Actual source code: ex30.c

  1: static const char help[] = "Steady-state 2D subduction flow, pressure and temperature solver.\n\
  2:        The flow is driven by the subducting slab.\n\
  3: ---------------------------------ex30 help---------------------------------\n\
  4:   -OPTION <DEFAULT> = (UNITS) DESCRIPTION.\n\n\
  5:   -width <320> = (km) width of domain.\n\
  6:   -depth <300> = (km) depth of domain.\n\
  7:   -slab_dip <45> = (degrees) dip angle of the slab (determines the grid aspect ratio).\n\
  8:   -lid_depth <35> = (km) depth of the static conductive lid.\n\
  9:   -fault_depth <35> = (km) depth of slab-wedge mechanical coupling\n\
 10:      (fault dept >= lid depth).\n\
 11: \n\
 12:   -ni <82> = grid cells in x-direction. (nj adjusts to accommodate\n\
 13:       the slab dip & depth). DO NOT USE -da_grid_x option!!!\n\
 14:   -ivisc <3> = rheology option.\n\
 15:       0 --- constant viscosity.\n\
 16:       1 --- olivine diffusion creep rheology (T&P-dependent, newtonian).\n\
 17:       2 --- olivine dislocation creep rheology (T&P-dependent, non-newtonian).\n\
 18:       3 --- Full mantle rheology, combination of 1 & 2.\n\
 19: \n\
 20:   -slab_velocity <5> = (cm/year) convergence rate of slab into subduction zone.\n\
 21:   -slab_age <50> = (million yrs) age of slab for thermal profile boundary condition.\n\
 22:   -lid_age <50> = (million yrs) age of lid for thermal profile boundary condition.\n\
 23: \n\
 24:   FOR OTHER PARAMETER OPTIONS AND THEIR DEFAULT VALUES, see SetParams() in ex30.c.\n\
 25: ---------------------------------ex30 help---------------------------------\n";


This PETSc 2.2.0 example by Richard F. Katz
http://www.ldeo.columbia.edu/~katz/

The problem is modeled by the partial differential equation system

\begin{eqnarray}
-\nabla P + \nabla \cdot [\eta (\nabla v + \nabla v^T)] & = & 0 \\
\nabla \cdot v & = & 0 \\
dT/dt + \nabla \cdot (vT) - 1/Pe \triangle^2(T) & = & 0 \\
\end{eqnarray}

\begin{eqnarray}
\eta(T,Eps\_dot) & = & \hbox{constant } \hbox{if ivisc} ==0 \\
& = & \hbox{diffusion creep (T,P-dependent) } \hbox{if ivisc} ==1 \\
& = & \hbox{dislocation creep (T,P,v-dependent)} \hbox{if ivisc} ==2 \\
& = & \hbox{mantle viscosity (difn and disl) } \hbox{if ivisc} ==3
\end{eqnarray}

which is uniformly discretized on a staggered mesh:
-------$w_{ij}$------
$u_{i-1j}$ $P,T_{ij}$ $u_{ij}$
------$w_{ij-1}$-----

 54: #include <petscsnes.h>
 55: #include <petscdm.h>
 56: #include <petscdmda.h>

 58: #define VISC_CONST   0
 59: #define VISC_DIFN    1
 60: #define VISC_DISL    2
 61: #define VISC_FULL    3
 62: #define CELL_CENTER  0
 63: #define CELL_CORNER  1
 64: #define BC_ANALYTIC  0
 65: #define BC_NOSTRESS  1
 66: #define BC_EXPERMNT  2
 67: #define ADVECT_FV    0
 68: #define ADVECT_FROMM 1
 69: #define PLATE_SLAB   0
 70: #define PLATE_LID    1
 71: #define EPS_ZERO     0.00000001

 73: typedef struct { /* holds the variables to be solved for */
 74:   PetscScalar u,w,p,T;
 75: } Field;

 77: typedef struct { /* parameters needed to compute viscosity */
 78:   PetscReal A,n,Estar,Vstar;
 79: } ViscParam;

 81: typedef struct { /* physical and miscelaneous parameters */
 82:   PetscReal width, depth, scaled_width, scaled_depth, peclet, potentialT;
 83:   PetscReal slab_dip, slab_age, slab_velocity, kappa, z_scale;
 84:   PetscReal c, d, sb, cb, skt, visc_cutoff, lid_age, eta0, continuation;
 85:   PetscReal L, V, lid_depth, fault_depth;
 86:   ViscParam diffusion, dislocation;
 87:   PetscInt  ivisc, adv_scheme, ibound, output_ivisc;
 88:   PetscBool quiet, param_test, output_to_file, pv_analytic;
 89:   PetscBool interrupted, stop_solve, toggle_kspmon, kspmon;
 90:   char      filename[PETSC_MAX_PATH_LEN];
 91: } Parameter;

 93: typedef struct { /* grid parameters */
 94:   DMBoundaryType   bx,by;
 95:   DMDAStencilType  stencil;
 96:   PetscInt         corner,ni,nj,jlid,jfault,inose;
 97:   PetscInt         dof,stencil_width,mglevels;
 98:   PetscReal        dx,dz;
 99: } GridInfo;

101: typedef struct { /* application context */
102:   Vec       x,Xguess;
103:   Parameter *param;
104:   GridInfo  *grid;
105: } AppCtx;

107: /* Callback functions (static interface) */
108: extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,Field**,Field**,void*);

110: /* Main routines */
111: extern PetscErrorCode SetParams(Parameter*, GridInfo*);
112: extern PetscErrorCode ReportParams(Parameter*, GridInfo*);
113: extern PetscErrorCode Initialize(DM);
114: extern PetscErrorCode UpdateSolution(SNES,AppCtx*, PetscInt*);
115: extern PetscErrorCode DoOutput(SNES,PetscInt);

117: /* Post-processing & misc */
118: extern PetscErrorCode ViscosityField(DM,Vec,Vec);
119: extern PetscErrorCode StressField(DM);
120: extern PetscErrorCode SNESConverged_Interactive(SNES, PetscInt, PetscReal, PetscReal, PetscReal, SNESConvergedReason*, void*);
121: extern PetscErrorCode InteractiveHandler(int, void*);

123: /*-----------------------------------------------------------------------*/
124: int main(int argc,char **argv)
125: /*-----------------------------------------------------------------------*/
126: {
127:   SNES           snes;
128:   AppCtx         *user;               /* user-defined work context */
129:   Parameter      param;
130:   GridInfo       grid;
131:   PetscInt       nits;
133:   MPI_Comm       comm;
134:   DM             da;

136:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
137:   PetscOptionsSetValue(NULL,"-file","ex30_output");
138:   PetscOptionsSetValue(NULL,"-snes_monitor_short",NULL);
139:   PetscOptionsSetValue(NULL,"-snes_max_it","20");
140:   PetscOptionsSetValue(NULL,"-ksp_max_it","1500");
141:   PetscOptionsSetValue(NULL,"-ksp_gmres_restart","300");
142:   PetscOptionsInsert(NULL,&argc,&argv,NULL);

144:   comm = PETSC_COMM_WORLD;

146:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
147:      Set up the problem parameters.
148:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
149:   SetParams(&param,&grid);
150:   ReportParams(&param,&grid);

152:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
153:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
154:   SNESCreate(comm,&snes);
155:   DMDACreate2d(comm,grid.bx,grid.by,grid.stencil,grid.ni,grid.nj,PETSC_DECIDE,PETSC_DECIDE,grid.dof,grid.stencil_width,0,0,&da);
156:   DMSetFromOptions(da);
157:   DMSetUp(da);
158:   SNESSetDM(snes,da);
159:   DMDASetFieldName(da,0,"x-velocity");
160:   DMDASetFieldName(da,1,"y-velocity");
161:   DMDASetFieldName(da,2,"pressure");
162:   DMDASetFieldName(da,3,"temperature");

164:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
165:      Create user context, set problem data, create vector data structures.
166:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
167:   PetscNew(&user);
168:   user->param = &param;
169:   user->grid  = &grid;
170:   DMSetApplicationContext(da,user);
171:   DMCreateGlobalVector(da,&(user->Xguess));

173:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
174:      Set up the SNES solver with callback functions.
175:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
176:   DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,(void*)user);
177:   SNESSetFromOptions(snes);

179:   SNESSetConvergenceTest(snes,SNESConverged_Interactive,(void*)user,NULL);
180:   PetscPushSignalHandler(InteractiveHandler,(void*)user);

182:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
183:      Initialize and solve the nonlinear system
184:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
185:   Initialize(da);
186:   UpdateSolution(snes,user,&nits);

188:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
189:      Output variables.
190:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
191:   DoOutput(snes,nits);

193:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
194:      Free work space.
195:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
196:   VecDestroy(&user->Xguess);
197:   VecDestroy(&user->x);
198:   PetscFree(user);
199:   SNESDestroy(&snes);
200:   DMDestroy(&da);
201:   PetscPopSignalHandler();
202:   PetscFinalize();
203:   return ierr;
204: }

206: /*=====================================================================
207:   PETSc INTERACTION FUNCTIONS (initialize & call SNESSolve)
208:   =====================================================================*/

210: /*---------------------------------------------------------------------*/
211: /*  manages solve: adaptive continuation method  */
212: PetscErrorCode UpdateSolution(SNES snes, AppCtx *user, PetscInt *nits)
213: {
214:   KSP                 ksp;
215:   PC                  pc;
216:   SNESConvergedReason reason = SNES_CONVERGED_ITERATING;
217:   Parameter           *param   = user->param;
218:   PetscReal           cont_incr=0.3;
219:   PetscInt            its;
220:   PetscErrorCode      ierr;
221:   PetscBool           q = PETSC_FALSE;
222:   DM                  dm;

225:   SNESGetDM(snes,&dm);
226:   DMCreateGlobalVector(dm,&user->x);
227:   SNESGetKSP(snes,&ksp);
228:   KSPGetPC(ksp, &pc);
229:   KSPSetComputeSingularValues(ksp, PETSC_TRUE);

231:   *nits=0;

233:   /* Isoviscous solve */
234:   if (param->ivisc == VISC_CONST && !param->stop_solve) {
235:     param->ivisc = VISC_CONST;

237:     SNESSolve(snes,0,user->x);
238:     SNESGetConvergedReason(snes,&reason);
239:     SNESGetIterationNumber(snes,&its);
240:     *nits += its;
241:     VecCopy(user->x,user->Xguess);
242:     if (param->stop_solve) goto done;
243:   }

245:   /* Olivine diffusion creep */
246:   if (param->ivisc >= VISC_DIFN && !param->stop_solve) {
247:     if (!q) {PetscPrintf(PETSC_COMM_WORLD,"Computing Variable Viscosity Solution\n");}

249:     /* continuation method on viscosity cutoff */
250:     for (param->continuation=0.0;; param->continuation+=cont_incr) {
251:       if (!q) {PetscPrintf(PETSC_COMM_WORLD," Continuation parameter = %g\n", (double)param->continuation);}

253:       /* solve the non-linear system */
254:       VecCopy(user->Xguess,user->x);
255:       SNESSolve(snes,0,user->x);
256:       SNESGetConvergedReason(snes,&reason);
257:       SNESGetIterationNumber(snes,&its);
258:       *nits += its;
259:       if (!q) {PetscPrintf(PETSC_COMM_WORLD," SNES iterations: %D, Cumulative: %D\n", its, *nits);}
260:       if (param->stop_solve) goto done;

262:       if (reason<0) {
263:         /* NOT converged */
264:         cont_incr = -PetscAbsReal(cont_incr)/2.0;
265:         if (PetscAbsReal(cont_incr)<0.01) goto done;

267:       } else {
268:         /* converged */
269:         VecCopy(user->x,user->Xguess);
270:         if (param->continuation >= 1.0) goto done;
271:         if (its<=3)      cont_incr = 0.30001;
272:         else if (its<=8) cont_incr = 0.15001;
273:         else             cont_incr = 0.10001;

275:         if (param->continuation+cont_incr > 1.0) cont_incr = 1.0 - param->continuation;
276:       } /* endif reason<0 */
277:     }
278:   }
279: done:
280:   if (param->stop_solve && !q) {PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: stopping solve.\n");}
281:   if (reason<0 && !q) {PetscPrintf(PETSC_COMM_WORLD,"FAILED TO CONVERGE: stopping solve.\n");}
282:   return(0);
283: }

285: /*=====================================================================
286:   PHYSICS FUNCTIONS (compute the discrete residual)
287:   =====================================================================*/

289: /*---------------------------------------------------------------------*/
290: PETSC_STATIC_INLINE PetscScalar UInterp(Field **x, PetscInt i, PetscInt j)
291: /*---------------------------------------------------------------------*/
292: {
293:   return 0.25*(x[j][i].u+x[j+1][i].u+x[j][i+1].u+x[j+1][i+1].u);
294: }

296: /*---------------------------------------------------------------------*/
297: PETSC_STATIC_INLINE PetscScalar WInterp(Field **x, PetscInt i, PetscInt j)
298: /*---------------------------------------------------------------------*/
299: {
300:   return 0.25*(x[j][i].w+x[j+1][i].w+x[j][i+1].w+x[j+1][i+1].w);
301: }

303: /*---------------------------------------------------------------------*/
304: PETSC_STATIC_INLINE PetscScalar PInterp(Field **x, PetscInt i, PetscInt j)
305: /*---------------------------------------------------------------------*/
306: {
307:   return 0.25*(x[j][i].p+x[j+1][i].p+x[j][i+1].p+x[j+1][i+1].p);
308: }

310: /*---------------------------------------------------------------------*/
311: PETSC_STATIC_INLINE PetscScalar TInterp(Field **x, PetscInt i, PetscInt j)
312: /*---------------------------------------------------------------------*/
313: {
314:   return 0.25*(x[j][i].T+x[j+1][i].T+x[j][i+1].T+x[j+1][i+1].T);
315: }

317: /*---------------------------------------------------------------------*/
318: /*  isoviscous analytic solution for IC */
319: PETSC_STATIC_INLINE PetscScalar HorizVelocity(PetscInt i, PetscInt j, AppCtx *user)
320: /*---------------------------------------------------------------------*/
321: {
322:   Parameter   *param = user->param;
323:   GridInfo    *grid  = user->grid;
324:   PetscScalar st, ct, th, c=param->c, d=param->d;
325:   PetscReal   x, z,r;

327:   x  = (i - grid->jlid)*grid->dx;  z = (j - grid->jlid - 0.5)*grid->dz;
328:   r  = PetscSqrtReal(x*x+z*z);
329:   st = z/r;
330:   ct = x/r;
331:   th = PetscAtanReal(z/x);
332:   return ct*(c*th*st+d*(st+th*ct)) + st*(c*(st-th*ct)+d*th*st);
333: }

335: /*---------------------------------------------------------------------*/
336: /*  isoviscous analytic solution for IC */
337: PETSC_STATIC_INLINE PetscScalar VertVelocity(PetscInt i, PetscInt j, AppCtx *user)
338: /*---------------------------------------------------------------------*/
339: {
340:   Parameter   *param = user->param;
341:   GridInfo    *grid  = user->grid;
342:   PetscScalar st, ct, th, c=param->c, d=param->d;
343:   PetscReal   x, z, r;

345:   x = (i - grid->jlid - 0.5)*grid->dx;  z = (j - grid->jlid)*grid->dz;
346:   r = PetscSqrtReal(x*x+z*z); st = z/r;  ct = x/r;  th = PetscAtanReal(z/x);
347:   return st*(c*th*st+d*(st+th*ct)) - ct*(c*(st-th*ct)+d*th*st);
348: }

350: /*---------------------------------------------------------------------*/
351: /*  isoviscous analytic solution for IC */
352: PETSC_STATIC_INLINE PetscScalar Pressure(PetscInt i, PetscInt j, AppCtx *user)
353: /*---------------------------------------------------------------------*/
354: {
355:   Parameter   *param = user->param;
356:   GridInfo    *grid  = user->grid;
357:   PetscScalar x, z, r, st, ct, c=param->c, d=param->d;

359:   x = (i - grid->jlid - 0.5)*grid->dx;  z = (j - grid->jlid - 0.5)*grid->dz;
360:   r = PetscSqrtReal(x*x+z*z);  st = z/r;  ct = x/r;
361:   return (-2.0*(c*ct-d*st)/r);
362: }

364: /*  computes the second invariant of the strain rate tensor */
365: PETSC_STATIC_INLINE PetscScalar CalcSecInv(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
366: /*---------------------------------------------------------------------*/
367: {
368:   Parameter   *param = user->param;
369:   GridInfo    *grid  = user->grid;
370:   PetscInt    ilim   =grid->ni-1, jlim=grid->nj-1;
371:   PetscScalar uN,uS,uE,uW,wN,wS,wE,wW;
372:   PetscScalar eps11, eps12, eps22;

374:   if (i<j) return EPS_ZERO;
375:   if (i==ilim) i--;
376:   if (j==jlim) j--;

378:   if (ipos==CELL_CENTER) { /* on cell center */
379:     if (j<=grid->jlid) return EPS_ZERO;

381:     uE = x[j][i].u; uW = x[j][i-1].u;
382:     wN = x[j][i].w; wS = x[j-1][i].w;
383:     wE = WInterp(x,i,j-1);
384:     if (i==j) {
385:       uN = param->cb; wW = param->sb;
386:     } else {
387:       uN = UInterp(x,i-1,j); wW = WInterp(x,i-1,j-1);
388:     }

390:     if (j==grid->jlid+1) uS = 0.0;
391:     else                 uS = UInterp(x,i-1,j-1);

393:   } else {       /* on CELL_CORNER */
394:     if (j<grid->jlid) return EPS_ZERO;

396:     uN = x[j+1][i].u;  uS = x[j][i].u;
397:     wE = x[j][i+1].w;  wW = x[j][i].w;
398:     if (i==j) {
399:       wN = param->sb;
400:       uW = param->cb;
401:     } else {
402:       wN = WInterp(x,i,j);
403:       uW = UInterp(x,i-1,j);
404:     }

406:     if (j==grid->jlid) {
407:       uE = 0.0;  uW = 0.0;
408:       uS = -uN;
409:       wS = -wN;
410:     } else {
411:       uE = UInterp(x,i,j);
412:       wS = WInterp(x,i,j-1);
413:     }
414:   }

416:   eps11 = (uE-uW)/grid->dx;  eps22 = (wN-wS)/grid->dz;
417:   eps12 = 0.5*((uN-uS)/grid->dz + (wE-wW)/grid->dx);

419:   return PetscSqrtReal(0.5*(eps11*eps11 + 2.0*eps12*eps12 + eps22*eps22));
420: }

422: /*---------------------------------------------------------------------*/
423: /*  computes the shear viscosity */
424: PETSC_STATIC_INLINE PetscScalar Viscosity(PetscScalar T, PetscScalar eps, PetscScalar z, Parameter *param)
425: /*---------------------------------------------------------------------*/
426: {
427:   PetscReal   result   =0.0;
428:   ViscParam   difn     =param->diffusion, disl=param->dislocation;
429:   PetscInt    iVisc    =param->ivisc;
430:   PetscScalar eps_scale=param->V/(param->L*1000.0);
431:   PetscScalar strain_power, v1, v2, P;
432:   PetscScalar rho_g = 32340.0, R=8.3144;

434:   P = rho_g*(z*param->L*1000.0); /* Pa */

436:   if (iVisc==VISC_CONST) {
437:     /* constant viscosity */
438:     return 1.0;
439:   } else if (iVisc==VISC_DIFN) {
440:     /* diffusion creep rheology */
441:     result = PetscRealPart((difn.A*PetscExpScalar((difn.Estar + P*difn.Vstar)/R/(T+273.0))/param->eta0));
442:   } else if (iVisc==VISC_DISL) {
443:     /* dislocation creep rheology */
444:     strain_power = PetscPowScalar(eps*eps_scale, (1.0-disl.n)/disl.n);

446:     result = PetscRealPart(disl.A*PetscExpScalar((disl.Estar + P*disl.Vstar)/disl.n/R/(T+273.0))*strain_power/param->eta0);
447:   } else if (iVisc==VISC_FULL) {
448:     /* dislocation/diffusion creep rheology */
449:     strain_power = PetscPowScalar(eps*eps_scale, (1.0-disl.n)/disl.n);

451:     v1 = difn.A*PetscExpScalar((difn.Estar + P*difn.Vstar)/R/(T+273.0))/param->eta0;
452:     v2 = disl.A*PetscExpScalar((disl.Estar + P*disl.Vstar)/disl.n/R/(T+273.0))*strain_power/param->eta0;

454:     result = PetscRealPart(1.0/(1.0/v1 + 1.0/v2));
455:   }

457:   /* max viscosity is param->eta0 */
458:   result = PetscMin(result, 1.0);
459:   /* min viscosity is param->visc_cutoff */
460:   result = PetscMax(result, param->visc_cutoff);
461:   /* continuation method */
462:   result = PetscPowReal(result,param->continuation);
463:   return result;
464: }

466: /*---------------------------------------------------------------------*/
467: /*  computes the residual of the x-component of eqn (1) above */
468: PETSC_STATIC_INLINE PetscScalar XMomentumResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
469: /*---------------------------------------------------------------------*/
470: {
471:   Parameter   *param=user->param;
472:   GridInfo    *grid =user->grid;
473:   PetscScalar dx    = grid->dx, dz=grid->dz;
474:   PetscScalar etaN,etaS,etaE,etaW,epsN=0.0,epsS=0.0,epsE=0.0,epsW=0.0;
475:   PetscScalar TE=0.0,TN=0.0,TS=0.0,TW=0.0, dPdx, residual, z_scale;
476:   PetscScalar dudxW,dudxE,dudzN,dudzS,dwdxN,dwdxS;
477:   PetscInt    jlim = grid->nj-1;

479:   z_scale = param->z_scale;

481:   if (param->ivisc==VISC_DIFN || param->ivisc>=VISC_DISL) { /* viscosity is T-dependent */
482:     TS = param->potentialT * TInterp(x,i,j-1) * PetscExpScalar((j-1.0)*dz*z_scale);
483:     if (j==jlim) TN = TS;
484:     else         TN = param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*z_scale);
485:     TW = param->potentialT * x[j][i].T        * PetscExpScalar((j-0.5)*dz*z_scale);
486:     TE = param->potentialT * x[j][i+1].T      * PetscExpScalar((j-0.5)*dz*z_scale);
487:     if (param->ivisc>=VISC_DISL) { /* olivine dislocation creep */
488:       epsN = CalcSecInv(x,i,j,  CELL_CORNER,user);
489:       epsS = CalcSecInv(x,i,j-1,CELL_CORNER,user);
490:       epsE = CalcSecInv(x,i+1,j,CELL_CENTER,user);
491:       epsW = CalcSecInv(x,i,j,  CELL_CENTER,user);
492:     }
493:   }
494:   etaN = Viscosity(TN,epsN,dz*(j+0.5),param);
495:   etaS = Viscosity(TS,epsS,dz*(j-0.5),param);
496:   etaW = Viscosity(TW,epsW,dz*j,param);
497:   etaE = Viscosity(TE,epsE,dz*j,param);

499:   dPdx = (x[j][i+1].p - x[j][i].p)/dx;
500:   if (j==jlim) dudzN = etaN * (x[j][i].w   - x[j][i+1].w)/dx;
501:   else         dudzN = etaN * (x[j+1][i].u - x[j][i].u)  /dz;
502:   dudzS = etaS * (x[j][i].u    - x[j-1][i].u)/dz;
503:   dudxE = etaE * (x[j][i+1].u  - x[j][i].u)  /dx;
504:   dudxW = etaW * (x[j][i].u    - x[j][i-1].u)/dx;

506:   residual = -dPdx                          /* X-MOMENTUM EQUATION*/
507:              +(dudxE - dudxW)/dx
508:              +(dudzN - dudzS)/dz;

510:   if (param->ivisc!=VISC_CONST) {
511:     dwdxN = etaN * (x[j][i+1].w   - x[j][i].w)  /dx;
512:     dwdxS = etaS * (x[j-1][i+1].w - x[j-1][i].w)/dx;

514:     residual += (dudxE - dudxW)/dx + (dwdxN - dwdxS)/dz;
515:   }

517:   return residual;
518: }

520: /*---------------------------------------------------------------------*/
521: /*  computes the residual of the z-component of eqn (1) above */
522: PETSC_STATIC_INLINE PetscScalar ZMomentumResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
523: /*---------------------------------------------------------------------*/
524: {
525:   Parameter   *param=user->param;
526:   GridInfo    *grid =user->grid;
527:   PetscScalar dx    = grid->dx, dz=grid->dz;
528:   PetscScalar etaN  =0.0,etaS=0.0,etaE=0.0,etaW=0.0,epsN=0.0,epsS=0.0,epsE=0.0,epsW=0.0;
529:   PetscScalar TE    =0.0,TN=0.0,TS=0.0,TW=0.0, dPdz, residual,z_scale;
530:   PetscScalar dudzE,dudzW,dwdxW,dwdxE,dwdzN,dwdzS;
531:   PetscInt    ilim = grid->ni-1;

533:   /* geometric and other parameters */
534:   z_scale = param->z_scale;

536:   /* viscosity */
537:   if (param->ivisc==VISC_DIFN || param->ivisc>=VISC_DISL) { /* viscosity is T-dependent */
538:     TN = param->potentialT * x[j+1][i].T      * PetscExpScalar((j+0.5)*dz*z_scale);
539:     TS = param->potentialT * x[j][i].T        * PetscExpScalar((j-0.5)*dz*z_scale);
540:     TW = param->potentialT * TInterp(x,i-1,j) * PetscExpScalar(j*dz*z_scale);
541:     if (i==ilim) TE = TW;
542:     else         TE = param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*z_scale);
543:     if (param->ivisc>=VISC_DISL) { /* olivine dislocation creep */
544:       epsN = CalcSecInv(x,i,j+1,CELL_CENTER,user);
545:       epsS = CalcSecInv(x,i,j,  CELL_CENTER,user);
546:       epsE = CalcSecInv(x,i,j,  CELL_CORNER,user);
547:       epsW = CalcSecInv(x,i-1,j,CELL_CORNER,user);
548:     }
549:   }
550:   etaN = Viscosity(TN,epsN,dz*(j+1.0),param);
551:   etaS = Viscosity(TS,epsS,dz*(j+0.0),param);
552:   etaW = Viscosity(TW,epsW,dz*(j+0.5),param);
553:   etaE = Viscosity(TE,epsE,dz*(j+0.5),param);

555:   dPdz  = (x[j+1][i].p - x[j][i].p)/dz;
556:   dwdzN = etaN * (x[j+1][i].w - x[j][i].w)/dz;
557:   dwdzS = etaS * (x[j][i].w - x[j-1][i].w)/dz;
558:   if (i==ilim) dwdxE = etaE * (x[j][i].u   - x[j+1][i].u)/dz;
559:   else         dwdxE = etaE * (x[j][i+1].w - x[j][i].w)  /dx;
560:   dwdxW = 2.0*etaW * (x[j][i].w - x[j][i-1].w)/dx;

562:   /* Z-MOMENTUM */
563:   residual = -dPdz                 /* constant viscosity terms */
564:              +(dwdzN - dwdzS)/dz
565:              +(dwdxE - dwdxW)/dx;

567:   if (param->ivisc!=VISC_CONST) {
568:     dudzE = etaE * (x[j+1][i].u - x[j][i].u)/dz;
569:     dudzW = etaW * (x[j+1][i-1].u - x[j][i-1].u)/dz;

571:     residual += (dwdzN - dwdzS)/dz + (dudzE - dudzW)/dx;
572:   }

574:   return residual;
575: }

577: /*---------------------------------------------------------------------*/
578: /*  computes the residual of eqn (2) above */
579: PETSC_STATIC_INLINE PetscScalar ContinuityResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
580: /*---------------------------------------------------------------------*/
581: {
582:   GridInfo    *grid =user->grid;
583:   PetscScalar uE,uW,wN,wS,dudx,dwdz;

585:   uW = x[j][i-1].u; uE = x[j][i].u; dudx = (uE - uW)/grid->dx;
586:   wS = x[j-1][i].w; wN = x[j][i].w; dwdz = (wN - wS)/grid->dz;

588:   return dudx + dwdz;
589: }

591: /*---------------------------------------------------------------------*/
592: /*  computes the residual of eqn (3) above */
593: PETSC_STATIC_INLINE PetscScalar EnergyResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
594: /*---------------------------------------------------------------------*/
595: {
596:   Parameter   *param=user->param;
597:   GridInfo    *grid =user->grid;
598:   PetscScalar dx    = grid->dx, dz=grid->dz;
599:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1, jlid=grid->jlid;
600:   PetscScalar TE, TN, TS, TW, residual;
601:   PetscScalar uE,uW,wN,wS;
602:   PetscScalar fN,fS,fE,fW,dTdxW,dTdxE,dTdzN,dTdzS;

604:   dTdzN = (x[j+1][i].T - x[j][i].T)  /dz;
605:   dTdzS = (x[j][i].T   - x[j-1][i].T)/dz;
606:   dTdxE = (x[j][i+1].T - x[j][i].T)  /dx;
607:   dTdxW = (x[j][i].T   - x[j][i-1].T)/dx;

609:   residual = ((dTdzN - dTdzS)/dz + /* diffusion term */
610:               (dTdxE - dTdxW)/dx)*dx*dz/param->peclet;

612:   if (j<=jlid && i>=j) {
613:     /* don't advect in the lid */
614:     return residual;
615:   } else if (i<j) {
616:     /* beneath the slab sfc */
617:     uW = uE = param->cb;
618:     wS = wN = param->sb;
619:   } else {
620:     /* advect in the slab and wedge */
621:     uW = x[j][i-1].u; uE = x[j][i].u;
622:     wS = x[j-1][i].w; wN = x[j][i].w;
623:   }

625:   if (param->adv_scheme==ADVECT_FV || i==ilim-1 || j==jlim-1 || i==1 || j==1) {
626:     /* finite volume advection */
627:     TS = (x[j][i].T + x[j-1][i].T)/2.0;
628:     TN = (x[j][i].T + x[j+1][i].T)/2.0;
629:     TE = (x[j][i].T + x[j][i+1].T)/2.0;
630:     TW = (x[j][i].T + x[j][i-1].T)/2.0;
631:     fN = wN*TN*dx; fS = wS*TS*dx;
632:     fE = uE*TE*dz; fW = uW*TW*dz;

634:   } else {
635:     /* Fromm advection scheme */
636:     fE =     (uE *(-x[j][i+2].T + 5.0*(x[j][i+1].T+x[j][i].T)-x[j][i-1].T)/8.0
637:               - PetscAbsScalar(uE)*(-x[j][i+2].T + 3.0*(x[j][i+1].T-x[j][i].T)+x[j][i-1].T)/8.0)*dz;
638:     fW =     (uW *(-x[j][i+1].T + 5.0*(x[j][i].T+x[j][i-1].T)-x[j][i-2].T)/8.0
639:               - PetscAbsScalar(uW)*(-x[j][i+1].T + 3.0*(x[j][i].T-x[j][i-1].T)+x[j][i-2].T)/8.0)*dz;
640:     fN =     (wN *(-x[j+2][i].T + 5.0*(x[j+1][i].T+x[j][i].T)-x[j-1][i].T)/8.0
641:               - PetscAbsScalar(wN)*(-x[j+2][i].T + 3.0*(x[j+1][i].T-x[j][i].T)+x[j-1][i].T)/8.0)*dx;
642:     fS =     (wS *(-x[j+1][i].T + 5.0*(x[j][i].T+x[j-1][i].T)-x[j-2][i].T)/8.0
643:               - PetscAbsScalar(wS)*(-x[j+1][i].T + 3.0*(x[j][i].T-x[j-1][i].T)+x[j-2][i].T)/8.0)*dx;
644:   }

646:   residual -= (fE - fW + fN - fS);

648:   return residual;
649: }

651: /*---------------------------------------------------------------------*/
652: /*  computes the shear stress---used on the boundaries */
653: PETSC_STATIC_INLINE PetscScalar ShearStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
654: /*---------------------------------------------------------------------*/
655: {
656:   Parameter   *param=user->param;
657:   GridInfo    *grid =user->grid;
658:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1;
659:   PetscScalar uN, uS, wE, wW;

661:   if (j<=grid->jlid || i<j || i==ilim || j==jlim) return EPS_ZERO;

663:   if (ipos==CELL_CENTER) { /* on cell center */

665:     wE = WInterp(x,i,j-1);
666:     if (i==j) {
667:       wW = param->sb;
668:       uN = param->cb;
669:     } else {
670:       wW = WInterp(x,i-1,j-1);
671:       uN = UInterp(x,i-1,j);
672:     }
673:     if (j==grid->jlid+1) uS = 0.0;
674:     else                 uS = UInterp(x,i-1,j-1);

676:   } else { /* on cell corner */

678:     uN = x[j+1][i].u;         uS = x[j][i].u;
679:     wW = x[j][i].w;           wE = x[j][i+1].w;

681:   }

683:   return (uN-uS)/grid->dz + (wE-wW)/grid->dx;
684: }

686: /*---------------------------------------------------------------------*/
687: /*  computes the normal stress---used on the boundaries */
688: PETSC_STATIC_INLINE PetscScalar XNormalStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
689: /*---------------------------------------------------------------------*/
690: {
691:   Parameter   *param=user->param;
692:   GridInfo    *grid =user->grid;
693:   PetscScalar dx    = grid->dx, dz=grid->dz;
694:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1, ivisc;
695:   PetscScalar epsC  =0.0, etaC, TC, uE, uW, pC, z_scale;
696:   if (i<j || j<=grid->jlid) return EPS_ZERO;

698:   ivisc=param->ivisc;  z_scale = param->z_scale;

700:   if (ipos==CELL_CENTER) { /* on cell center */

702:     TC = param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*z_scale);
703:     if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CENTER,user);
704:     etaC = Viscosity(TC,epsC,dz*j,param);

706:     uW = x[j][i-1].u;   uE = x[j][i].u;
707:     pC = x[j][i].p;

709:   } else { /* on cell corner */
710:     if (i==ilim || j==jlim) return EPS_ZERO;

712:     TC = param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*z_scale);
713:     if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CORNER,user);
714:     etaC = Viscosity(TC,epsC,dz*(j+0.5),param);

716:     if (i==j) uW = param->sb;
717:     else      uW = UInterp(x,i-1,j);
718:     uE = UInterp(x,i,j); pC = PInterp(x,i,j);
719:   }

721:   return 2.0*etaC*(uE-uW)/dx - pC;
722: }

724: /*---------------------------------------------------------------------*/
725: /*  computes the normal stress---used on the boundaries */
726: PETSC_STATIC_INLINE PetscScalar ZNormalStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
727: /*---------------------------------------------------------------------*/
728: {
729:   Parameter   *param=user->param;
730:   GridInfo    *grid =user->grid;
731:   PetscScalar dz    =grid->dz;
732:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1, ivisc;
733:   PetscScalar epsC  =0.0, etaC, TC;
734:   PetscScalar pC, wN, wS, z_scale;
735:   if (i<j || j<=grid->jlid) return EPS_ZERO;

737:   ivisc=param->ivisc;  z_scale = param->z_scale;

739:   if (ipos==CELL_CENTER) { /* on cell center */

741:     TC = param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*z_scale);
742:     if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CENTER,user);
743:     etaC = Viscosity(TC,epsC,dz*j,param);
744:     wN   = x[j][i].w; wS = x[j-1][i].w; pC = x[j][i].p;

746:   } else { /* on cell corner */
747:     if ((i==ilim) || (j==jlim)) return EPS_ZERO;

749:     TC = param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*z_scale);
750:     if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CORNER,user);
751:     etaC = Viscosity(TC,epsC,dz*(j+0.5),param);
752:     if (i==j) wN = param->sb;
753:     else      wN = WInterp(x,i,j);
754:     wS = WInterp(x,i,j-1); pC = PInterp(x,i,j);
755:   }

757:   return 2.0*etaC*(wN-wS)/dz - pC;
758: }

760: /*---------------------------------------------------------------------*/

762: /*=====================================================================
763:   INITIALIZATION, POST-PROCESSING AND OUTPUT FUNCTIONS
764:   =====================================================================*/

766: /*---------------------------------------------------------------------*/
767: /* initializes the problem parameters and checks for
768:    command line changes */
769: PetscErrorCode SetParams(Parameter *param, GridInfo *grid)
770: /*---------------------------------------------------------------------*/
771: {
772:   PetscErrorCode ierr, ierr_out=0;
773:   PetscReal      SEC_PER_YR                    = 3600.00*24.00*365.2500;
774:   PetscReal      alpha_g_on_cp_units_inverse_km=4.0e-5*9.8;

776:   /* domain geometry */
777:   param->slab_dip    = 45.0;
778:   param->width       = 320.0;                                              /* km */
779:   param->depth       = 300.0;                                              /* km */
780:   param->lid_depth   = 35.0;                                               /* km */
781:   param->fault_depth = 35.0;                                               /* km */

783:   PetscOptionsGetReal(NULL,NULL,"-slab_dip",&(param->slab_dip),NULL);
784:   PetscOptionsGetReal(NULL,NULL,"-width",&(param->width),NULL);
785:   PetscOptionsGetReal(NULL,NULL,"-depth",&(param->depth),NULL);
786:   PetscOptionsGetReal(NULL,NULL,"-lid_depth",&(param->lid_depth),NULL);
787:   PetscOptionsGetReal(NULL,NULL,"-fault_depth",&(param->fault_depth),NULL);

789:   param->slab_dip = param->slab_dip*PETSC_PI/180.0;                    /* radians */

791:   /* grid information */
792:   PetscOptionsGetInt(NULL,NULL, "-jfault",&(grid->jfault),NULL);
793:   grid->ni = 82;
794:   PetscOptionsGetInt(NULL,NULL, "-ni",&(grid->ni),NULL);

796:   grid->dx            = param->width/((PetscReal)(grid->ni-2));               /* km */
797:   grid->dz            = grid->dx*PetscTanReal(param->slab_dip);               /* km */
798:   grid->nj            = (PetscInt)(param->depth/grid->dz + 3.0);         /* gridpoints*/
799:   param->depth        = grid->dz*(grid->nj-2);                             /* km */
800:   grid->inose         = 0;                                          /* gridpoints*/
801:   PetscOptionsGetInt(NULL,NULL,"-inose",&(grid->inose),NULL);
802:   grid->bx            = DM_BOUNDARY_NONE;
803:   grid->by            = DM_BOUNDARY_NONE;
804:   grid->stencil       = DMDA_STENCIL_BOX;
805:   grid->dof           = 4;
806:   grid->stencil_width = 2;
807:   grid->mglevels      = 1;

809:   /* boundary conditions */
810:   param->pv_analytic = PETSC_FALSE;
811:   param->ibound      = BC_NOSTRESS;
812:   PetscOptionsGetInt(NULL,NULL,"-ibound",&(param->ibound),NULL);

814:   /* physical constants */
815:   param->slab_velocity = 5.0;               /* cm/yr */
816:   param->slab_age      = 50.0;              /* Ma */
817:   param->lid_age       = 50.0;              /* Ma */
818:   param->kappa         = 0.7272e-6;         /* m^2/sec */
819:   param->potentialT    = 1300.0;            /* degrees C */

821:   PetscOptionsGetReal(NULL,NULL,"-slab_velocity",&(param->slab_velocity),NULL);
822:   PetscOptionsGetReal(NULL,NULL,"-slab_age",&(param->slab_age),NULL);
823:   PetscOptionsGetReal(NULL,NULL,"-lid_age",&(param->lid_age),NULL);
824:   PetscOptionsGetReal(NULL,NULL,"-kappa",&(param->kappa),NULL);
825:   PetscOptionsGetReal(NULL,NULL,"-potentialT",&(param->potentialT),NULL);

827:   /* viscosity */
828:   param->ivisc        = 3;                  /* 0=isovisc, 1=difn creep, 2=disl creep, 3=full */
829:   param->eta0         = 1e24;               /* Pa-s */
830:   param->visc_cutoff  = 0.0;                /* factor of eta_0 */
831:   param->continuation = 1.0;

833:   /* constants for diffusion creep */
834:   param->diffusion.A     = 1.8e7;             /* Pa-s */
835:   param->diffusion.n     = 1.0;               /* dim'less */
836:   param->diffusion.Estar = 375e3;             /* J/mol */
837:   param->diffusion.Vstar = 5e-6;              /* m^3/mol */

839:   /* constants for param->dislocationocation creep */
840:   param->dislocation.A     = 2.8969e4;        /* Pa-s */
841:   param->dislocation.n     = 3.5;             /* dim'less */
842:   param->dislocation.Estar = 530e3;           /* J/mol */
843:   param->dislocation.Vstar = 14e-6;           /* m^3/mol */

845:   PetscOptionsGetInt(NULL,NULL, "-ivisc",&(param->ivisc),NULL);
846:   PetscOptionsGetReal(NULL,NULL,"-visc_cutoff",&(param->visc_cutoff),NULL);

848:   param->output_ivisc = param->ivisc;

850:   PetscOptionsGetInt(NULL,NULL,"-output_ivisc",&(param->output_ivisc),NULL);
851:   PetscOptionsGetReal(NULL,NULL,"-vstar",&(param->dislocation.Vstar),NULL);

853:   /* output options */
854:   param->quiet      = PETSC_FALSE;
855:   param->param_test = PETSC_FALSE;

857:   PetscOptionsHasName(NULL,NULL,"-quiet",&(param->quiet));
858:   PetscOptionsHasName(NULL,NULL,"-test",&(param->param_test));
859:   PetscOptionsGetString(NULL,NULL,"-file",param->filename,sizeof(param->filename),&(param->output_to_file));

861:   /* advection */
862:   param->adv_scheme = ADVECT_FROMM;       /* advection scheme: 0=finite vol, 1=Fromm */

864:   PetscOptionsGetInt(NULL,NULL,"-adv_scheme",&(param->adv_scheme),NULL);

866:   /* misc. flags */
867:   param->stop_solve    = PETSC_FALSE;
868:   param->interrupted   = PETSC_FALSE;
869:   param->kspmon        = PETSC_FALSE;
870:   param->toggle_kspmon = PETSC_FALSE;

872:   /* derived parameters for slab angle */
873:   param->sb = PetscSinReal(param->slab_dip);
874:   param->cb = PetscCosReal(param->slab_dip);
875:   param->c  =  param->slab_dip*param->sb/(param->slab_dip*param->slab_dip-param->sb*param->sb);
876:   param->d  = (param->slab_dip*param->cb-param->sb)/(param->slab_dip*param->slab_dip-param->sb*param->sb);

878:   /* length, velocity and time scale for non-dimensionalization */
879:   param->L = PetscMin(param->width,param->depth);               /* km */
880:   param->V = param->slab_velocity/100.0/SEC_PER_YR;             /* m/sec */

882:   /* other unit conversions and derived parameters */
883:   param->scaled_width = param->width/param->L;                  /* dim'less */
884:   param->scaled_depth = param->depth/param->L;                  /* dim'less */
885:   param->lid_depth    = param->lid_depth/param->L;              /* dim'less */
886:   param->fault_depth  = param->fault_depth/param->L;            /* dim'less */
887:   grid->dx            = grid->dx/param->L;                      /* dim'less */
888:   grid->dz            = grid->dz/param->L;                      /* dim'less */
889:   grid->jlid          = (PetscInt)(param->lid_depth/grid->dz);       /* gridcells */
890:   grid->jfault        = (PetscInt)(param->fault_depth/grid->dz);     /* gridcells */
891:   param->lid_depth    = grid->jlid*grid->dz;                    /* dim'less */
892:   param->fault_depth  = grid->jfault*grid->dz;                  /* dim'less */
893:   grid->corner        = grid->jlid+1;                           /* gridcells */
894:   param->peclet       = param->V                                /* m/sec */
895:                         * param->L*1000.0                       /* m */
896:                         / param->kappa;                         /* m^2/sec */
897:   param->z_scale = param->L * alpha_g_on_cp_units_inverse_km;
898:   param->skt     = PetscSqrtReal(param->kappa*param->slab_age*SEC_PER_YR);
899:   PetscOptionsGetReal(NULL,NULL,"-peclet",&(param->peclet),NULL);

901:   return ierr_out;
902: }

904: /*---------------------------------------------------------------------*/
905: /*  prints a report of the problem parameters to stdout */
906: PetscErrorCode ReportParams(Parameter *param, GridInfo *grid)
907: /*---------------------------------------------------------------------*/
908: {
909:   PetscErrorCode ierr, ierr_out=0;
910:   char           date[30];

912:   PetscGetDate(date,30);

914:   if (!(param->quiet)) {
915:     PetscPrintf(PETSC_COMM_WORLD,"---------------------BEGIN ex30 PARAM REPORT-------------------\n");
916:     PetscPrintf(PETSC_COMM_WORLD,"Domain: \n");
917:     PetscPrintf(PETSC_COMM_WORLD,"  Width = %g km,         Depth = %g km\n",(double)param->width,(double)param->depth);
918:     PetscPrintf(PETSC_COMM_WORLD,"  Slab dip = %g degrees,  Slab velocity = %g cm/yr\n",(double)(param->slab_dip*180.0/PETSC_PI),(double)param->slab_velocity);
919:     PetscPrintf(PETSC_COMM_WORLD,"  Lid depth = %5.2f km,   Fault depth = %5.2f km\n",(double)(param->lid_depth*param->L),(double)(param->fault_depth*param->L));

921:     PetscPrintf(PETSC_COMM_WORLD,"\nGrid: \n");
922:     PetscPrintf(PETSC_COMM_WORLD,"  [ni,nj] = %D, %D       [dx,dz] = %g, %g km\n",grid->ni,grid->nj,(double)(grid->dx*param->L),(double)(grid->dz*param->L));
923:     PetscPrintf(PETSC_COMM_WORLD,"  jlid = %3D              jfault = %3D \n",grid->jlid,grid->jfault);
924:     PetscPrintf(PETSC_COMM_WORLD,"  Pe = %g\n",(double)param->peclet);

926:     PetscPrintf(PETSC_COMM_WORLD,"\nRheology:");
927:     if (param->ivisc==VISC_CONST) {
928:       PetscPrintf(PETSC_COMM_WORLD,"                 Isoviscous \n");
929:       if (param->pv_analytic) {
930:         PetscPrintf(PETSC_COMM_WORLD,"                          Pressure and Velocity prescribed! \n");
931:       }
932:     } else if (param->ivisc==VISC_DIFN) {
933:       PetscPrintf(PETSC_COMM_WORLD,"                 Diffusion Creep (T-Dependent Newtonian) \n");
934:       PetscPrintf(PETSC_COMM_WORLD,"                          Viscosity range: %g--%g Pa-sec \n",(double)param->eta0,(double)(param->visc_cutoff*param->eta0));
935:     } else if (param->ivisc==VISC_DISL) {
936:       PetscPrintf(PETSC_COMM_WORLD,"                 Dislocation Creep (T-Dependent Non-Newtonian) \n");
937:       PetscPrintf(PETSC_COMM_WORLD,"                          Viscosity range: %g--%g Pa-sec \n",(double)param->eta0,(double)(param->visc_cutoff*param->eta0));
938:     } else if (param->ivisc==VISC_FULL) {
939:       PetscPrintf(PETSC_COMM_WORLD,"                 Full Rheology \n");
940:       PetscPrintf(PETSC_COMM_WORLD,"                          Viscosity range: %g--%g Pa-sec \n",(double)param->eta0,(double)(param->visc_cutoff*param->eta0));
941:     } else {
942:       PetscPrintf(PETSC_COMM_WORLD,"                 Invalid! \n");
943:       ierr_out = 1;
944:     }

946:     PetscPrintf(PETSC_COMM_WORLD,"Boundary condition:");
947:     if (param->ibound==BC_ANALYTIC) {
948:       PetscPrintf(PETSC_COMM_WORLD,"       Isoviscous Analytic Dirichlet \n");
949:     } else if (param->ibound==BC_NOSTRESS) {
950:       PetscPrintf(PETSC_COMM_WORLD,"       Stress-Free (normal & shear stress)\n");
951:     } else if (param->ibound==BC_EXPERMNT) {
952:       PetscPrintf(PETSC_COMM_WORLD,"       Experimental boundary condition \n");
953:     } else {
954:       PetscPrintf(PETSC_COMM_WORLD,"       Invalid! \n");
955:       ierr_out = 1;
956:     }

958:     if (param->output_to_file)
959: #if defined(PETSC_HAVE_MATLAB_ENGINE)
960:       PetscPrintf(PETSC_COMM_WORLD,"Output Destination:       Mat file \"%s\"\n",param->filename);
961: #else
962:       PetscPrintf(PETSC_COMM_WORLD,"Output Destination:       PETSc binary file \"%s\"\n",param->filename);
963: #endif
964:     if (param->output_ivisc != param->ivisc) {
965:       PetscPrintf(PETSC_COMM_WORLD,"                          Output viscosity: -ivisc %D\n",param->output_ivisc);
966:     }

968:     PetscPrintf(PETSC_COMM_WORLD,"---------------------END ex30 PARAM REPORT---------------------\n");
969:   }
970:   if (param->param_test) PetscEnd();
971:   return ierr_out;
972: }

974: /* ------------------------------------------------------------------- */
975: /*  generates an inital guess using the analytic solution for isoviscous
976:     corner flow */
977: PetscErrorCode Initialize(DM da)
978: /* ------------------------------------------------------------------- */
979: {
980:   AppCtx         *user;
981:   Parameter      *param;
982:   GridInfo       *grid;
983:   PetscInt       i,j,is,js,im,jm;
985:   Field          **x;
986:   Vec            Xguess;

988:   /* Get the fine grid */
989:   DMGetApplicationContext(da,&user);
990:   Xguess = user->Xguess;
991:   param  = user->param;
992:   grid   = user->grid;
993:   DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
994:   DMDAVecGetArray(da,Xguess,(void**)&x);

996:   /* Compute initial guess */
997:   for (j=js; j<js+jm; j++) {
998:     for (i=is; i<is+im; i++) {
999:       if (i<j)                x[j][i].u = param->cb;
1000:       else if (j<=grid->jlid) x[j][i].u = 0.0;
1001:       else                    x[j][i].u = HorizVelocity(i,j,user);

1003:       if (i<=j)               x[j][i].w = param->sb;
1004:       else if (j<=grid->jlid) x[j][i].w = 0.0;
1005:       else                    x[j][i].w = VertVelocity(i,j,user);

1007:       if (i<j || j<=grid->jlid) x[j][i].p = 0.0;
1008:       else                      x[j][i].p = Pressure(i,j,user);

1010:       x[j][i].T = PetscMin(grid->dz*(j-0.5),1.0);
1011:     }
1012:   }

1014:   /* Restore x to Xguess */
1015:   DMDAVecRestoreArray(da,Xguess,(void**)&x);

1017:   return 0;
1018: }

1020: /*---------------------------------------------------------------------*/
1021: /*  controls output to a file */
1022: PetscErrorCode DoOutput(SNES snes, PetscInt its)
1023: /*---------------------------------------------------------------------*/
1024: {
1025:   AppCtx         *user;
1026:   Parameter      *param;
1027:   GridInfo       *grid;
1028:   PetscInt       ivt;
1030:   PetscMPIInt    rank;
1031:   PetscViewer    viewer;
1032:   Vec            res, pars;
1033:   MPI_Comm       comm;
1034:   DM             da;

1036:   SNESGetDM(snes,&da);
1037:   DMGetApplicationContext(da,&user);
1038:   param = user->param;
1039:   grid  = user->grid;
1040:   ivt   = param->ivisc;

1042:   param->ivisc = param->output_ivisc;

1044:   /* compute final residual and final viscosity/strain rate fields */
1045:   SNESGetFunction(snes, &res, NULL, NULL);
1046:   ViscosityField(da, user->x, user->Xguess);

1048:   /* get the communicator and the rank of the processor */
1049:   PetscObjectGetComm((PetscObject)snes, &comm);
1050:   MPI_Comm_rank(comm, &rank);

1052:   if (param->output_to_file) { /* send output to binary file */
1053:     VecCreate(comm, &pars);
1054:     if (!rank) { /* on processor 0 */
1055:       VecSetSizes(pars, 20, PETSC_DETERMINE);
1056:       VecSetFromOptions(pars);
1057:       VecSetValue(pars,0, (PetscScalar)(grid->ni),INSERT_VALUES);
1058:       VecSetValue(pars,1, (PetscScalar)(grid->nj),INSERT_VALUES);
1059:       VecSetValue(pars,2, (PetscScalar)(grid->dx),INSERT_VALUES);
1060:       VecSetValue(pars,3, (PetscScalar)(grid->dz),INSERT_VALUES);
1061:       VecSetValue(pars,4, (PetscScalar)(param->L),INSERT_VALUES);
1062:       VecSetValue(pars,5, (PetscScalar)(param->V),INSERT_VALUES);
1063:       /* skipped 6 intentionally */
1064:       VecSetValue(pars,7, (PetscScalar)(param->slab_dip),INSERT_VALUES);
1065:       VecSetValue(pars,8, (PetscScalar)(grid->jlid),INSERT_VALUES);
1066:       VecSetValue(pars,9, (PetscScalar)(param->lid_depth),INSERT_VALUES);
1067:       VecSetValue(pars,10,(PetscScalar)(grid->jfault),INSERT_VALUES);
1068:       VecSetValue(pars,11,(PetscScalar)(param->fault_depth),INSERT_VALUES);
1069:       VecSetValue(pars,12,(PetscScalar)(param->potentialT),INSERT_VALUES);
1070:       VecSetValue(pars,13,(PetscScalar)(param->ivisc),INSERT_VALUES);
1071:       VecSetValue(pars,14,(PetscScalar)(param->visc_cutoff),INSERT_VALUES);
1072:       VecSetValue(pars,15,(PetscScalar)(param->ibound),INSERT_VALUES);
1073:       VecSetValue(pars,16,(PetscScalar)(its),INSERT_VALUES);
1074:     } else { /* on some other processor */
1075:       VecSetSizes(pars, 0, PETSC_DETERMINE);
1076:       VecSetFromOptions(pars);
1077:     }
1078:     VecAssemblyBegin(pars); VecAssemblyEnd(pars);

1080:     /* create viewer */
1081: #if defined(PETSC_HAVE_MATLAB_ENGINE)
1082:     PetscViewerMatlabOpen(PETSC_COMM_WORLD,param->filename,FILE_MODE_WRITE,&viewer);
1083: #else
1084:     PetscViewerBinaryOpen(PETSC_COMM_WORLD,param->filename,FILE_MODE_WRITE,&viewer);
1085: #endif

1087:     /* send vectors to viewer */
1088:     PetscObjectSetName((PetscObject)res,"res");
1089:     VecView(res,viewer);
1090:     PetscObjectSetName((PetscObject)user->x,"out");
1091:     VecView(user->x, viewer);
1092:     PetscObjectSetName((PetscObject)(user->Xguess),"aux");
1093:     VecView(user->Xguess, viewer);
1094:     StressField(da); /* compute stress fields */
1095:     PetscObjectSetName((PetscObject)(user->Xguess),"str");
1096:     VecView(user->Xguess, viewer);
1097:     PetscObjectSetName((PetscObject)pars,"par");
1098:     VecView(pars, viewer);

1100:     /* destroy viewer and vector */
1101:     PetscViewerDestroy(&viewer);
1102:     VecDestroy(&pars);
1103:   }

1105:   param->ivisc = ivt;
1106:   return 0;
1107: }

1109: /* ------------------------------------------------------------------- */
1110: /* Compute both the second invariant of the strain rate tensor and the viscosity, at both cell centers and cell corners */
1111: PetscErrorCode ViscosityField(DM da, Vec X, Vec V)
1112: /* ------------------------------------------------------------------- */
1113: {
1114:   AppCtx         *user;
1115:   Parameter      *param;
1116:   GridInfo       *grid;
1117:   Vec            localX;
1118:   Field          **v, **x;
1119:   PetscReal      eps, /* dx,*/ dz, T, epsC, TC;
1120:   PetscInt       i,j,is,js,im,jm,ilim,jlim,ivt;

1124:   DMGetApplicationContext(da,&user);
1125:   param        = user->param;
1126:   grid         = user->grid;
1127:   ivt          = param->ivisc;
1128:   param->ivisc = param->output_ivisc;

1130:   DMGetLocalVector(da, &localX);
1131:   DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX);
1132:   DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX);
1133:   DMDAVecGetArray(da,localX,(void**)&x);
1134:   DMDAVecGetArray(da,V,(void**)&v);

1136:   /* Parameters */
1137:   /* dx = grid->dx; */ dz = grid->dz;

1139:   ilim = grid->ni-1; jlim = grid->nj-1;

1141:   /* Compute real temperature, strain rate and viscosity */
1142:   DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1143:   for (j=js; j<js+jm; j++) {
1144:     for (i=is; i<is+im; i++) {
1145:       T = PetscRealPart(param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*param->z_scale));
1146:       if (i<ilim && j<jlim) {
1147:         TC = PetscRealPart(param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*param->z_scale));
1148:       } else {
1149:         TC = T;
1150:       }
1151:       eps  = PetscRealPart((CalcSecInv(x,i,j,CELL_CENTER,user)));
1152:       epsC = PetscRealPart(CalcSecInv(x,i,j,CELL_CORNER,user));

1154:       v[j][i].u = eps;
1155:       v[j][i].w = epsC;
1156:       v[j][i].p = Viscosity(T,eps,dz*(j-0.5),param);
1157:       v[j][i].T = Viscosity(TC,epsC,dz*j,param);
1158:     }
1159:   }
1160:   DMDAVecRestoreArray(da,V,(void**)&v);
1161:   DMDAVecRestoreArray(da,localX,(void**)&x);
1162:   DMRestoreLocalVector(da, &localX);

1164:   param->ivisc = ivt;
1165:   return(0);
1166: }

1168: /* ------------------------------------------------------------------- */
1169: /* post-processing: compute stress everywhere */
1170: PetscErrorCode StressField(DM da)
1171: /* ------------------------------------------------------------------- */
1172: {
1173:   AppCtx         *user;
1174:   PetscInt       i,j,is,js,im,jm;
1176:   Vec            locVec;
1177:   Field          **x, **y;

1179:   DMGetApplicationContext(da,&user);

1181:   /* Get the fine grid of Xguess and X */
1182:   DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1183:   DMDAVecGetArray(da,user->Xguess,(void**)&x);

1185:   DMGetLocalVector(da, &locVec);
1186:   DMGlobalToLocalBegin(da, user->x, INSERT_VALUES, locVec);
1187:   DMGlobalToLocalEnd(da, user->x, INSERT_VALUES, locVec);
1188:   DMDAVecGetArray(da,locVec,(void**)&y);

1190:   /* Compute stress on the corner points */
1191:   for (j=js; j<js+jm; j++) {
1192:     for (i=is; i<is+im; i++) {
1193:       x[j][i].u = ShearStress(y,i,j,CELL_CENTER,user);
1194:       x[j][i].w = ShearStress(y,i,j,CELL_CORNER,user);
1195:       x[j][i].p = XNormalStress(y,i,j,CELL_CENTER,user);
1196:       x[j][i].T = ZNormalStress(y,i,j,CELL_CENTER,user);
1197:     }
1198:   }

1200:   /* Restore the fine grid of Xguess and X */
1201:   DMDAVecRestoreArray(da,user->Xguess,(void**)&x);
1202:   DMDAVecRestoreArray(da,locVec,(void**)&y);
1203:   DMRestoreLocalVector(da, &locVec);
1204:   return 0;
1205: }

1207: /*=====================================================================
1208:   UTILITY FUNCTIONS
1209:   =====================================================================*/

1211: /*---------------------------------------------------------------------*/
1212: /* returns the velocity of the subducting slab and handles fault nodes
1213:    for BC */
1214: PETSC_STATIC_INLINE PetscScalar SlabVel(char c, PetscInt i, PetscInt j, AppCtx *user)
1215: /*---------------------------------------------------------------------*/
1216: {
1217:   Parameter *param = user->param;
1218:   GridInfo  *grid  = user->grid;

1220:   if (c=='U' || c=='u') {
1221:     if (i<j-1) return param->cb;
1222:     else if (j<=grid->jfault) return 0.0;
1223:     else return param->cb;

1225:   } else {
1226:     if (i<j) return param->sb;
1227:     else if (j<=grid->jfault) return 0.0;
1228:     else return param->sb;
1229:   }
1230: }

1232: /*---------------------------------------------------------------------*/
1233: /*  solution to diffusive half-space cooling model for BC */
1234: PETSC_STATIC_INLINE PetscScalar PlateModel(PetscInt j, PetscInt plate, AppCtx *user)
1235: /*---------------------------------------------------------------------*/
1236: {
1237:   Parameter     *param = user->param;
1238:   PetscScalar   z;
1239:   if (plate==PLATE_LID) z = (j-0.5)*user->grid->dz;
1240:   else z = (j-0.5)*user->grid->dz*param->cb;  /* PLATE_SLAB */
1241: #if defined(PETSC_HAVE_ERF)
1242:   return (PetscReal)(erf((double)PetscRealPart(z*param->L/2.0/param->skt)));
1243: #else
1244:   (*PetscErrorPrintf)("erf() not available on this machine\n");
1245:   MPI_Abort(PETSC_COMM_SELF,1);
1246: #endif
1247: }

1249: /*=====================================================================
1250:   INTERACTIVE SIGNAL HANDLING
1251:   =====================================================================*/

1253: /* ------------------------------------------------------------------- */
1254: PetscErrorCode SNESConverged_Interactive(SNES snes, PetscInt it,PetscReal xnorm, PetscReal snorm, PetscReal fnorm, SNESConvergedReason *reason, void *ctx)
1255: /* ------------------------------------------------------------------- */
1256: {
1257:   AppCtx         *user  = (AppCtx*) ctx;
1258:   Parameter      *param = user->param;
1259:   KSP            ksp;

1263:   if (param->interrupted) {
1264:     param->interrupted = PETSC_FALSE;
1265:     PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: exiting SNES solve. \n");
1266:     *reason = SNES_CONVERGED_FNORM_ABS;
1267:     return(0);
1268:   } else if (param->toggle_kspmon) {
1269:     param->toggle_kspmon = PETSC_FALSE;

1271:     SNESGetKSP(snes, &ksp);

1273:     if (param->kspmon) {
1274:       KSPMonitorCancel(ksp);

1276:       param->kspmon = PETSC_FALSE;
1277:       PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: deactivating ksp singular value monitor. \n");
1278:     } else {
1279:       PetscViewerAndFormat *vf;
1280:       PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_DEFAULT,&vf);
1281:       KSPMonitorSet(ksp,(PetscErrorCode (*)(KSP,PetscInt,PetscReal,void*))KSPMonitorSingularValue,vf,(PetscErrorCode (*)(void**))PetscViewerAndFormatDestroy);

1283:       param->kspmon = PETSC_TRUE;
1284:       PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: activating ksp singular value monitor. \n");
1285:     }
1286:   }
1287:   PetscFunctionReturn(SNESConvergedDefault(snes,it,xnorm,snorm,fnorm,reason,ctx));
1288: }

1290: /* ------------------------------------------------------------------- */
1291: #include <signal.h>
1292: PetscErrorCode InteractiveHandler(int signum, void *ctx)
1293: /* ------------------------------------------------------------------- */
1294: {
1295:   AppCtx    *user  = (AppCtx*) ctx;
1296:   Parameter *param = user->param;

1298:   if (signum == SIGILL) {
1299:     param->toggle_kspmon = PETSC_TRUE;
1300: #if !defined(PETSC_MISSING_SIGCONT)
1301:   } else if (signum == SIGCONT) {
1302:     param->interrupted = PETSC_TRUE;
1303: #endif
1304: #if !defined(PETSC_MISSING_SIGURG)
1305:   } else if (signum == SIGURG) {
1306:     param->stop_solve = PETSC_TRUE;
1307: #endif
1308:   }
1309:   return 0;
1310: }

1312: /*---------------------------------------------------------------------*/
1313: /*  main call-back function that computes the processor-local piece
1314:     of the residual */
1315: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,Field **x,Field **f,void *ptr)
1316: /*---------------------------------------------------------------------*/
1317: {
1318:   AppCtx      *user  = (AppCtx*)ptr;
1319:   Parameter   *param = user->param;
1320:   GridInfo    *grid  = user->grid;
1321:   PetscScalar mag_w, mag_u;
1322:   PetscInt    i,j,mx,mz,ilim,jlim;
1323:   PetscInt    is,ie,js,je,ibound;    /* ,ivisc */

1326:   /* Define global and local grid parameters */
1327:   mx   = info->mx;     mz   = info->my;
1328:   ilim = mx-1;         jlim = mz-1;
1329:   is   = info->xs;     ie   = info->xs+info->xm;
1330:   js   = info->ys;     je   = info->ys+info->ym;

1332:   /* Define geometric and numeric parameters */
1333:   /* ivisc = param->ivisc; */ ibound = param->ibound;

1335:   for (j=js; j<je; j++) {
1336:     for (i=is; i<ie; i++) {

1338:       /************* X-MOMENTUM/VELOCITY *************/
1339:       if (i<j) f[j][i].u = x[j][i].u - SlabVel('U',i,j,user);
1340:       else if (j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1341:         /* in the lithospheric lid */
1342:         f[j][i].u = x[j][i].u - 0.0;
1343:       } else if (i==ilim) {
1344:         /* on the right side boundary */
1345:         if (ibound==BC_ANALYTIC) {
1346:           f[j][i].u = x[j][i].u - HorizVelocity(i,j,user);
1347:         } else {
1348:           f[j][i].u = XNormalStress(x,i,j,CELL_CENTER,user) - EPS_ZERO;
1349:         }

1351:       } else if (j==jlim) {
1352:         /* on the bottom boundary */
1353:         if (ibound==BC_ANALYTIC) {
1354:           f[j][i].u = x[j][i].u - HorizVelocity(i,j,user);
1355:         } else if (ibound==BC_NOSTRESS) {
1356:           f[j][i].u = XMomentumResidual(x,i,j,user);
1357:         } else {
1358:           /* experimental boundary condition */
1359:         }

1361:       } else {
1362:         /* in the mantle wedge */
1363:         f[j][i].u = XMomentumResidual(x,i,j,user);
1364:       }

1366:       /************* Z-MOMENTUM/VELOCITY *************/
1367:       if (i<=j) {
1368:         f[j][i].w = x[j][i].w - SlabVel('W',i,j,user);

1370:       } else if (j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1371:         /* in the lithospheric lid */
1372:         f[j][i].w = x[j][i].w - 0.0;

1374:       } else if (j==jlim) {
1375:         /* on the bottom boundary */
1376:         if (ibound==BC_ANALYTIC) {
1377:           f[j][i].w = x[j][i].w - VertVelocity(i,j,user);
1378:         } else {
1379:           f[j][i].w = ZNormalStress(x,i,j,CELL_CENTER,user) - EPS_ZERO;
1380:         }

1382:       } else if (i==ilim) {
1383:         /* on the right side boundary */
1384:         if (ibound==BC_ANALYTIC) {
1385:           f[j][i].w = x[j][i].w - VertVelocity(i,j,user);
1386:         } else if (ibound==BC_NOSTRESS) {
1387:           f[j][i].w = ZMomentumResidual(x,i,j,user);
1388:         } else {
1389:           /* experimental boundary condition */
1390:         }

1392:       } else {
1393:         /* in the mantle wedge */
1394:         f[j][i].w =  ZMomentumResidual(x,i,j,user);
1395:       }

1397:       /************* CONTINUITY/PRESSURE *************/
1398:       if (i<j || j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1399:         /* in the lid or slab */
1400:         f[j][i].p = x[j][i].p;

1402:       } else if ((i==ilim || j==jlim) && ibound==BC_ANALYTIC) {
1403:         /* on an analytic boundary */
1404:         f[j][i].p = x[j][i].p - Pressure(i,j,user);

1406:       } else {
1407:         /* in the mantle wedge */
1408:         f[j][i].p = ContinuityResidual(x,i,j,user);
1409:       }

1411:       /************* TEMPERATURE *************/
1412:       if (j==0) {
1413:         /* on the surface */
1414:         f[j][i].T = x[j][i].T + x[j+1][i].T + PetscMax(PetscRealPart(x[j][i].T),0.0);

1416:       } else if (i==0) {
1417:         /* slab inflow boundary */
1418:         f[j][i].T = x[j][i].T - PlateModel(j,PLATE_SLAB,user);

1420:       } else if (i==ilim) {
1421:         /* right side boundary */
1422:         mag_u = 1.0 - PetscPowRealInt((1.0-PetscMax(PetscMin(PetscRealPart(x[j][i-1].u)/param->cb,1.0),0.0)), 5);
1423:         f[j][i].T = x[j][i].T - mag_u*x[j-1][i-1].T - (1.0-mag_u)*PlateModel(j,PLATE_LID,user);

1425:       } else if (j==jlim) {
1426:         /* bottom boundary */
1427:         mag_w = 1.0 - PetscPowRealInt((1.0-PetscMax(PetscMin(PetscRealPart(x[j-1][i].w)/param->sb,1.0),0.0)), 5);
1428:         f[j][i].T = x[j][i].T - mag_w*x[j-1][i-1].T - (1.0-mag_w);

1430:       } else {
1431:         /* in the mantle wedge */
1432:         f[j][i].T = EnergyResidual(x,i,j,user);
1433:       }
1434:     }
1435:   }
1436:   return(0);
1437: }

1439: /*TEST

1441:    build:
1442:       requires: !complex erf

1444:    test:
1445:       args: -ni 18
1446:       filter: grep -v Destination
1447:       requires: !single

1449: TEST*/