin,iMax |
166 |
jmc |
1.5 |
rCenter = 0.5 _d 0 *deltaTMom*rTrans(i,j) |
167 |
jmc |
1.2 |
& *recip_rAs(i,j,bi,bj)*rkSign |
168 |
|
|
rUpwind = ABS(rCenter)*upwindFac |
169 |
jmc |
1.1 |
b5d(i,j,k) = b5d(i,j,k) |
170 |
jmc |
1.2 |
& - (rCenter+rUpwind) |
171 |
heimbach |
1.4 |
& *_recip_hFacS(i,j,k,bi,bj)*recip_drF(k) |
172 |
jmc |
1.6 |
& *recip_deepFac2C(k)*recip_rhoFacC(k) |
173 |
jmc |
1.1 |
c5d(i,j,k) = c5d(i,j,k) |
174 |
jmc |
1.2 |
& + (rCenter+rUpwind) |
175 |
heimbach |
1.4 |
& *_recip_hFacS(i,j,k,bi,bj)*recip_drF(k) |
176 |
jmc |
1.6 |
& *recip_deepFac2C(k)*recip_rhoFacC(k) |
177 |
jmc |
1.1 |
c5d(i,j,k-1) = c5d(i,j,k-1) |
178 |
jmc |
1.2 |
& - (rCenter-rUpwind) |
179 |
heimbach |
1.4 |
& *_recip_hFacS(i,j,k-1,bi,bj)*recip_drF(k-1) |
180 |
jmc |
1.6 |
& *recip_deepFac2C(k-1)*recip_rhoFacC(k-1) |
181 |
jmc |
1.1 |
d5d(i,j,k-1) = d5d(i,j,k-1) |
182 |
jmc |
1.2 |
& + (rCenter-rUpwind) |
183 |
heimbach |
1.4 |
& *_recip_hFacS(i,j,k-1,bi,bj)*recip_drF(k-1) |
184 |
jmc |
1.6 |
& *recip_deepFac2C(k-1)*recip_rhoFacC(k-1) |
185 |
jmc |
1.1 |
ENDDO |
186 |
|
|
ENDDO |
187 |
|
|
ELSE |
188 |
|
|
C- space Centered advection scheme, Flux form: |
189 |
|
|
DO j=jMin,jMax |
190 |
|
|
DO i=iMin,iMax |
191 |
jmc |
1.5 |
rCenter = 0.5 _d 0 *deltaTMom*rTrans(i,j) |
192 |
jmc |
1.2 |
& *recip_rAs(i,j,bi,bj)*rkSign |
193 |
jmc |
1.1 |
b5d(i,j,k) = b5d(i,j,k) |
194 |
heimbach |
1.4 |
& - rCenter*_recip_hFacS(i,j,k,bi,bj)*recip_drF(k) |
195 |
jmc |
1.6 |
& *recip_deepFac2C(k)*recip_rhoFacC(k) |
196 |
jmc |
1.1 |
c5d(i,j,k) = c5d(i,j,k) |
197 |
heimbach |
1.4 |
& - rCenter*_recip_hFacS(i,j,k,bi,bj)*recip_drF(k) |
198 |
jmc |
1.6 |
& *recip_deepFac2C(k)*recip_rhoFacC(k) |
199 |
jmc |
1.1 |
c5d(i,j,k-1) = c5d(i,j,k-1) |
200 |
heimbach |
1.4 |
& + rCenter*_recip_hFacS(i,j,k-1,bi,bj)*recip_drF(k-1) |
201 |
jmc |
1.6 |
& *recip_deepFac2C(k-1)*recip_rhoFacC(k-1) |
202 |
jmc |
1.1 |
d5d(i,j,k-1) = d5d(i,j,k-1) |
203 |
heimbach |
1.4 |
& + rCenter*_recip_hFacS(i,j,k-1,bi,bj)*recip_drF(k-1) |
204 |
jmc |
1.6 |
& *recip_deepFac2C(k-1)*recip_rhoFacC(k-1) |
205 |
jmc |
1.1 |
ENDDO |
206 |
|
|
ENDDO |
207 |
|
|
STOP 'MOM_IMPLICIT_R: Flux Form not yet finished.' |
208 |
|
|
ENDIF |
209 |
|
|
|
210 |
|
|
C-- end k loop |
211 |
|
|
ENDDO |
212 |
|
|
|
213 |
|
|
C-- end if momImplVertAdv |
214 |
|
|
ENDIF |
215 |
|
|
|
216 |
jmc |
1.8 |
IF ( diagonalNumber .EQ. 1 ) THEN |
217 |
|
|
errCode = 0 |
218 |
|
|
DO k=1,Nr |
219 |
|
|
DO j=jMin,jMax |
220 |
|
|
DO i=iMin,iMax |
221 |
|
|
IF ( c5d(i,j,k).NE.zeroRL ) THEN |
222 |
|
|
c5d(i,j,k) = 1. _d 0 / c5d(i,j,k) |
223 |
|
|
ELSE |
224 |
|
|
c5d(i,j,k) = 0. _d 0 |
225 |
|
|
errCode = 1 |
226 |
|
|
ENDIF |
227 |
|
|
ENDDO |
228 |
|
|
ENDDO |
229 |
|
|
DO j=jMin,jMax |
230 |
|
|
DO i=iMin,iMax |
231 |
|
|
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)*c5d(i,j,k) |
232 |
|
|
ENDDO |
233 |
|
|
ENDDO |
234 |
|
|
ENDDO |
235 |
|
|
IF (errCode.GE.1) THEN |
236 |
|
|
STOP 'MOM_IMPLICIT_R: error when solving 1-Diag problem.' |
237 |
|
|
ENDIF |
238 |
|
|
ELSEIF ( diagonalNumber .EQ. 3 ) THEN |
239 |
jmc |
1.1 |
C-- Solve tri-diagonal system : |
240 |
jmc |
1.7 |
errCode = -1 |
241 |
jmc |
1.1 |
CALL SOLVE_TRIDIAGONAL( iMin,iMax, jMin,jMax, |
242 |
|
|
I b5d, c5d, d5d, |
243 |
jmc |
1.5 |
U gV(1-OLx,1-OLy,1,bi,bj), |
244 |
jmc |
1.1 |
O errCode, |
245 |
|
|
I bi, bj, myThid ) |
246 |
|
|
IF (errCode.GE.1) THEN |
247 |
|
|
STOP 'MOM_IMPLICIT_R: error when solving 3-Diag problem.' |
248 |
|
|
ENDIF |
249 |
jmc |
1.8 |
ELSE |
250 |
jmc |
1.1 |
STOP 'MOM_IMPLICIT_R: no solver available.' |
251 |
|
|
ENDIF |
252 |
|
|
|
253 |
jmc |
1.8 |
#ifdef ALLOW_SOLVE4_PS_AND_DRAG |
254 |
|
|
IF ( selectImplicitDrag.EQ.2 ) THEN |
255 |
|
|
DO k=1,Nr |
256 |
|
|
DO j=jMin,jMax |
257 |
|
|
DO i=iMin,iMax |
258 |
|
|
dV_psFacY(i,j,k,bi,bj) = maskS(i,j,k,bi,bj) |
259 |
|
|
& *recip_deepFacC(k)*recip_rhoFacC(k) |
260 |
|
|
ENDDO |
261 |
|
|
ENDDO |
262 |
|
|
ENDDO |
263 |
|
|
IF ( diagonalNumber .EQ. 1 ) THEN |
264 |
|
|
DO k=1,Nr |
265 |
|
|
DO j=jMin,jMax |
266 |
|
|
DO i=iMin,iMax |
267 |
|
|
dV_psFacY(i,j,k,bi,bj) = dV_psFacY(i,j,k,bi,bj)*c5d(i,j,k) |
268 |
|
|
ENDDO |
269 |
|
|
ENDDO |
270 |
|
|
ENDDO |
271 |
|
|
ELSEIF ( diagonalNumber .EQ. 3 ) THEN |
272 |
|
|
CALL SOLVE_TRIDIAGONAL( iMin,iMax, jMin,jMax, |
273 |
|
|
I b5d, c5d, d5d, |
274 |
|
|
U dV_psFacY(1-OLx,1-OLy,1,bi,bj), |
275 |
|
|
O errCode, |
276 |
|
|
I bi, bj, myThid ) |
277 |
|
|
ENDIF |
278 |
|
|
ENDIF |
279 |
|
|
#endif /* ALLOW_SOLVE4_PS_AND_DRAG */ |
280 |
|
|
|
281 |
jmc |
1.3 |
#ifdef ALLOW_DIAGNOSTICS |
282 |
|
|
C-- Diagnostics of vertical viscous flux: |
283 |
|
|
IF ( useDiagnostics .AND. implicitViscosity ) THEN |
284 |
|
|
diagName = 'VISrI_Vm' |
285 |
|
|
IF ( DIAGNOSTICS_IS_ON(diagName,myThid) ) THEN |
286 |
|
|
DO k= 1,Nr |
287 |
|
|
IF ( k.EQ.1 ) THEN |
288 |
|
|
C- Note: Needs to call DIAGNOSTICS_FILL at level k=1 even if array == 0 |
289 |
|
|
C otherwise counter is not incremented !! |
290 |
|
|
DO j=1-OLy,sNy+OLy |
291 |
|
|
DO i=1-OLx,sNx+OLx |
292 |
|
|
vf(i,j) = 0. _d 0 |
293 |
|
|
ENDDO |
294 |
|
|
ENDDO |
295 |
|
|
ELSE |
296 |
|
|
DO j=jMin,jMax |
297 |
|
|
DO i=iMin,iMax |
298 |
jmc |
1.6 |
vf(i,j) = -rAs(i,j,bi,bj)*deepFac2F(k)*rhoFacF(k) |
299 |
|
|
& * kappaRV(i,j,k)*recip_drC(k)*rkSign |
300 |
|
|
& * (gV(i,j,k,bi,bj) - gV(i,j,k-1,bi,bj)) |
301 |
jmc |
1.3 |
& *_maskS(i,j,k,bi,bj) |
302 |
|
|
& *_maskS(i,j,k-1,bi,bj) |
303 |
|
|
ENDDO |
304 |
|
|
ENDDO |
305 |
|
|
ENDIF |
306 |
|
|
CALL DIAGNOSTICS_FILL(vf,diagName, k,1, 2,bi,bj, myThid) |
307 |
|
|
ENDDO |
308 |
|
|
ENDIF |
309 |
|
|
ENDIF |
310 |
|
|
#endif /* ALLOW_DIAGNOSTICS */ |
311 |
|
|
|
312 |
jmc |
1.1 |
RETURN |
313 |
|
|
END |