1 |
C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_calc_rhs.F,v 1.13 2002/03/24 02:12:50 heimbach Exp $ |
2 |
C $Name: $ |
3 |
|
4 |
#include "GAD_OPTIONS.h" |
5 |
|
6 |
CBOP |
7 |
C !ROUTINE: GAD_CALC_RHS |
8 |
|
9 |
C !INTERFACE: ========================================================== |
10 |
SUBROUTINE GAD_CALC_RHS( |
11 |
I bi,bj,iMin,iMax,jMin,jMax,k,kM1,kUp,kDown, |
12 |
I xA,yA,uTrans,vTrans,rTrans,maskUp, |
13 |
I diffKh, diffK4, KappaRT, Tracer, |
14 |
I tracerIdentity, advectionScheme, calcAdvection, |
15 |
U fVerT, gTracer, |
16 |
I myThid ) |
17 |
|
18 |
C !DESCRIPTION: |
19 |
C Calculates the tendancy of a tracer due to advection and diffusion. |
20 |
C It calculates the fluxes in each direction indepentently and then |
21 |
C sets the tendancy to the divergence of these fluxes. The advective |
22 |
C fluxes are only calculated here when using the linear advection schemes |
23 |
C otherwise only the diffusive and parameterized fluxes are calculated. |
24 |
C |
25 |
C Contributions to the flux are calculated and added: |
26 |
C \begin{equation*} |
27 |
C {\bf F} = {\bf F}_{adv} + {\bf F}_{diff} +{\bf F}_{GM} + {\bf F}_{KPP} |
28 |
C \end{equation*} |
29 |
C |
30 |
C The tendancy is the divergence of the fluxes: |
31 |
C \begin{equation*} |
32 |
C G_\theta = G_\theta + \nabla \cdot {\bf F} |
33 |
C \end{equation*} |
34 |
C |
35 |
C The tendancy is assumed to contain data on entry. |
36 |
|
37 |
C !USES: =============================================================== |
38 |
IMPLICIT NONE |
39 |
#include "SIZE.h" |
40 |
#include "EEPARAMS.h" |
41 |
#include "PARAMS.h" |
42 |
#include "GRID.h" |
43 |
#include "DYNVARS.h" |
44 |
#include "GAD.h" |
45 |
|
46 |
#ifdef ALLOW_AUTODIFF_TAMC |
47 |
#include "tamc.h" |
48 |
#include "tamc_keys.h" |
49 |
#endif /* ALLOW_AUTODIFF_TAMC */ |
50 |
|
51 |
C !INPUT PARAMETERS: =================================================== |
52 |
C bi,bj :: tile indices |
53 |
C iMin,iMax,jMin,jMax :: loop range for called routines |
54 |
C kup :: index into 2 1/2D array, toggles between 1 and 2 |
55 |
C kdown :: index into 2 1/2D array, toggles between 2 and 1 |
56 |
C kp1 :: =k+1 for k<Nr, =Nr for k=Nr |
57 |
C xA,yA :: areas of X and Y face of tracer cells |
58 |
C uTrans,vTrans,rTrans :: 2-D arrays of volume transports at U,V and W points |
59 |
C maskUp :: 2-D array for mask at W points |
60 |
C diffKh :: horizontal diffusion coefficient |
61 |
C diffK4 :: bi-harmonic diffusion coefficient |
62 |
C KappaRT :: 3-D array for vertical diffusion coefficient |
63 |
C Tracer :: tracer field |
64 |
C tracerIdentity :: identifier for the tracer (required only for KPP) |
65 |
C advectionScheme :: advection scheme to use |
66 |
C calcAdvection :: =False if Advec terms computed with multiDim scheme |
67 |
C myThid :: thread number |
68 |
INTEGER bi,bj,iMin,iMax,jMin,jMax |
69 |
INTEGER k,kUp,kDown,kM1 |
70 |
_RS xA (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
71 |
_RS yA (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
72 |
_RL uTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
73 |
_RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
74 |
_RL rTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
75 |
_RS maskUp(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
76 |
_RL diffKh, diffK4 |
77 |
_RL KappaRT(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
78 |
_RL Tracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy) |
79 |
INTEGER tracerIdentity |
80 |
INTEGER advectionScheme |
81 |
LOGICAL calcAdvection |
82 |
INTEGER myThid |
83 |
|
84 |
C !OUTPUT PARAMETERS: ================================================== |
85 |
C gTracer :: tendancy array |
86 |
C fVerT :: 2 1/2D arrays for vertical advective flux |
87 |
_RL gTracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy) |
88 |
_RL fVerT (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
89 |
|
90 |
C !LOCAL VARIABLES: ==================================================== |
91 |
C i,j :: loop indices |
92 |
C df4 :: used for storing del^2 T for bi-harmonic term |
93 |
C fZon :: zonal flux |
94 |
C fmer :: meridional flux |
95 |
C af :: advective flux |
96 |
C df :: diffusive flux |
97 |
C localT :: local copy of tracer field |
98 |
INTEGER i,j |
99 |
_RL df4 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
100 |
_RL fZon (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
101 |
_RL fMer (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
102 |
_RL af (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
103 |
_RL df (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
104 |
_RL localT(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
105 |
CEOP |
106 |
|
107 |
#ifdef ALLOW_AUTODIFF_TAMC |
108 |
C-- only the kUp part of fverT is set in this subroutine |
109 |
C-- the kDown is still required |
110 |
fVerT(1,1,kDown) = fVerT(1,1,kDown) |
111 |
#endif |
112 |
|
113 |
DO j=1-OLy,sNy+OLy |
114 |
DO i=1-OLx,sNx+OLx |
115 |
fZon(i,j) = 0. _d 0 |
116 |
fMer(i,j) = 0. _d 0 |
117 |
fVerT(i,j,kUp) = 0. _d 0 |
118 |
df(i,j) = 0. _d 0 |
119 |
df4(i,j) = 0. _d 0 |
120 |
localT(i,j) = 0. _d 0 |
121 |
ENDDO |
122 |
ENDDO |
123 |
|
124 |
C-- Make local copy of tracer array |
125 |
DO j=1-OLy,sNy+OLy |
126 |
DO i=1-OLx,sNx+OLx |
127 |
localT(i,j)=tracer(i,j,k,bi,bj) |
128 |
ENDDO |
129 |
ENDDO |
130 |
|
131 |
C-- Unless we have already calculated the advection terms we initialize |
132 |
C the tendency to zero. |
133 |
IF (calcAdvection) THEN |
134 |
DO j=1-Oly,sNy+Oly |
135 |
DO i=1-Olx,sNx+Olx |
136 |
gTracer(i,j,k,bi,bj)=0. _d 0 |
137 |
ENDDO |
138 |
ENDDO |
139 |
ENDIF |
140 |
|
141 |
C-- Pre-calculate del^2 T if bi-harmonic coefficient is non-zero |
142 |
IF (diffK4 .NE. 0.) THEN |
143 |
CALL GAD_GRAD_X(bi,bj,k,xA,localT,fZon,myThid) |
144 |
CALL GAD_GRAD_Y(bi,bj,k,yA,localT,fMer,myThid) |
145 |
CALL GAD_DEL2(bi,bj,k,fZon,fMer,df4,myThid) |
146 |
ENDIF |
147 |
|
148 |
C-- Initialize net flux in X direction |
149 |
DO j=1-Oly,sNy+Oly |
150 |
DO i=1-Olx,sNx+Olx |
151 |
fZon(i,j) = 0. _d 0 |
152 |
ENDDO |
153 |
ENDDO |
154 |
|
155 |
C- Advective flux in X |
156 |
IF (calcAdvection) THEN |
157 |
IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN |
158 |
CALL GAD_C2_ADV_X(bi,bj,k,uTrans,localT,af,myThid) |
159 |
ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN |
160 |
CALL GAD_FLUXLIMIT_ADV_X( |
161 |
& bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid) |
162 |
ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN |
163 |
CALL GAD_U3_ADV_X(bi,bj,k,uTrans,localT,af,myThid) |
164 |
ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN |
165 |
CALL GAD_C4_ADV_X(bi,bj,k,uTrans,localT,af,myThid) |
166 |
ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN |
167 |
CALL GAD_DST3_ADV_X( |
168 |
& bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid) |
169 |
ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
170 |
CALL GAD_DST3FL_ADV_X( |
171 |
& bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid) |
172 |
ELSE |
173 |
STOP 'GAD_CALC_RHS: Bad advectionScheme (X)' |
174 |
ENDIF |
175 |
DO j=1-Oly,sNy+Oly |
176 |
DO i=1-Olx,sNx+Olx |
177 |
fZon(i,j) = fZon(i,j) + af(i,j) |
178 |
ENDDO |
179 |
ENDDO |
180 |
ENDIF |
181 |
|
182 |
C- Diffusive flux in X |
183 |
IF (diffKh.NE.0.) THEN |
184 |
CALL GAD_DIFF_X(bi,bj,k,xA,diffKh,localT,df,myThid) |
185 |
ELSE |
186 |
DO j=1-Oly,sNy+Oly |
187 |
DO i=1-Olx,sNx+Olx |
188 |
df(i,j) = 0. _d 0 |
189 |
ENDDO |
190 |
ENDDO |
191 |
ENDIF |
192 |
|
193 |
#ifdef ALLOW_GMREDI |
194 |
C- GM/Redi flux in X |
195 |
IF (useGMRedi) THEN |
196 |
C *note* should update GMREDI_XTRANSPORT to use localT and set df *aja* |
197 |
CALL GMREDI_XTRANSPORT( |
198 |
I iMin,iMax,jMin,jMax,bi,bj,K, |
199 |
I xA,Tracer, |
200 |
U df, |
201 |
I myThid) |
202 |
ENDIF |
203 |
#endif |
204 |
DO j=1-Oly,sNy+Oly |
205 |
DO i=1-Olx,sNx+Olx |
206 |
fZon(i,j) = fZon(i,j) + df(i,j) |
207 |
ENDDO |
208 |
ENDDO |
209 |
|
210 |
C- Bi-harmonic duffusive flux in X |
211 |
IF (diffK4 .NE. 0.) THEN |
212 |
CALL GAD_BIHARM_X(bi,bj,k,xA,df4,diffK4,df,myThid) |
213 |
DO j=1-Oly,sNy+Oly |
214 |
DO i=1-Olx,sNx+Olx |
215 |
fZon(i,j) = fZon(i,j) + df(i,j) |
216 |
ENDDO |
217 |
ENDDO |
218 |
ENDIF |
219 |
|
220 |
C-- Initialize net flux in Y direction |
221 |
DO j=1-Oly,sNy+Oly |
222 |
DO i=1-Olx,sNx+Olx |
223 |
fMer(i,j) = 0. _d 0 |
224 |
ENDDO |
225 |
ENDDO |
226 |
|
227 |
C- Advective flux in Y |
228 |
IF (calcAdvection) THEN |
229 |
IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN |
230 |
CALL GAD_C2_ADV_Y(bi,bj,k,vTrans,localT,af,myThid) |
231 |
ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN |
232 |
CALL GAD_FLUXLIMIT_ADV_Y( |
233 |
& bi,bj,k,deltaTtracer,vTrans,vVel,localT,af,myThid) |
234 |
ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN |
235 |
CALL GAD_U3_ADV_Y(bi,bj,k,vTrans,localT,af,myThid) |
236 |
ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN |
237 |
CALL GAD_C4_ADV_Y(bi,bj,k,vTrans,localT,af,myThid) |
238 |
ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN |
239 |
CALL GAD_DST3_ADV_Y( |
240 |
& bi,bj,k,deltaTtracer,vTrans,vVel,localT,af,myThid) |
241 |
ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
242 |
CALL GAD_DST3FL_ADV_Y( |
243 |
& bi,bj,k,deltaTtracer,vTrans,vVel,localT,af,myThid) |
244 |
ELSE |
245 |
STOP 'GAD_CALC_RHS: Bad advectionScheme (Y)' |
246 |
ENDIF |
247 |
DO j=1-Oly,sNy+Oly |
248 |
DO i=1-Olx,sNx+Olx |
249 |
fMer(i,j) = fMer(i,j) + af(i,j) |
250 |
ENDDO |
251 |
ENDDO |
252 |
ENDIF |
253 |
|
254 |
C- Diffusive flux in Y |
255 |
IF (diffKh.NE.0.) THEN |
256 |
CALL GAD_DIFF_Y(bi,bj,k,yA,diffKh,localT,df,myThid) |
257 |
ELSE |
258 |
DO j=1-Oly,sNy+Oly |
259 |
DO i=1-Olx,sNx+Olx |
260 |
df(i,j) = 0. _d 0 |
261 |
ENDDO |
262 |
ENDDO |
263 |
ENDIF |
264 |
|
265 |
#ifdef ALLOW_GMREDI |
266 |
C- GM/Redi flux in Y |
267 |
IF (useGMRedi) THEN |
268 |
C *note* should update GMREDI_YTRANSPORT to use localT and set df *aja* |
269 |
CALL GMREDI_YTRANSPORT( |
270 |
I iMin,iMax,jMin,jMax,bi,bj,K, |
271 |
I yA,Tracer, |
272 |
U df, |
273 |
I myThid) |
274 |
ENDIF |
275 |
#endif |
276 |
DO j=1-Oly,sNy+Oly |
277 |
DO i=1-Olx,sNx+Olx |
278 |
fMer(i,j) = fMer(i,j) + df(i,j) |
279 |
ENDDO |
280 |
ENDDO |
281 |
|
282 |
C- Bi-harmonic flux in Y |
283 |
IF (diffK4 .NE. 0.) THEN |
284 |
CALL GAD_BIHARM_Y(bi,bj,k,yA,df4,diffK4,df,myThid) |
285 |
DO j=1-Oly,sNy+Oly |
286 |
DO i=1-Olx,sNx+Olx |
287 |
fMer(i,j) = fMer(i,j) + df(i,j) |
288 |
ENDDO |
289 |
ENDDO |
290 |
ENDIF |
291 |
|
292 |
C- Advective flux in R |
293 |
IF (calcAdvection) THEN |
294 |
C Note: wVel needs to be masked |
295 |
IF (K.GE.2) THEN |
296 |
C- Compute vertical advective flux in the interior: |
297 |
IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN |
298 |
CALL GAD_C2_ADV_R(bi,bj,k,rTrans,tracer,af,myThid) |
299 |
ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN |
300 |
CALL GAD_FLUXLIMIT_ADV_R( |
301 |
& bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid) |
302 |
ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN |
303 |
CALL GAD_U3_ADV_R(bi,bj,k,rTrans,tracer,af,myThid) |
304 |
ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN |
305 |
CALL GAD_C4_ADV_R(bi,bj,k,rTrans,tracer,af,myThid) |
306 |
ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN |
307 |
CALL GAD_DST3_ADV_R( |
308 |
& bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid) |
309 |
ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
310 |
CALL GAD_DST3FL_ADV_R( |
311 |
& bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid) |
312 |
ELSE |
313 |
STOP 'GAD_CALC_RHS: Bad advectionScheme (R)' |
314 |
ENDIF |
315 |
C- Surface "correction" term at k>1 : |
316 |
DO j=1-Oly,sNy+Oly |
317 |
DO i=1-Olx,sNx+Olx |
318 |
af(i,j) = af(i,j) |
319 |
& + (maskC(i,j,k,bi,bj)-maskC(i,j,k-1,bi,bj))* |
320 |
& rTrans(i,j)*Tracer(i,j,k,bi,bj) |
321 |
ENDDO |
322 |
ENDDO |
323 |
ELSE |
324 |
C- Surface "correction" term at k=1 : |
325 |
DO j=1-Oly,sNy+Oly |
326 |
DO i=1-Olx,sNx+Olx |
327 |
af(i,j) = rTrans(i,j)*Tracer(i,j,k,bi,bj) |
328 |
ENDDO |
329 |
ENDDO |
330 |
ENDIF |
331 |
C- add the advective flux to fVerT |
332 |
DO j=1-Oly,sNy+Oly |
333 |
DO i=1-Olx,sNx+Olx |
334 |
fVerT(i,j,kUp) = fVerT(i,j,kUp) + af(i,j) |
335 |
ENDDO |
336 |
ENDDO |
337 |
ENDIF |
338 |
|
339 |
C- Diffusive flux in R |
340 |
C Note: For K=1 then KM1=1 and this gives a dT/dr = 0 upper |
341 |
C boundary condition. |
342 |
IF (implicitDiffusion) THEN |
343 |
DO j=1-Oly,sNy+Oly |
344 |
DO i=1-Olx,sNx+Olx |
345 |
df(i,j) = 0. _d 0 |
346 |
ENDDO |
347 |
ENDDO |
348 |
ELSE |
349 |
CALL GAD_DIFF_R(bi,bj,k,KappaRT,tracer,df,myThid) |
350 |
ENDIF |
351 |
|
352 |
#ifdef ALLOW_GMREDI |
353 |
C- GM/Redi flux in R |
354 |
IF (useGMRedi) THEN |
355 |
C *note* should update GMREDI_RTRANSPORT to set df *aja* |
356 |
CALL GMREDI_RTRANSPORT( |
357 |
I iMin,iMax,jMin,jMax,bi,bj,K, |
358 |
I Tracer, |
359 |
U df, |
360 |
I myThid) |
361 |
ENDIF |
362 |
#endif |
363 |
|
364 |
DO j=1-Oly,sNy+Oly |
365 |
DO i=1-Olx,sNx+Olx |
366 |
fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j) |
367 |
ENDDO |
368 |
ENDDO |
369 |
|
370 |
#ifdef ALLOW_KPP |
371 |
C- Add non local KPP transport term (ghat) to diffusive T flux. |
372 |
IF (useKPP) THEN |
373 |
DO j=1-Oly,sNy+Oly |
374 |
DO i=1-Olx,sNx+Olx |
375 |
df(i,j) = 0. _d 0 |
376 |
ENDDO |
377 |
ENDDO |
378 |
IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN |
379 |
C *note* should update KPP_TRANSPORT_T to set df *aja* |
380 |
CALL KPP_TRANSPORT_T( |
381 |
I iMin,iMax,jMin,jMax,bi,bj,k,km1, |
382 |
I KappaRT, |
383 |
U df ) |
384 |
ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN |
385 |
CALL KPP_TRANSPORT_S( |
386 |
I iMin,iMax,jMin,jMax,bi,bj,k,km1, |
387 |
I KappaRT, |
388 |
U df ) |
389 |
ELSE |
390 |
STOP 'GAD_CALC_RHS: Ooops' |
391 |
ENDIF |
392 |
DO j=1-Oly,sNy+Oly |
393 |
DO i=1-Olx,sNx+Olx |
394 |
fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j) |
395 |
ENDDO |
396 |
ENDDO |
397 |
ENDIF |
398 |
#endif |
399 |
|
400 |
C-- Divergence of fluxes |
401 |
DO j=1-Oly,sNy+Oly-1 |
402 |
DO i=1-Olx,sNx+Olx-1 |
403 |
gTracer(i,j,k,bi,bj)=gTracer(i,j,k,bi,bj) |
404 |
& -_recip_hFacC(i,j,k,bi,bj)*recip_drF(k) |
405 |
& *recip_rA(i,j,bi,bj) |
406 |
& *( |
407 |
& +( fZon(i+1,j)-fZon(i,j) ) |
408 |
& +( fMer(i,j+1)-fMer(i,j) ) |
409 |
& +( fVerT(i,j,kUp)-fVerT(i,j,kDown) )*rkFac |
410 |
& ) |
411 |
ENDDO |
412 |
ENDDO |
413 |
|
414 |
RETURN |
415 |
END |