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revision 1.3 by adcroft, Mon Sep 17 19:48:04 2001 UTC revision 1.14 by heimbach, Tue Nov 12 20:42:24 2002 UTC
# Line 1  Line 1 
1  C $Header$  C $Header$
2  C $Name$  C $Name$
3    
4    CBOI
5    C !TITLE: pkg/generic\_advdiff
6    C !AUTHORS: adcroft@mit.edu
7    C !INTRODUCTION: Generic Advection Diffusion Package
8    C
9    C Package "generic\_advdiff" provides a common set of routines for calculating
10    C advective/diffusive fluxes for tracers (cell centered quantities on a C-grid).
11    C
12    C Many different advection schemes are available: the standard centered
13    C second order, centered fourth order and upwind biased third order schemes
14    C are known as linear methods and require some stable time-stepping method
15    C such as Adams-Bashforth. Alternatives such as flux-limited schemes are
16    C stable in the forward sense and are best combined with the multi-dimensional
17    C method provided in gad\_advection.
18    C
19    C There are two high-level routines:
20    C  \begin{itemize}
21    C  \item{GAD\_CALC\_RHS} calculates all fluxes at time level "n" and is used
22    C  for the standard linear schemes. This must be used in conjuction with
23    C  Adams-Bashforth time-stepping. Diffusive and parameterized fluxes are
24    C  always calculated here.
25    C  \item{GAD\_ADVECTION} calculates just the advective fluxes using the
26    C  non-linear schemes and can not be used in conjuction with Adams-Bashforth
27    C  time-stepping.
28    C  \end{itemize}
29    CEOI
30    
31  #include "GAD_OPTIONS.h"  #include "GAD_OPTIONS.h"
32    
33    CBOP
34    C !ROUTINE: GAD_ADVECTION
35    
36    C !INTERFACE: ==========================================================
37        SUBROUTINE GAD_ADVECTION(bi,bj,advectionScheme,tracerIdentity,        SUBROUTINE GAD_ADVECTION(bi,bj,advectionScheme,tracerIdentity,
38       U                         Tracer,Gtracer,       U                         Tracer,Gtracer,
39       I                         myTime,myIter,myThid)       I                         myTime,myIter,myThid)
 C     /==========================================================\  
 C     | SUBROUTINE GAD_ADVECTION                                 |  
 C     | o Solves the pure advection tracer equation.             |  
 C     |==========================================================|  
 C     \==========================================================/  
       IMPLICIT NONE  
40    
41  C     == Global variables ===  C !DESCRIPTION:
42    C Calculates the tendancy of a tracer due to advection.
43    C It uses the multi-dimensional method given in \ref{sect:multiDimAdvection}
44    C and can only be used for the non-linear advection schemes such as the
45    C direct-space-time method and flux-limiters.
46    C
47    C The algorithm is as follows:
48    C \begin{itemize}
49    C \item{$\theta^{(n+1/3)} = \theta^{(n)}
50    C      - \Delta t \partial_x (u\theta^{(n)}) + \theta^{(n)} \partial_x u$}
51    C \item{$\theta^{(n+2/3)} = \theta^{(n+1/3)}
52    C      - \Delta t \partial_y (v\theta^{(n+1/3)}) + \theta^{(n)} \partial_y v$}
53    C \item{$\theta^{(n+3/3)} = \theta^{(n+2/3)}
54    C      - \Delta t \partial_r (w\theta^{(n+2/3)}) + \theta^{(n)} \partial_r w$}
55    C \item{$G_\theta = ( \theta^{(n+3/3)} - \theta^{(n)} )/\Delta t$}
56    C \end{itemize}
57    C
58    C The tendancy (output) is over-written by this routine.
59    
60    C !USES: ===============================================================
61          IMPLICIT NONE
62  #include "SIZE.h"  #include "SIZE.h"
63  #include "EEPARAMS.h"  #include "EEPARAMS.h"
64  #include "PARAMS.h"  #include "PARAMS.h"
65  #include "DYNVARS.h"  #include "DYNVARS.h"
66  #include "GRID.h"  #include "GRID.h"
67  #include "GAD.h"  #include "GAD.h"
68    #ifdef ALLOW_AUTODIFF_TAMC
69  C     == Routine arguments ==  # include "tamc.h"
70    # include "tamc_keys.h"
71    #endif
72    
73    C !INPUT PARAMETERS: ===================================================
74    C  bi,bj                :: tile indices
75    C  advectionScheme      :: advection scheme to use
76    C  tracerIdentity       :: identifier for the tracer (required only for OBCS)
77    C  Tracer               :: tracer field
78    C  myTime               :: current time
79    C  myIter               :: iteration number
80    C  myThid               :: thread number
81        INTEGER bi,bj        INTEGER bi,bj
82        INTEGER advectionScheme        INTEGER advectionScheme
83        INTEGER tracerIdentity        INTEGER tracerIdentity
84        _RL Tracer(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)        _RL Tracer(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)
       _RL Gtracer(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)  
85        _RL myTime        _RL myTime
86        INTEGER myIter        INTEGER myIter
87        INTEGER myThid        INTEGER myThid
88    
89  C     == Local variables  C !OUTPUT PARAMETERS: ==================================================
90    C  gTracer              :: tendancy array
91          _RL gTracer(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)
92    
93    C !LOCAL VARIABLES: ====================================================
94    C  maskUp               :: 2-D array for mask at W points
95    C  iMin,iMax,jMin,jMax  :: loop range for called routines
96    C  i,j,k                :: loop indices
97    C  kup                  :: index into 2 1/2D array, toggles between 1 and 2
98    C  kdown                :: index into 2 1/2D array, toggles between 2 and 1
99    C  kp1                  :: =k+1 for k<Nr, =Nr for k=Nr
100    C  xA,yA                :: areas of X and Y face of tracer cells
101    C  uTrans,vTrans,rTrans :: 2-D arrays of volume transports at U,V and W points
102    C  rTransKp1            :: vertical volume transport at interface k+1
103    C  af                   :: 2-D array for horizontal advective flux
104    C  fVerT                :: 2 1/2D arrays for vertical advective flux
105    C  localTij             :: 2-D array used as temporary local copy of tracer fld
106    C  localTijk            :: 3-D array used as temporary local copy of tracer fld
107    C  kp1Msk               :: flag (0,1) to act as over-riding mask for W levels
108    C  calc_fluxes_X        :: logical to indicate to calculate fluxes in X dir
109    C  calc_fluxes_Y        :: logical to indicate to calculate fluxes in Y dir
110    C  nipass               :: number of passes to make in multi-dimensional method
111    C  ipass                :: number of the current pass being made
112        _RS maskUp  (1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RS maskUp  (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
113        INTEGER iMin,iMax,jMin,jMax        INTEGER iMin,iMax,jMin,jMax
114        INTEGER i,j,k,kup,kDown,kp1        INTEGER i,j,k,kup,kDown
115        _RS xA      (1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RS xA      (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
116        _RS yA      (1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RS yA      (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
117        _RL uTrans  (1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL uTrans  (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
118        _RL vTrans  (1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL vTrans  (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
119        _RL rTrans  (1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL rTrans  (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
120          _RL rTransKp1(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
121        _RL af      (1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL af      (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
122        _RL fVerT   (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)        _RL fVerT   (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
123        _RL localTij(1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL localTij(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
# Line 47  C     == Local variables Line 125  C     == Local variables
125        _RL kp1Msk        _RL kp1Msk
126        LOGICAL calc_fluxes_X,calc_fluxes_Y        LOGICAL calc_fluxes_X,calc_fluxes_Y
127        INTEGER nipass,ipass        INTEGER nipass,ipass
128    CEOP
129    
130    #ifdef ALLOW_AUTODIFF_TAMC
131              act0 = tracerIdentity - 1
132              max0 = maxpass
133              act1 = bi - myBxLo(myThid)
134              max1 = myBxHi(myThid) - myBxLo(myThid) + 1
135              act2 = bj - myByLo(myThid)
136              max2 = myByHi(myThid) - myByLo(myThid) + 1
137              act3 = myThid - 1
138              max3 = nTx*nTy
139              act4 = ikey_dynamics - 1
140              igadkey = (act0 + 1)
141         &                      + act1*max0
142         &                      + act2*max0*max1
143         &                      + act3*max0*max1*max2
144         &                      + act4*max0*max1*max2*max3
145              if (tracerIdentity.GT.maxpass)
146         &         STOP 'maxpass seems smaller than tracerIdentity'
147    #endif /* ALLOW_AUTODIFF_TAMC */
148    
149  C--   Set up work arrays with valid (i.e. not NaN) values  C--   Set up work arrays with valid (i.e. not NaN) values
150  C     These inital values do not alter the numerical results. They  C     These inital values do not alter the numerical results. They
# Line 62  C     uninitialised but inert locations. Line 160  C     uninitialised but inert locations.
160          rTrans(i,j)  = 0. _d 0          rTrans(i,j)  = 0. _d 0
161          fVerT(i,j,1) = 0. _d 0          fVerT(i,j,1) = 0. _d 0
162          fVerT(i,j,2) = 0. _d 0          fVerT(i,j,2) = 0. _d 0
163            rTransKp1(i,j)= 0. _d 0
164         ENDDO         ENDDO
165        ENDDO        ENDDO
166    
# Line 72  C     uninitialised but inert locations. Line 171  C     uninitialised but inert locations.
171    
172  C--   Start of k loop for horizontal fluxes  C--   Start of k loop for horizontal fluxes
173        DO k=1,Nr        DO k=1,Nr
174    #ifdef ALLOW_AUTODIFF_TAMC
175             kkey = (igadkey-1)*Nr + k
176    CADJ STORE tracer(:,:,k,bi,bj) =
177    CADJ &     comlev1_bibj_k_gad, key=kkey, byte=isbyte
178    #endif /* ALLOW_AUTODIFF_TAMC */
179    
180  C--   Get temporary terms used by tendency routines  C--   Get temporary terms used by tendency routines
181        CALL CALC_COMMON_FACTORS (        CALL CALC_COMMON_FACTORS (
# Line 79  C--   Get temporary terms used by tenden Line 183  C--   Get temporary terms used by tenden
183       O         xA,yA,uTrans,vTrans,rTrans,maskUp,       O         xA,yA,uTrans,vTrans,rTrans,maskUp,
184       I         myThid)       I         myThid)
185    
186    #ifdef ALLOW_GMREDI
187    C--   Residual transp = Bolus transp + Eulerian transp
188           IF (useGMRedi)
189         &   CALL GMREDI_CALC_UVFLOW(
190         &            uTrans, vTrans, bi, bj, k, myThid)
191    #endif /* ALLOW_GMREDI */
192    
193  C--   Make local copy of tracer array  C--   Make local copy of tracer array
194        DO j=1-OLy,sNy+OLy        DO j=1-OLy,sNy+OLy
195         DO i=1-OLx,sNx+OLx         DO i=1-OLx,sNx+OLx
# Line 88  C--   Make local copy of tracer array Line 199  C--   Make local copy of tracer array
199    
200        IF (useCubedSphereExchange) THEN        IF (useCubedSphereExchange) THEN
201         nipass=3         nipass=3
202    #ifdef ALLOW_AUTODIFF_TAMC
203           if ( nipass.GT.maxcube )
204         &      STOP 'maxcube needs to be = 3'
205    #endif
206        ELSE        ELSE
207         nipass=1         nipass=1
208        ENDIF        ENDIF
209         nipass=1  cph       nipass=1
210    
211  C--   Multiple passes for different directions on different tiles  C--   Multiple passes for different directions on different tiles
212        DO ipass=1,nipass        DO ipass=1,nipass
213    #ifdef ALLOW_AUTODIFF_TAMC
214             passkey = ipass + (k-1)      *maxcube
215         &                   + (igadkey-1)*maxcube*Nr
216             IF (nipass .GT. maxpass) THEN
217              STOP 'GAD_ADVECTION: nipass > maxcube. check tamc.h'
218             ENDIF
219    #endif /* ALLOW_AUTODIFF_TAMC */
220    
221        IF (nipass.EQ.3) THEN        IF (nipass.EQ.3) THEN
222         calc_fluxes_X=.FALSE.         calc_fluxes_X=.FALSE.
# Line 138  C-    Advective flux in X Line 260  C-    Advective flux in X
260          af(i,j) = 0.          af(i,j) = 0.
261         ENDDO         ENDDO
262        ENDDO        ENDDO
263    
264    #ifdef ALLOW_AUTODIFF_TAMC
265    #ifndef DISABLE_MULTIDIM_ADVECTION
266    CADJ STORE localTij(:,:)  =
267    CADJ &     comlev1_bibj_k_gad_pass, key=passkey, byte=isbyte
268    #endif
269    #endif /* ALLOW_AUTODIFF_TAMC */
270    
271        IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN        IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
272         CALL GAD_FLUXLIMIT_ADV_X(         CALL GAD_FLUXLIMIT_ADV_X(
273       &      bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)       &      bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)
# Line 148  C-    Advective flux in X Line 278  C-    Advective flux in X
278         CALL GAD_DST3FL_ADV_X(         CALL GAD_DST3FL_ADV_X(
279       &       bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)       &       bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)
280        ELSE        ELSE
281         STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim'         STOP 'GAD_ADVECTION: adv. scheme incompatibale with multi-dim'
282        ENDIF        ENDIF
283    
284        DO j=1-Oly,sNy+Oly        DO j=1-Oly,sNy+Oly
285         DO i=1-Olx,sNx+Olx-1         DO i=1-Olx,sNx+Olx-1
286          localTij(i,j)=localTij(i,j)-deltaTtracer*          localTij(i,j)=localTij(i,j)-deltaTtracer*
# Line 196  C-    Advective flux in Y Line 327  C-    Advective flux in Y
327          af(i,j) = 0.          af(i,j) = 0.
328         ENDDO         ENDDO
329        ENDDO        ENDDO
330    
331    #ifdef ALLOW_AUTODIFF_TAMC
332    #ifndef DISABLE_MULTIDIM_ADVECTION
333    CADJ STORE localTij(:,:)  =
334    CADJ &     comlev1_bibj_k_gad_pass, key=passkey, byte=isbyte
335    #endif
336    #endif /* ALLOW_AUTODIFF_TAMC */
337    
338        IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN        IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
339         CALL GAD_FLUXLIMIT_ADV_Y(         CALL GAD_FLUXLIMIT_ADV_Y(
340       &       bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid)       &       bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid)
# Line 208  C-    Advective flux in Y Line 347  C-    Advective flux in Y
347        ELSE        ELSE
348         STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim'         STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim'
349        ENDIF        ENDIF
350    
351        DO j=1-Oly,sNy+Oly-1        DO j=1-Oly,sNy+Oly-1
352         DO i=1-Olx,sNx+Olx         DO i=1-Olx,sNx+Olx
353          localTij(i,j)=localTij(i,j)-deltaTtracer*          localTij(i,j)=localTij(i,j)-deltaTtracer*
# Line 247  C--   End of K loop for horizontal fluxe Line 387  C--   End of K loop for horizontal fluxe
387    
388  C--   Start of k loop for vertical flux  C--   Start of k loop for vertical flux
389        DO k=Nr,1,-1        DO k=Nr,1,-1
390    #ifdef ALLOW_AUTODIFF_TAMC
391             kkey = (ikey-1)*Nr + k
392    #endif /* ALLOW_AUTODIFF_TAMC */
393    
394  C--   kup    Cycles through 1,2 to point to w-layer above  C--   kup    Cycles through 1,2 to point to w-layer above
395  C--   kDown  Cycles through 2,1 to point to w-layer below  C--   kDown  Cycles through 2,1 to point to w-layer below
396        kup  = 1+MOD(k+1,2)        kup  = 1+MOD(k+1,2)
397        kDown= 1+MOD(k,2)        kDown= 1+MOD(k,2)
398    c     kp1=min(Nr,k+1)
399          kp1Msk=1.
400          if (k.EQ.Nr) kp1Msk=0.
401    
402  C--   Get temporary terms used by tendency routines  #ifdef ALLOW_AUTODIFF_TAMC
403        CALL CALC_COMMON_FACTORS (  CADJ STORE localTijk(:,:,k)  
404       I         bi,bj,iMin,iMax,jMin,jMax,k,  CADJ &     = comlev1_bibj_k_gad, key=kkey, byte=isbyte
405       O         xA,yA,uTrans,vTrans,rTrans,maskUp,  CADJ STORE rTrans(:,:)  
406       I         myThid)  CADJ &     = comlev1_bibj_k_gad, key=kkey, byte=isbyte
407    #endif /* ALLOW_AUTODIFF_TAMC */
408    
409  C-    Advective flux in R  C-- Compute Vertical transport
410        DO j=1-Oly,sNy+Oly  C     Note: wVel needs to be masked
411         DO i=1-Olx,sNx+Olx  
412          af(i,j) = 0.        IF (k.EQ.1) THEN
413    C- Surface interface :
414    
415           DO j=1-Oly,sNy+Oly
416            DO i=1-Olx,sNx+Olx
417             rTransKp1(i,j) = rTrans(i,j)
418             rTrans(i,j) = 0.
419             fVerT(i,j,kUp) = 0.
420            ENDDO
421         ENDDO         ENDDO
       ENDDO  
422    
423  C     Note: wVel needs to be masked        ELSE
424        IF (K.GE.2) THEN  C- Interior interface :
425           DO j=1-Oly,sNy+Oly
426            DO i=1-Olx,sNx+Olx
427             rTransKp1(i,j) = kp1Msk*rTrans(i,j)
428             rTrans(i,j) = wVel(i,j,k,bi,bj)*rA(i,j,bi,bj)
429         &               *maskC(i,j,k-1,bi,bj)
430             af(i,j) = 0.
431            ENDDO
432           ENDDO
433    
434    #ifdef ALLOW_GMREDI
435    C--   Residual transp = Bolus transp + Eulerian transp
436           IF (useGMRedi)
437         &   CALL GMREDI_CALC_WFLOW(
438         &                    rTrans, bi, bj, k, myThid)
439    #endif /* ALLOW_GMREDI */
440    
441  C-    Compute vertical advective flux in the interior:  C-    Compute vertical advective flux in the interior:
442         IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN         IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
443          CALL GAD_FLUXLIMIT_ADV_R(          CALL GAD_FLUXLIMIT_ADV_R(
# Line 281  C-    Compute vertical advective flux in Line 451  C-    Compute vertical advective flux in
451         ELSE         ELSE
452          STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim'          STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim'
453         ENDIF         ENDIF
454  C-    Surface "correction" term at k>1 :  C-    add the advective flux to fVerT
        DO j=1-Oly,sNy+Oly  
         DO i=1-Olx,sNx+Olx  
          af(i,j) = af(i,j)  
      &           + (maskC(i,j,k,bi,bj)-maskC(i,j,k-1,bi,bj))*  
      &             rTrans(i,j)*localTijk(i,j,k)  
         ENDDO  
        ENDDO  
       ELSE  
 C-    Surface "correction" term at k=1 :  
455         DO j=1-Oly,sNy+Oly         DO j=1-Oly,sNy+Oly
456          DO i=1-Olx,sNx+Olx          DO i=1-Olx,sNx+Olx
457           af(i,j) = rTrans(i,j)*localTijk(i,j,k)           fVerT(i,j,kUp) = af(i,j)
458          ENDDO          ENDDO
        ENDDO  
       ENDIF  
 C-    add the advective flux to fVerT  
       DO j=1-Oly,sNy+Oly  
        DO i=1-Olx,sNx+Olx  
         fVerT(i,j,kUp) = af(i,j)  
459         ENDDO         ENDDO
460        ENDDO  
461    C- end Surface/Interior if bloc
462          ENDIF
463    
464  C--   Divergence of fluxes  C--   Divergence of fluxes
       kp1=min(Nr,k+1)  
       kp1Msk=1.  
       if (k.EQ.Nr) kp1Msk=0.  
465        DO j=1-Oly,sNy+Oly        DO j=1-Oly,sNy+Oly
466         DO i=1-Olx,sNx+Olx         DO i=1-Olx,sNx+Olx
467          localTij(i,j)=localTijk(i,j,k)-deltaTtracer*          localTij(i,j)=localTijk(i,j,k)-deltaTtracer*
468       &    _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)       &    _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
469       &    *recip_rA(i,j,bi,bj)       &    *recip_rA(i,j,bi,bj)
470       &    *( fVerT(i,j,kUp)-fVerT(i,j,kDown)       &    *( fVerT(i,j,kUp)-fVerT(i,j,kDown)
471       &      -tracer(i,j,k,bi,bj)*rA(i,j,bi,bj)*       &      -tracer(i,j,k,bi,bj)*(rTrans(i,j)-rTransKp1(i,j))
      &        (wVel(i,j,k,bi,bj)-kp1Msk*wVel(i,j,kp1,bi,bj))  
472       &     )*rkFac       &     )*rkFac
473          gTracer(i,j,k,bi,bj)=          gTracer(i,j,k,bi,bj)=
474       &   (localTij(i,j)-tracer(i,j,k,bi,bj))/deltaTtracer       &   (localTij(i,j)-tracer(i,j,k,bi,bj))/deltaTtracer
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