Actual source code: ex30.c
petsc-3.5.4 2015-05-23
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:
-------$w_{ij}$------
$u_{i-1j}$ $P,T_{ij}$ $u_{ij}$
------$w_{ij-1}$-----
55: #include <petscsnes.h>
56: #include <petscdm.h>
57: #include <petscdmda.h>
59: #define VISC_CONST 0
60: #define VISC_DIFN 1
61: #define VISC_DISL 2
62: #define VISC_FULL 3
63: #define CELL_CENTER 0
64: #define CELL_CORNER 1
65: #define BC_ANALYTIC 0
66: #define BC_NOSTRESS 1
67: #define BC_EXPERMNT 2
68: #define ADVECT_FV 0
69: #define ADVECT_FROMM 1
70: #define PLATE_SLAB 0
71: #define PLATE_LID 1
72: #define EPS_ZERO 0.00000001
74: typedef struct { /* holds the variables to be solved for */
75: PetscScalar u,w,p,T;
76: } Field;
78: typedef struct { /* parameters needed to compute viscosity */
79: PetscReal A,n,Estar,Vstar;
80: } ViscParam;
82: typedef struct { /* physical and miscelaneous parameters */
83: PetscReal width, depth, scaled_width, scaled_depth, peclet, potentialT;
84: PetscReal slab_dip, slab_age, slab_velocity, kappa, z_scale;
85: PetscReal c, d, sb, cb, skt, visc_cutoff, lid_age, eta0, continuation;
86: PetscReal L, V, lid_depth, fault_depth;
87: ViscParam diffusion, dislocation;
88: PetscInt ivisc, adv_scheme, ibound, output_ivisc;
89: PetscBool quiet, param_test, output_to_file, pv_analytic;
90: PetscBool interrupted, stop_solve, toggle_kspmon, kspmon;
91: char filename[PETSC_MAX_PATH_LEN];
92: } Parameter;
94: typedef struct { /* grid parameters */
95: DMBoundaryType bx,by;
96: DMDAStencilType stencil;
97: PetscInt corner,ni,nj,jlid,jfault,inose;
98: PetscInt dof,stencil_width,mglevels;
99: PetscReal dx,dz;
100: } GridInfo;
102: typedef struct { /* application context */
103: Vec x,Xguess;
104: Parameter *param;
105: GridInfo *grid;
106: } AppCtx;
108: /* Callback functions (static interface) */
109: extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,Field**,Field**,void*);
111: /* Main routines */
112: extern PetscErrorCode SetParams(Parameter*, GridInfo*);
113: extern PetscErrorCode ReportParams(Parameter*, GridInfo*);
114: extern PetscErrorCode Initialize(DM);
115: extern PetscErrorCode UpdateSolution(SNES,AppCtx*, PetscInt*);
116: extern PetscErrorCode DoOutput(SNES,PetscInt);
118: /* Post-processing & misc */
119: extern PetscErrorCode ViscosityField(DM,Vec,Vec);
120: extern PetscErrorCode StressField(DM);
121: extern PetscErrorCode SNESConverged_Interactive(SNES, PetscInt, PetscReal, PetscReal, PetscReal, SNESConvergedReason*, void*);
122: extern PetscErrorCode InteractiveHandler(int, void*);
123: extern PetscBool OptionsHasName(const char pre[],const char name[]);
125: /*-----------------------------------------------------------------------*/
128: int main(int argc,char **argv)
129: /*-----------------------------------------------------------------------*/
130: {
131: SNES snes;
132: AppCtx *user; /* user-defined work context */
133: Parameter param;
134: GridInfo grid;
135: PetscInt nits;
137: MPI_Comm comm;
138: DM da;
140: PetscInitialize(&argc,&argv,(char*)0,help);
141: PetscOptionsSetValue("-file","ex30_output");
142: PetscOptionsSetValue("-snes_monitor_short",NULL);
143: PetscOptionsSetValue("-snes_max_it","20");
144: PetscOptionsSetValue("-ksp_max_it","1500");
145: PetscOptionsSetValue("-ksp_gmres_restart","300");
146: PetscOptionsInsert(&argc,&argv,NULL);
148: comm = PETSC_COMM_WORLD;
150: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
151: Set up the problem parameters.
152: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
153: SetParams(¶m,&grid);
154: ReportParams(¶m,&grid);
156: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
157: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
158: SNESCreate(comm,&snes);
159: DMDACreate2d(comm,grid.bx,grid.by,grid.stencil,grid.ni,grid.nj,PETSC_DECIDE,PETSC_DECIDE,grid.dof,grid.stencil_width,0,0,&da);
160: SNESSetDM(snes,da);
161: DMDASetFieldName(da,0,"x-velocity");
162: DMDASetFieldName(da,1,"y-velocity");
163: DMDASetFieldName(da,2,"pressure");
164: DMDASetFieldName(da,3,"temperature");
167: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
168: Create user context, set problem data, create vector data structures.
169: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
170: PetscMalloc(sizeof(AppCtx),&user);
171: user->param = ¶m;
172: user->grid = &grid;
173: DMSetApplicationContext(da,user);
174: DMCreateGlobalVector(da,&(user->Xguess));
177: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178: Set up the SNES solver with callback functions.
179: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
180: DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,(void*)user);
181: SNESSetFromOptions(snes);
184: SNESSetConvergenceTest(snes,SNESConverged_Interactive,(void*)user,NULL);
185: PetscPushSignalHandler(InteractiveHandler,(void*)user);
187: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
188: Initialize and solve the nonlinear system
189: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
190: Initialize(da);
191: UpdateSolution(snes,user,&nits);
193: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
194: Output variables.
195: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
196: DoOutput(snes,nits);
198: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199: Free work space.
200: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
201: VecDestroy(&user->Xguess);
202: VecDestroy(&user->x);
203: PetscFree(user);
204: SNESDestroy(&snes);
205: DMDestroy(&da);
206: PetscPopSignalHandler();
207: PetscFinalize();
208: return 0;
209: }
211: /*=====================================================================
212: PETSc INTERACTION FUNCTIONS (initialize & call SNESSolve)
213: =====================================================================*/
215: /*---------------------------------------------------------------------*/
218: /* manages solve: adaptive continuation method */
219: PetscErrorCode UpdateSolution(SNES snes, AppCtx *user, PetscInt *nits)
220: {
221: KSP ksp;
222: PC pc;
223: SNESConvergedReason reason;
224: Parameter *param = user->param;
225: PetscReal cont_incr=0.3;
226: PetscInt its;
227: PetscErrorCode ierr;
228: PetscBool q = PETSC_FALSE;
229: DM dm;
232: SNESGetDM(snes,&dm);
233: DMCreateGlobalVector(dm,&user->x);
234: SNESGetKSP(snes,&ksp);
235: KSPGetPC(ksp, &pc);
236: KSPSetComputeSingularValues(ksp, PETSC_TRUE);
238: *nits=0;
240: /* Isoviscous solve */
241: if (param->ivisc == VISC_CONST && !param->stop_solve) {
242: param->ivisc = VISC_CONST;
244: SNESSolve(snes,0,user->x);
245: SNESGetConvergedReason(snes,&reason);
246: SNESGetIterationNumber(snes,&its);
247: *nits += its;
248: VecCopy(user->x,user->Xguess);
249: if (param->stop_solve) goto done;
250: }
252: /* Olivine diffusion creep */
253: if (param->ivisc >= VISC_DIFN && !param->stop_solve) {
254: if (!q) PetscPrintf(PETSC_COMM_WORLD,"Computing Variable Viscosity Solution\n");
256: /* continuation method on viscosity cutoff */
257: for (param->continuation=0.0;; param->continuation+=cont_incr) {
258: if (!q) PetscPrintf(PETSC_COMM_WORLD," Continuation parameter = %g\n", (double)param->continuation);
260: /* solve the non-linear system */
261: VecCopy(user->Xguess,user->x);
262: SNESSolve(snes,0,user->x);
263: SNESGetConvergedReason(snes,&reason);
264: SNESGetIterationNumber(snes,&its);
265: *nits += its;
266: if (!q) PetscPrintf(PETSC_COMM_WORLD," SNES iterations: %D, Cumulative: %D\n", its, *nits);
267: if (param->stop_solve) goto done;
269: if (reason<0) {
270: /* NOT converged */
271: cont_incr = -fabs(cont_incr)/2.0;
272: if (fabs(cont_incr)<0.01) goto done;
274: } else {
275: /* converged */
276: VecCopy(user->x,user->Xguess);
277: if (param->continuation >= 1.0) goto done;
278: if (its<=3) cont_incr = 0.30001;
279: else if (its<=8) cont_incr = 0.15001;
280: else cont_incr = 0.10001;
282: if (param->continuation+cont_incr > 1.0) cont_incr = 1.0 - param->continuation;
283: } /* endif reason<0 */
284: }
285: }
286: done:
287: if (param->stop_solve && !q) PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: stopping solve.\n");
288: if (reason<0 && !q) PetscPrintf(PETSC_COMM_WORLD,"FAILED TO CONVERGE: stopping solve.\n");
289: return(0);
290: }
293: /*=====================================================================
294: PHYSICS FUNCTIONS (compute the discrete residual)
295: =====================================================================*/
298: /*---------------------------------------------------------------------*/
301: PETSC_STATIC_INLINE PetscScalar UInterp(Field **x, PetscInt i, PetscInt j)
302: /*---------------------------------------------------------------------*/
303: {
304: return 0.25*(x[j][i].u+x[j+1][i].u+x[j][i+1].u+x[j+1][i+1].u);
305: }
307: /*---------------------------------------------------------------------*/
310: PETSC_STATIC_INLINE PetscScalar WInterp(Field **x, PetscInt i, PetscInt j)
311: /*---------------------------------------------------------------------*/
312: {
313: return 0.25*(x[j][i].w+x[j+1][i].w+x[j][i+1].w+x[j+1][i+1].w);
314: }
316: /*---------------------------------------------------------------------*/
319: PETSC_STATIC_INLINE PetscScalar PInterp(Field **x, PetscInt i, PetscInt j)
320: /*---------------------------------------------------------------------*/
321: {
322: return 0.25*(x[j][i].p+x[j+1][i].p+x[j][i+1].p+x[j+1][i+1].p);
323: }
325: /*---------------------------------------------------------------------*/
328: PETSC_STATIC_INLINE PetscScalar TInterp(Field **x, PetscInt i, PetscInt j)
329: /*---------------------------------------------------------------------*/
330: {
331: return 0.25*(x[j][i].T+x[j+1][i].T+x[j][i+1].T+x[j+1][i+1].T);
332: }
334: /*---------------------------------------------------------------------*/
337: /* isoviscous analytic solution for IC */
338: PETSC_STATIC_INLINE PassiveScalar HorizVelocity(PetscInt i, PetscInt j, AppCtx *user)
339: /*---------------------------------------------------------------------*/
340: {
341: Parameter *param = user->param;
342: GridInfo *grid = user->grid;
343: PetscScalar st, ct, th, c=param->c, d=param->d;
344: PetscReal x, z,r;
346: x = (i - grid->jlid)*grid->dx; z = (j - grid->jlid - 0.5)*grid->dz;
347: r = PetscSqrtReal(x*x+z*z);
348: st = z/r;
349: ct = x/r;
350: th = atan(z/x);
351: return ct*(c*th*st+d*(st+th*ct)) + st*(c*(st-th*ct)+d*th*st);
352: }
354: /*---------------------------------------------------------------------*/
357: /* isoviscous analytic solution for IC */
358: PETSC_STATIC_INLINE PetscScalar VertVelocity(PetscInt i, PetscInt j, AppCtx *user)
359: /*---------------------------------------------------------------------*/
360: {
361: Parameter *param = user->param;
362: GridInfo *grid = user->grid;
363: PetscScalar st, ct, th, c=param->c, d=param->d;
364: PetscReal x, z, r;
366: x = (i - grid->jlid - 0.5)*grid->dx; z = (j - grid->jlid)*grid->dz;
367: r = PetscSqrtReal(x*x+z*z); st = z/r; ct = x/r; th = atan(z/x);
368: return st*(c*th*st+d*(st+th*ct)) - ct*(c*(st-th*ct)+d*th*st);
369: }
371: /*---------------------------------------------------------------------*/
374: /* isoviscous analytic solution for IC */
375: PETSC_STATIC_INLINE PetscScalar Pressure(PetscInt i, PetscInt j, AppCtx *user)
376: /*---------------------------------------------------------------------*/
377: {
378: Parameter *param = user->param;
379: GridInfo *grid = user->grid;
380: PetscScalar x, z, r, st, ct, c=param->c, d=param->d;
382: x = (i - grid->jlid - 0.5)*grid->dx; z = (j - grid->jlid - 0.5)*grid->dz;
383: r = PetscSqrtReal(x*x+z*z); st = z/r; ct = x/r;
384: return (-2.0*(c*ct-d*st)/r);
385: }
389: /* computes the second invariant of the strain rate tensor */
390: PETSC_STATIC_INLINE PetscScalar CalcSecInv(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
391: /*---------------------------------------------------------------------*/
392: {
393: Parameter *param = user->param;
394: GridInfo *grid = user->grid;
395: PetscInt ilim =grid->ni-1, jlim=grid->nj-1;
396: PetscScalar uN,uS,uE,uW,wN,wS,wE,wW;
397: PetscScalar eps11, eps12, eps22;
399: if (i<j) return EPS_ZERO;
400: if (i==ilim) i--;
401: if (j==jlim) j--;
403: if (ipos==CELL_CENTER) { /* on cell center */
404: if (j<=grid->jlid) return EPS_ZERO;
406: uE = x[j][i].u; uW = x[j][i-1].u;
407: wN = x[j][i].w; wS = x[j-1][i].w;
408: wE = WInterp(x,i,j-1);
409: if (i==j) {
410: uN = param->cb; wW = param->sb;
411: } else {
412: uN = UInterp(x,i-1,j); wW = WInterp(x,i-1,j-1);
413: }
415: if (j==grid->jlid+1) uS = 0.0;
416: else uS = UInterp(x,i-1,j-1);
418: } else { /* on CELL_CORNER */
419: if (j<grid->jlid) return EPS_ZERO;
421: uN = x[j+1][i].u; uS = x[j][i].u;
422: wE = x[j][i+1].w; wW = x[j][i].w;
423: if (i==j) {
424: wN = param->sb;
425: uW = param->cb;
426: } else {
427: wN = WInterp(x,i,j);
428: uW = UInterp(x,i-1,j);
429: }
431: if (j==grid->jlid) {
432: uE = 0.0; uW = 0.0;
433: uS = -uN;
434: wS = -wN;
435: } else {
436: uE = UInterp(x,i,j);
437: wS = WInterp(x,i,j-1);
438: }
439: }
441: eps11 = (uE-uW)/grid->dx; eps22 = (wN-wS)/grid->dz;
442: eps12 = 0.5*((uN-uS)/grid->dz + (wE-wW)/grid->dx);
444: return PetscSqrtReal(0.5*(eps11*eps11 + 2.0*eps12*eps12 + eps22*eps22));
445: }
447: /*---------------------------------------------------------------------*/
450: /* computes the shear viscosity */
451: PETSC_STATIC_INLINE PetscScalar Viscosity(PetscScalar T, PetscScalar eps, PassiveScalar z, Parameter *param)
452: /*---------------------------------------------------------------------*/
453: {
454: PetscReal result =0.0;
455: ViscParam difn =param->diffusion, disl=param->dislocation;
456: PetscInt iVisc =param->ivisc;
457: PetscScalar eps_scale=param->V/(param->L*1000.0);
458: PetscScalar strain_power, v1, v2, P;
459: PetscScalar rho_g = 32340.0, R=8.3144;
461: P = rho_g*(z*param->L*1000.0); /* Pa */
463: if (iVisc==VISC_CONST) {
464: /* constant viscosity */
465: return 1.0;
466: } else if (iVisc==VISC_DIFN) {
467: /* diffusion creep rheology */
468: result = PetscRealPart((difn.A*PetscExpScalar((difn.Estar + P*difn.Vstar)/R/(T+273.0))/param->eta0));
469: } else if (iVisc==VISC_DISL) {
470: /* dislocation creep rheology */
471: strain_power = PetscPowScalar(eps*eps_scale, (1.0-disl.n)/disl.n);
473: result = PetscRealPart(disl.A*PetscExpScalar((disl.Estar + P*disl.Vstar)/disl.n/R/(T+273.0))*strain_power/param->eta0);
474: } else if (iVisc==VISC_FULL) {
475: /* dislocation/diffusion creep rheology */
476: strain_power = PetscPowScalar(eps*eps_scale, (1.0-disl.n)/disl.n);
478: v1 = difn.A*PetscExpScalar((difn.Estar + P*difn.Vstar)/R/(T+273.0))/param->eta0;
479: v2 = disl.A*PetscExpScalar((disl.Estar + P*disl.Vstar)/disl.n/R/(T+273.0))*strain_power/param->eta0;
481: result = PetscRealPart(1.0/(1.0/v1 + 1.0/v2));
482: }
484: /* max viscosity is param->eta0 */
485: result = PetscMin(result, 1.0);
486: /* min viscosity is param->visc_cutoff */
487: result = PetscMax(result, param->visc_cutoff);
488: /* continuation method */
489: result = PetscPowReal(result,param->continuation);
490: return result;
491: }
493: /*---------------------------------------------------------------------*/
496: /* computes the residual of the x-component of eqn (1) above */
497: PETSC_STATIC_INLINE PetscScalar XMomentumResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
498: /*---------------------------------------------------------------------*/
499: {
500: Parameter *param=user->param;
501: GridInfo *grid =user->grid;
502: PetscScalar dx = grid->dx, dz=grid->dz;
503: PetscScalar etaN,etaS,etaE,etaW,epsN=0.0,epsS=0.0,epsE=0.0,epsW=0.0;
504: PetscScalar TE=0.0,TN=0.0,TS=0.0,TW=0.0, dPdx, residual, z_scale;
505: PetscScalar dudxW,dudxE,dudzN,dudzS,dwdxN,dwdxS;
506: PetscInt jlim = grid->nj-1;
508: z_scale = param->z_scale;
510: if (param->ivisc==VISC_DIFN || param->ivisc>=VISC_DISL) { /* viscosity is T-dependent */
511: TS = param->potentialT * TInterp(x,i,j-1) * PetscExpScalar((j-1.0)*dz*z_scale);
512: if (j==jlim) TN = TS;
513: else TN = param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*z_scale);
514: TW = param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*z_scale);
515: TE = param->potentialT * x[j][i+1].T * PetscExpScalar((j-0.5)*dz*z_scale);
516: if (param->ivisc>=VISC_DISL) { /* olivine dislocation creep */
517: epsN = CalcSecInv(x,i,j, CELL_CORNER,user);
518: epsS = CalcSecInv(x,i,j-1,CELL_CORNER,user);
519: epsE = CalcSecInv(x,i+1,j,CELL_CENTER,user);
520: epsW = CalcSecInv(x,i,j, CELL_CENTER,user);
521: }
522: }
523: etaN = Viscosity(TN,epsN,dz*(j+0.5),param);
524: etaS = Viscosity(TS,epsS,dz*(j-0.5),param);
525: etaW = Viscosity(TW,epsW,dz*j,param);
526: etaE = Viscosity(TE,epsE,dz*j,param);
528: dPdx = (x[j][i+1].p - x[j][i].p)/dx;
529: if (j==jlim) dudzN = etaN * (x[j][i].w - x[j][i+1].w)/dx;
530: else dudzN = etaN * (x[j+1][i].u - x[j][i].u) /dz;
531: dudzS = etaS * (x[j][i].u - x[j-1][i].u)/dz;
532: dudxE = etaE * (x[j][i+1].u - x[j][i].u) /dx;
533: dudxW = etaW * (x[j][i].u - x[j][i-1].u)/dx;
535: residual = -dPdx /* X-MOMENTUM EQUATION*/
536: +(dudxE - dudxW)/dx
537: +(dudzN - dudzS)/dz;
539: if (param->ivisc!=VISC_CONST) {
540: dwdxN = etaN * (x[j][i+1].w - x[j][i].w) /dx;
541: dwdxS = etaS * (x[j-1][i+1].w - x[j-1][i].w)/dx;
543: residual += (dudxE - dudxW)/dx + (dwdxN - dwdxS)/dz;
544: }
546: return residual;
547: }
549: /*---------------------------------------------------------------------*/
552: /* computes the residual of the z-component of eqn (1) above */
553: PETSC_STATIC_INLINE PetscScalar ZMomentumResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
554: /*---------------------------------------------------------------------*/
555: {
556: Parameter *param=user->param;
557: GridInfo *grid =user->grid;
558: PetscScalar dx = grid->dx, dz=grid->dz;
559: 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;
560: PetscScalar TE =0.0,TN=0.0,TS=0.0,TW=0.0, dPdz, residual,z_scale;
561: PetscScalar dudzE,dudzW,dwdxW,dwdxE,dwdzN,dwdzS;
562: PetscInt ilim = grid->ni-1;
564: /* geometric and other parameters */
565: z_scale = param->z_scale;
567: /* viscosity */
568: if (param->ivisc==VISC_DIFN || param->ivisc>=VISC_DISL) { /* viscosity is T-dependent */
569: TN = param->potentialT * x[j+1][i].T * PetscExpScalar((j+0.5)*dz*z_scale);
570: TS = param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*z_scale);
571: TW = param->potentialT * TInterp(x,i-1,j) * PetscExpScalar(j*dz*z_scale);
572: if (i==ilim) TE = TW;
573: else TE = param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*z_scale);
574: if (param->ivisc>=VISC_DISL) { /* olivine dislocation creep */
575: epsN = CalcSecInv(x,i,j+1,CELL_CENTER,user);
576: epsS = CalcSecInv(x,i,j, CELL_CENTER,user);
577: epsE = CalcSecInv(x,i,j, CELL_CORNER,user);
578: epsW = CalcSecInv(x,i-1,j,CELL_CORNER,user);
579: }
580: }
581: etaN = Viscosity(TN,epsN,dz*(j+1.0),param);
582: etaS = Viscosity(TS,epsS,dz*(j+0.0),param);
583: etaW = Viscosity(TW,epsW,dz*(j+0.5),param);
584: etaE = Viscosity(TE,epsE,dz*(j+0.5),param);
586: dPdz = (x[j+1][i].p - x[j][i].p)/dz;
587: dwdzN = etaN * (x[j+1][i].w - x[j][i].w)/dz;
588: dwdzS = etaS * (x[j][i].w - x[j-1][i].w)/dz;
589: if (i==ilim) dwdxE = etaE * (x[j][i].u - x[j+1][i].u)/dz;
590: else dwdxE = etaE * (x[j][i+1].w - x[j][i].w) /dx;
591: dwdxW = 2.0*etaW * (x[j][i].w - x[j][i-1].w)/dx;
593: /* Z-MOMENTUM */
594: residual = -dPdz /* constant viscosity terms */
595: +(dwdzN - dwdzS)/dz
596: +(dwdxE - dwdxW)/dx;
598: if (param->ivisc!=VISC_CONST) {
599: dudzE = etaE * (x[j+1][i].u - x[j][i].u)/dz;
600: dudzW = etaW * (x[j+1][i-1].u - x[j][i-1].u)/dz;
602: residual += (dwdzN - dwdzS)/dz + (dudzE - dudzW)/dx;
603: }
605: return residual;
606: }
608: /*---------------------------------------------------------------------*/
611: /* computes the residual of eqn (2) above */
612: PETSC_STATIC_INLINE PetscScalar ContinuityResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
613: /*---------------------------------------------------------------------*/
614: {
615: GridInfo *grid =user->grid;
616: PetscScalar uE,uW,wN,wS,dudx,dwdz;
618: uW = x[j][i-1].u; uE = x[j][i].u; dudx = (uE - uW)/grid->dx;
619: wS = x[j-1][i].w; wN = x[j][i].w; dwdz = (wN - wS)/grid->dz;
621: return dudx + dwdz;
622: }
624: /*---------------------------------------------------------------------*/
627: /* computes the residual of eqn (3) above */
628: PETSC_STATIC_INLINE PetscScalar EnergyResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
629: /*---------------------------------------------------------------------*/
630: {
631: Parameter *param=user->param;
632: GridInfo *grid =user->grid;
633: PetscScalar dx = grid->dx, dz=grid->dz;
634: PetscInt ilim =grid->ni-1, jlim=grid->nj-1, jlid=grid->jlid;
635: PetscScalar TE, TN, TS, TW, residual;
636: PetscScalar uE,uW,wN,wS;
637: PetscScalar fN,fS,fE,fW,dTdxW,dTdxE,dTdzN,dTdzS;
639: dTdzN = (x[j+1][i].T - x[j][i].T) /dz;
640: dTdzS = (x[j][i].T - x[j-1][i].T)/dz;
641: dTdxE = (x[j][i+1].T - x[j][i].T) /dx;
642: dTdxW = (x[j][i].T - x[j][i-1].T)/dx;
644: residual = ((dTdzN - dTdzS)/dz + /* diffusion term */
645: (dTdxE - dTdxW)/dx)*dx*dz/param->peclet;
647: if (j<=jlid && i>=j) {
648: /* don't advect in the lid */
649: return residual;
650: } else if (i<j) {
651: /* beneath the slab sfc */
652: uW = uE = param->cb;
653: wS = wN = param->sb;
654: } else {
655: /* advect in the slab and wedge */
656: uW = x[j][i-1].u; uE = x[j][i].u;
657: wS = x[j-1][i].w; wN = x[j][i].w;
658: }
660: if (param->adv_scheme==ADVECT_FV || i==ilim-1 || j==jlim-1 || i==1 || j==1) {
661: /* finite volume advection */
662: TS = (x[j][i].T + x[j-1][i].T)/2.0;
663: TN = (x[j][i].T + x[j+1][i].T)/2.0;
664: TE = (x[j][i].T + x[j][i+1].T)/2.0;
665: TW = (x[j][i].T + x[j][i-1].T)/2.0;
666: fN = wN*TN*dx; fS = wS*TS*dx;
667: fE = uE*TE*dz; fW = uW*TW*dz;
669: } else {
670: /* Fromm advection scheme */
671: 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
672: - 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;
673: 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
674: - 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;
675: 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
676: - 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;
677: 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
678: - 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;
679: }
681: residual -= (fE - fW + fN - fS);
683: return residual;
684: }
686: /*---------------------------------------------------------------------*/
689: /* computes the shear stress---used on the boundaries */
690: PETSC_STATIC_INLINE PetscScalar ShearStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
691: /*---------------------------------------------------------------------*/
692: {
693: Parameter *param=user->param;
694: GridInfo *grid =user->grid;
695: PetscInt ilim =grid->ni-1, jlim=grid->nj-1;
696: PetscScalar uN, uS, wE, wW;
698: if (j<=grid->jlid || i<j || i==ilim || j==jlim) return EPS_ZERO;
700: if (ipos==CELL_CENTER) { /* on cell center */
702: wE = WInterp(x,i,j-1);
703: if (i==j) {
704: wW = param->sb;
705: uN = param->cb;
706: } else {
707: wW = WInterp(x,i-1,j-1);
708: uN = UInterp(x,i-1,j);
709: }
710: if (j==grid->jlid+1) uS = 0.0;
711: else uS = UInterp(x,i-1,j-1);
713: } else { /* on cell corner */
715: uN = x[j+1][i].u; uS = x[j][i].u;
716: wW = x[j][i].w; wE = x[j][i+1].w;
718: }
720: return (uN-uS)/grid->dz + (wE-wW)/grid->dx;
721: }
723: /*---------------------------------------------------------------------*/
726: /* computes the normal stress---used on the boundaries */
727: PETSC_STATIC_INLINE PetscScalar XNormalStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
728: /*---------------------------------------------------------------------*/
729: {
730: Parameter *param=user->param;
731: GridInfo *grid =user->grid;
732: PetscScalar dx = grid->dx, dz=grid->dz;
733: PetscInt ilim =grid->ni-1, jlim=grid->nj-1, ivisc;
734: PetscScalar epsC =0.0, etaC, TC, uE, uW, pC, 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);
745: uW = x[j][i-1].u; uE = x[j][i].u;
746: pC = x[j][i].p;
748: } else { /* on cell corner */
749: if (i==ilim || j==jlim) return EPS_ZERO;
751: TC = param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*z_scale);
752: if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CORNER,user);
753: etaC = Viscosity(TC,epsC,dz*(j+0.5),param);
755: if (i==j) uW = param->sb;
756: else uW = UInterp(x,i-1,j);
757: uE = UInterp(x,i,j); pC = PInterp(x,i,j);
758: }
760: return 2.0*etaC*(uE-uW)/dx - pC;
761: }
763: /*---------------------------------------------------------------------*/
766: /* computes the normal stress---used on the boundaries */
767: PETSC_STATIC_INLINE PetscScalar ZNormalStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
768: /*---------------------------------------------------------------------*/
769: {
770: Parameter *param=user->param;
771: GridInfo *grid =user->grid;
772: PetscScalar dz =grid->dz;
773: PetscInt ilim =grid->ni-1, jlim=grid->nj-1, ivisc;
774: PetscScalar epsC =0.0, etaC, TC;
775: PetscScalar pC, wN, wS, z_scale;
776: if (i<j || j<=grid->jlid) return EPS_ZERO;
778: ivisc=param->ivisc; z_scale = param->z_scale;
780: if (ipos==CELL_CENTER) { /* on cell center */
782: TC = param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*z_scale);
783: if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CENTER,user);
784: etaC = Viscosity(TC,epsC,dz*j,param);
785: wN = x[j][i].w; wS = x[j-1][i].w; pC = x[j][i].p;
787: } else { /* on cell corner */
788: if ((i==ilim) || (j==jlim)) return EPS_ZERO;
790: TC = param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*z_scale);
791: if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CORNER,user);
792: etaC = Viscosity(TC,epsC,dz*(j+0.5),param);
793: if (i==j) wN = param->sb;
794: else wN = WInterp(x,i,j);
795: wS = WInterp(x,i,j-1); pC = PInterp(x,i,j);
796: }
798: return 2.0*etaC*(wN-wS)/dz - pC;
799: }
801: /*---------------------------------------------------------------------*/
803: /*=====================================================================
804: INITIALIZATION, POST-PROCESSING AND OUTPUT FUNCTIONS
805: =====================================================================*/
807: /*---------------------------------------------------------------------*/
810: /* initializes the problem parameters and checks for
811: command line changes */
812: PetscErrorCode SetParams(Parameter *param, GridInfo *grid)
813: /*---------------------------------------------------------------------*/
814: {
815: PetscErrorCode ierr, ierr_out=0;
816: PetscReal SEC_PER_YR = 3600.00*24.00*365.2500;
817: PetscReal alpha_g_on_cp_units_inverse_km=4.0e-5*9.8;
819: /* domain geometry */
820: param->slab_dip = 45.0;
821: param->width = 320.0; /* km */
822: param->depth = 300.0; /* km */
823: param->lid_depth = 35.0; /* km */
824: param->fault_depth = 35.0; /* km */
826: PetscOptionsGetReal(NULL,"-slab_dip",&(param->slab_dip),NULL);
827: PetscOptionsGetReal(NULL,"-width",&(param->width),NULL);
828: PetscOptionsGetReal(NULL,"-depth",&(param->depth),NULL);
829: PetscOptionsGetReal(NULL,"-lid_depth",&(param->lid_depth),NULL);
830: PetscOptionsGetReal(NULL,"-fault_depth",&(param->fault_depth),NULL);
832: param->slab_dip = param->slab_dip*PETSC_PI/180.0; /* radians */
834: /* grid information */
835: PetscOptionsGetInt(NULL, "-jfault",&(grid->jfault),NULL);
836: grid->ni = 82;
837: PetscOptionsGetInt(NULL, "-ni",&(grid->ni),NULL);
839: grid->dx = param->width/((PetscReal)(grid->ni-2)); /* km */
840: grid->dz = grid->dx*tan(param->slab_dip); /* km */
841: grid->nj = (PetscInt)(param->depth/grid->dz + 3.0); /* gridpoints*/
842: param->depth = grid->dz*(grid->nj-2); /* km */
843: grid->inose = 0; /* gridpoints*/
844: PetscOptionsGetInt(NULL,"-inose",&(grid->inose),NULL);
845: grid->bx = DM_BOUNDARY_NONE;
846: grid->by = DM_BOUNDARY_NONE;
847: grid->stencil = DMDA_STENCIL_BOX;
848: grid->dof = 4;
849: grid->stencil_width = 2;
850: grid->mglevels = 1;
852: /* boundary conditions */
853: param->pv_analytic = PETSC_FALSE;
854: param->ibound = BC_NOSTRESS;
855: PetscOptionsGetInt(NULL,"-ibound",&(param->ibound),NULL);
857: /* physical constants */
858: param->slab_velocity = 5.0; /* cm/yr */
859: param->slab_age = 50.0; /* Ma */
860: param->lid_age = 50.0; /* Ma */
861: param->kappa = 0.7272e-6; /* m^2/sec */
862: param->potentialT = 1300.0; /* degrees C */
864: PetscOptionsGetReal(NULL,"-slab_velocity",&(param->slab_velocity),NULL);
865: PetscOptionsGetReal(NULL,"-slab_age",&(param->slab_age),NULL);
866: PetscOptionsGetReal(NULL,"-lid_age",&(param->lid_age),NULL);
867: PetscOptionsGetReal(NULL,"-kappa",&(param->kappa),NULL);
868: PetscOptionsGetReal(NULL,"-potentialT",&(param->potentialT),NULL);
870: /* viscosity */
871: param->ivisc = 3; /* 0=isovisc, 1=difn creep, 2=disl creep, 3=full */
872: param->eta0 = 1e24; /* Pa-s */
873: param->visc_cutoff = 0.0; /* factor of eta_0 */
874: param->continuation = 1.0;
876: /* constants for diffusion creep */
877: param->diffusion.A = 1.8e7; /* Pa-s */
878: param->diffusion.n = 1.0; /* dim'less */
879: param->diffusion.Estar = 375e3; /* J/mol */
880: param->diffusion.Vstar = 5e-6; /* m^3/mol */
882: /* constants for param->dislocationocation creep */
883: param->dislocation.A = 2.8969e4; /* Pa-s */
884: param->dislocation.n = 3.5; /* dim'less */
885: param->dislocation.Estar = 530e3; /* J/mol */
886: param->dislocation.Vstar = 14e-6; /* m^3/mol */
888: PetscOptionsGetInt(NULL, "-ivisc",&(param->ivisc),NULL);
889: PetscOptionsGetReal(NULL,"-visc_cutoff",&(param->visc_cutoff),NULL);
891: param->output_ivisc = param->ivisc;
893: PetscOptionsGetInt(NULL,"-output_ivisc",&(param->output_ivisc),NULL);
894: PetscOptionsGetReal(NULL,"-vstar",&(param->dislocation.Vstar),NULL);
896: /* output options */
897: param->quiet = PETSC_FALSE;
898: param->param_test = PETSC_FALSE;
900: PetscOptionsHasName(NULL,"-quiet",&(param->quiet));
901: PetscOptionsHasName(NULL,"-test",&(param->param_test));
902: PetscOptionsGetString(NULL,"-file",param->filename,PETSC_MAX_PATH_LEN,&(param->output_to_file));
904: /* advection */
905: param->adv_scheme = ADVECT_FROMM; /* advection scheme: 0=finite vol, 1=Fromm */
907: PetscOptionsGetInt(NULL,"-adv_scheme",&(param->adv_scheme),NULL);
909: /* misc. flags */
910: param->stop_solve = PETSC_FALSE;
911: param->interrupted = PETSC_FALSE;
912: param->kspmon = PETSC_FALSE;
913: param->toggle_kspmon = PETSC_FALSE;
915: /* derived parameters for slab angle */
916: param->sb = PetscSinReal(param->slab_dip);
917: param->cb = PetscCosReal(param->slab_dip);
918: param->c = param->slab_dip*param->sb/(param->slab_dip*param->slab_dip-param->sb*param->sb);
919: param->d = (param->slab_dip*param->cb-param->sb)/(param->slab_dip*param->slab_dip-param->sb*param->sb);
921: /* length, velocity and time scale for non-dimensionalization */
922: param->L = PetscMin(param->width,param->depth); /* km */
923: param->V = param->slab_velocity/100.0/SEC_PER_YR; /* m/sec */
925: /* other unit conversions and derived parameters */
926: param->scaled_width = param->width/param->L; /* dim'less */
927: param->scaled_depth = param->depth/param->L; /* dim'less */
928: param->lid_depth = param->lid_depth/param->L; /* dim'less */
929: param->fault_depth = param->fault_depth/param->L; /* dim'less */
930: grid->dx = grid->dx/param->L; /* dim'less */
931: grid->dz = grid->dz/param->L; /* dim'less */
932: grid->jlid = (PetscInt)(param->lid_depth/grid->dz); /* gridcells */
933: grid->jfault = (PetscInt)(param->fault_depth/grid->dz); /* gridcells */
934: param->lid_depth = grid->jlid*grid->dz; /* dim'less */
935: param->fault_depth = grid->jfault*grid->dz; /* dim'less */
936: grid->corner = grid->jlid+1; /* gridcells */
937: param->peclet = param->V /* m/sec */
938: * param->L*1000.0 /* m */
939: / param->kappa; /* m^2/sec */
940: param->z_scale = param->L * alpha_g_on_cp_units_inverse_km;
941: param->skt = PetscSqrtReal(param->kappa*param->slab_age*SEC_PER_YR);
942: PetscOptionsGetReal(NULL,"-peclet",&(param->peclet),NULL);
944: return ierr_out;
945: }
947: /*---------------------------------------------------------------------*/
950: /* prints a report of the problem parameters to stdout */
951: PetscErrorCode ReportParams(Parameter *param, GridInfo *grid)
952: /*---------------------------------------------------------------------*/
953: {
954: PetscErrorCode ierr, ierr_out=0;
955: char date[30];
957: PetscGetDate(date,30);
959: if (!(param->quiet)) {
960: PetscPrintf(PETSC_COMM_WORLD,"---------------------BEGIN ex30 PARAM REPORT-------------------\n");
961: /* PetscPrintf(PETSC_COMM_WORLD," %s\n",&(date[0]));*/
963: PetscPrintf(PETSC_COMM_WORLD,"Domain: \n");
964: PetscPrintf(PETSC_COMM_WORLD," Width = %g km, Depth = %g km\n",(double)param->width,(double)param->depth);
965: 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);
966: PetscPrintf(PETSC_COMM_WORLD," Lid depth = %5.2f km, Fault depth = %5.2f km\n",param->lid_depth*param->L,param->fault_depth*param->L);
968: PetscPrintf(PETSC_COMM_WORLD,"\nGrid: \n");
969: 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));
970: PetscPrintf(PETSC_COMM_WORLD," jlid = %3D jfault = %3D \n",grid->jlid,grid->jfault);
971: PetscPrintf(PETSC_COMM_WORLD," Pe = %g\n",(double)param->peclet);
973: PetscPrintf(PETSC_COMM_WORLD,"\nRheology:");
974: if (param->ivisc==VISC_CONST) {
975: PetscPrintf(PETSC_COMM_WORLD," Isoviscous \n");
976: if (param->pv_analytic) {
977: PetscPrintf(PETSC_COMM_WORLD," Pressure and Velocity prescribed! \n");
978: }
979: } else if (param->ivisc==VISC_DIFN) {
980: PetscPrintf(PETSC_COMM_WORLD," Diffusion Creep (T-Dependent Newtonian) \n");
981: PetscPrintf(PETSC_COMM_WORLD," Viscosity range: %g--%g Pa-sec \n",(double)param->eta0,(double)(param->visc_cutoff*param->eta0));
982: } else if (param->ivisc==VISC_DISL) {
983: PetscPrintf(PETSC_COMM_WORLD," Dislocation Creep (T-Dependent Non-Newtonian) \n");
984: PetscPrintf(PETSC_COMM_WORLD," Viscosity range: %g--%g Pa-sec \n",(double)param->eta0,(double)(param->visc_cutoff*param->eta0));
985: } else if (param->ivisc==VISC_FULL) {
986: PetscPrintf(PETSC_COMM_WORLD," Full Rheology \n");
987: PetscPrintf(PETSC_COMM_WORLD," Viscosity range: %g--%g Pa-sec \n",(double)param->eta0,(double)(param->visc_cutoff*param->eta0));
988: } else {
989: PetscPrintf(PETSC_COMM_WORLD," Invalid! \n");
990: ierr_out = 1;
991: }
993: PetscPrintf(PETSC_COMM_WORLD,"Boundary condition:");
994: if (param->ibound==BC_ANALYTIC) {
995: PetscPrintf(PETSC_COMM_WORLD," Isoviscous Analytic Dirichlet \n");
996: } else if (param->ibound==BC_NOSTRESS) {
997: PetscPrintf(PETSC_COMM_WORLD," Stress-Free (normal & shear stress)\n");
998: } else if (param->ibound==BC_EXPERMNT) {
999: PetscPrintf(PETSC_COMM_WORLD," Experimental boundary condition \n");
1000: } else {
1001: PetscPrintf(PETSC_COMM_WORLD," Invalid! \n");
1002: ierr_out = 1;
1003: }
1005: if (param->output_to_file)
1006: #if defined(PETSC_HAVE_MATLAB_ENGINE)
1007: PetscPrintf(PETSC_COMM_WORLD,"Output Destination: Mat file \"%s\"\n",param->filename);
1008: #else
1009: PetscPrintf(PETSC_COMM_WORLD,"Output Destination: PETSc binary file \"%s\"\n",param->filename);
1010: #endif
1011: if (param->output_ivisc != param->ivisc) {
1012: PetscPrintf(PETSC_COMM_WORLD," Output viscosity: -ivisc %D\n",param->output_ivisc);
1013: }
1015: PetscPrintf(PETSC_COMM_WORLD,"---------------------END ex30 PARAM REPORT---------------------\n");
1016: }
1017: if (param->param_test) PetscEnd();
1018: return ierr_out;
1019: }
1021: /* ------------------------------------------------------------------- */
1024: /* generates an inital guess using the analytic solution for isoviscous
1025: corner flow */
1026: PetscErrorCode Initialize(DM da)
1027: /* ------------------------------------------------------------------- */
1028: {
1029: AppCtx *user;
1030: Parameter *param;
1031: GridInfo *grid;
1032: PetscInt i,j,is,js,im,jm;
1034: Field **x;
1035: Vec Xguess;
1037: /* Get the fine grid */
1038: DMGetApplicationContext(da,&user);
1039: Xguess = user->Xguess;
1040: param = user->param;
1041: grid = user->grid;
1042: DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1043: DMDAVecGetArray(da,Xguess,(void**)&x);
1045: /* Compute initial guess */
1046: for (j=js; j<js+jm; j++) {
1047: for (i=is; i<is+im; i++) {
1048: if (i<j) x[j][i].u = param->cb;
1049: else if (j<=grid->jlid) x[j][i].u = 0.0;
1050: else x[j][i].u = HorizVelocity(i,j,user);
1052: if (i<=j) x[j][i].w = param->sb;
1053: else if (j<=grid->jlid) x[j][i].w = 0.0;
1054: else x[j][i].w = VertVelocity(i,j,user);
1056: if (i<j || j<=grid->jlid) x[j][i].p = 0.0;
1057: else x[j][i].p = Pressure(i,j,user);
1059: x[j][i].T = PetscMin(grid->dz*(j-0.5),1.0);
1060: }
1061: }
1063: /* Restore x to Xguess */
1064: DMDAVecRestoreArray(da,Xguess,(void**)&x);
1066: return 0;
1067: }
1069: /*---------------------------------------------------------------------*/
1072: /* controls output to a file */
1073: PetscErrorCode DoOutput(SNES snes, PetscInt its)
1074: /*---------------------------------------------------------------------*/
1075: {
1076: AppCtx *user;
1077: Parameter *param;
1078: GridInfo *grid;
1079: PetscInt ivt;
1081: PetscMPIInt rank;
1082: PetscViewer viewer;
1083: Vec res, pars;
1084: MPI_Comm comm;
1085: DM da;
1087: SNESGetDM(snes,&da);
1088: DMGetApplicationContext(da,&user);
1089: param = user->param;
1090: grid = user->grid;
1091: ivt = param->ivisc;
1093: param->ivisc = param->output_ivisc;
1095: /* compute final residual and final viscosity/strain rate fields */
1096: SNESGetFunction(snes, &res, NULL, NULL);
1097: ViscosityField(da, user->x, user->Xguess);
1099: /* get the communicator and the rank of the processor */
1100: PetscObjectGetComm((PetscObject)snes, &comm);
1101: MPI_Comm_rank(comm, &rank);
1103: if (param->output_to_file) { /* send output to binary file */
1104: VecCreate(comm, &pars);
1105: if (!rank) { /* on processor 0 */
1106: VecSetSizes(pars, 20, PETSC_DETERMINE);
1107: VecSetFromOptions(pars);
1108: VecSetValue(pars,0, (PetscScalar)(grid->ni),INSERT_VALUES);
1109: VecSetValue(pars,1, (PetscScalar)(grid->nj),INSERT_VALUES);
1110: VecSetValue(pars,2, (PetscScalar)(grid->dx),INSERT_VALUES);
1111: VecSetValue(pars,3, (PetscScalar)(grid->dz),INSERT_VALUES);
1112: VecSetValue(pars,4, (PetscScalar)(param->L),INSERT_VALUES);
1113: VecSetValue(pars,5, (PetscScalar)(param->V),INSERT_VALUES);
1114: /* skipped 6 intentionally */
1115: VecSetValue(pars,7, (PetscScalar)(param->slab_dip),INSERT_VALUES);
1116: VecSetValue(pars,8, (PetscScalar)(grid->jlid),INSERT_VALUES);
1117: VecSetValue(pars,9, (PetscScalar)(param->lid_depth),INSERT_VALUES);
1118: VecSetValue(pars,10,(PetscScalar)(grid->jfault),INSERT_VALUES);
1119: VecSetValue(pars,11,(PetscScalar)(param->fault_depth),INSERT_VALUES);
1120: VecSetValue(pars,12,(PetscScalar)(param->potentialT),INSERT_VALUES);
1121: VecSetValue(pars,13,(PetscScalar)(param->ivisc),INSERT_VALUES);
1122: VecSetValue(pars,14,(PetscScalar)(param->visc_cutoff),INSERT_VALUES);
1123: VecSetValue(pars,15,(PetscScalar)(param->ibound),INSERT_VALUES);
1124: VecSetValue(pars,16,(PetscScalar)(its),INSERT_VALUES);
1125: } else { /* on some other processor */
1126: VecSetSizes(pars, 0, PETSC_DETERMINE);
1127: VecSetFromOptions(pars);
1128: }
1129: VecAssemblyBegin(pars); VecAssemblyEnd(pars);
1131: /* create viewer */
1132: #if defined(PETSC_HAVE_MATLAB_ENGINE)
1133: PetscViewerMatlabOpen(PETSC_COMM_WORLD,param->filename,FILE_MODE_WRITE,&viewer);
1134: #else
1135: PetscViewerBinaryOpen(PETSC_COMM_WORLD,param->filename,FILE_MODE_WRITE,&viewer);
1136: #endif
1138: /* send vectors to viewer */
1139: PetscObjectSetName((PetscObject)res,"res");
1140: VecView(res,viewer);
1141: PetscObjectSetName((PetscObject)user->x,"out");
1142: VecView(user->x, viewer);
1143: PetscObjectSetName((PetscObject)(user->Xguess),"aux");
1144: VecView(user->Xguess, viewer);
1145: StressField(da); /* compute stress fields */
1146: PetscObjectSetName((PetscObject)(user->Xguess),"str");
1147: VecView(user->Xguess, viewer);
1148: PetscObjectSetName((PetscObject)pars,"par");
1149: VecView(pars, viewer);
1151: /* destroy viewer and vector */
1152: PetscViewerDestroy(&viewer);
1153: VecDestroy(&pars);
1154: }
1156: param->ivisc = ivt;
1157: return 0;
1158: }
1160: /* ------------------------------------------------------------------- */
1163: /* Compute both the second invariant of the strain rate tensor and the viscosity, at both cell centers and cell corners */
1164: PetscErrorCode ViscosityField(DM da, Vec X, Vec V)
1165: /* ------------------------------------------------------------------- */
1166: {
1167: AppCtx *user;
1168: Parameter *param;
1169: GridInfo *grid;
1170: Vec localX;
1171: Field **v, **x;
1172: PassiveReal eps, /* dx,*/ dz, T, epsC, TC;
1173: PetscInt i,j,is,js,im,jm,ilim,jlim,ivt;
1177: DMGetApplicationContext(da,&user);
1178: param = user->param;
1179: grid = user->grid;
1180: ivt = param->ivisc;
1181: param->ivisc = param->output_ivisc;
1183: DMGetLocalVector(da, &localX);
1184: DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX);
1185: DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX);
1186: DMDAVecGetArray(da,localX,(void**)&x);
1187: DMDAVecGetArray(da,V,(void**)&v);
1189: /* Parameters */
1190: /* dx = grid->dx; */ dz = grid->dz;
1192: ilim = grid->ni-1; jlim = grid->nj-1;
1194: /* Compute real temperature, strain rate and viscosity */
1195: DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1196: for (j=js; j<js+jm; j++) {
1197: for (i=is; i<is+im; i++) {
1198: T = PetscRealPart(param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*param->z_scale));
1199: if (i<ilim && j<jlim) {
1200: TC = PetscRealPart(param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*param->z_scale));
1201: } else {
1202: TC = T;
1203: }
1204: eps = PetscRealPart((CalcSecInv(x,i,j,CELL_CENTER,user)));
1205: epsC = PetscRealPart(CalcSecInv(x,i,j,CELL_CORNER,user));
1207: v[j][i].u = eps;
1208: v[j][i].w = epsC;
1209: v[j][i].p = Viscosity(T,eps,dz*(j-0.5),param);
1210: v[j][i].T = Viscosity(TC,epsC,dz*j,param);
1211: }
1212: }
1213: DMDAVecRestoreArray(da,V,(void**)&v);
1214: DMDAVecRestoreArray(da,localX,(void**)&x);
1215: DMRestoreLocalVector(da, &localX);
1217: param->ivisc = ivt;
1218: return(0);
1219: }
1221: /* ------------------------------------------------------------------- */
1224: /* post-processing: compute stress everywhere */
1225: PetscErrorCode StressField(DM da)
1226: /* ------------------------------------------------------------------- */
1227: {
1228: AppCtx *user;
1229: PetscInt i,j,is,js,im,jm;
1231: Vec locVec;
1232: Field **x, **y;
1234: DMGetApplicationContext(da,&user);
1236: /* Get the fine grid of Xguess and X */
1237: DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1238: DMDAVecGetArray(da,user->Xguess,(void**)&x);
1240: DMGetLocalVector(da, &locVec);
1241: DMGlobalToLocalBegin(da, user->x, INSERT_VALUES, locVec);
1242: DMGlobalToLocalEnd(da, user->x, INSERT_VALUES, locVec);
1243: DMDAVecGetArray(da,locVec,(void**)&y);
1245: /* Compute stress on the corner points */
1246: for (j=js; j<js+jm; j++) {
1247: for (i=is; i<is+im; i++) {
1248: x[j][i].u = ShearStress(y,i,j,CELL_CENTER,user);
1249: x[j][i].w = ShearStress(y,i,j,CELL_CORNER,user);
1250: x[j][i].p = XNormalStress(y,i,j,CELL_CENTER,user);
1251: x[j][i].T = ZNormalStress(y,i,j,CELL_CENTER,user);
1252: }
1253: }
1255: /* Restore the fine grid of Xguess and X */
1256: DMDAVecRestoreArray(da,user->Xguess,(void**)&x);
1257: DMDAVecRestoreArray(da,locVec,(void**)&y);
1258: DMRestoreLocalVector(da, &locVec);
1259: return 0;
1260: }
1262: /*=====================================================================
1263: UTILITY FUNCTIONS
1264: =====================================================================*/
1266: /*---------------------------------------------------------------------*/
1269: /* returns the velocity of the subducting slab and handles fault nodes
1270: for BC */
1271: PETSC_STATIC_INLINE PassiveScalar SlabVel(char c, PetscInt i, PetscInt j, AppCtx *user)
1272: /*---------------------------------------------------------------------*/
1273: {
1274: Parameter *param = user->param;
1275: GridInfo *grid = user->grid;
1277: if (c=='U' || c=='u') {
1278: if (i<j-1) return param->cb;
1279: else if (j<=grid->jfault) return 0.0;
1280: else return param->cb;
1282: } else {
1283: if (i<j) return param->sb;
1284: else if (j<=grid->jfault) return 0.0;
1285: else return param->sb;
1286: }
1287: }
1289: /*---------------------------------------------------------------------*/
1292: /* solution to diffusive half-space cooling model for BC */
1293: PETSC_STATIC_INLINE PassiveScalar PlateModel(PetscInt j, PetscInt plate, AppCtx *user)
1294: /*---------------------------------------------------------------------*/
1295: {
1296: Parameter *param = user->param;
1297: PassiveScalar z;
1298: if (plate==PLATE_LID) z = (j-0.5)*user->grid->dz;
1299: else z = (j-0.5)*user->grid->dz*param->cb; /* PLATE_SLAB */
1300: #if defined(PETSC_HAVE_ERF)
1301: return (erf(PetscRealPart(z*param->L/2.0/param->skt)));
1302: #else
1303: SETERRQ(PETSC_COMM_SELF,1,"erf() not available on this machine");
1304: #endif
1305: }
1308: /* ------------------------------------------------------------------- */
1311: /* utility function */
1312: PetscBool OptionsHasName(const char pre[],const char name[])
1313: /* ------------------------------------------------------------------- */
1314: {
1315: PetscBool retval;
1317: PetscOptionsHasName(pre,name,&retval);CHKERRABORT(PETSC_COMM_WORLD,ierr);
1318: return retval;
1319: }
1321: /*=====================================================================
1322: INTERACTIVE SIGNAL HANDLING
1323: =====================================================================*/
1325: /* ------------------------------------------------------------------- */
1328: PetscErrorCode SNESConverged_Interactive(SNES snes, PetscInt it,PetscReal xnorm, PetscReal snorm, PetscReal fnorm, SNESConvergedReason *reason, void *ctx)
1329: /* ------------------------------------------------------------------- */
1330: {
1331: AppCtx *user = (AppCtx*) ctx;
1332: Parameter *param = user->param;
1333: KSP ksp;
1337: if (param->interrupted) {
1338: param->interrupted = PETSC_FALSE;
1339: PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: exiting SNES solve. \n");
1340: *reason = SNES_CONVERGED_FNORM_ABS;
1341: return(0);
1342: } else if (param->toggle_kspmon) {
1343: param->toggle_kspmon = PETSC_FALSE;
1345: SNESGetKSP(snes, &ksp);
1347: if (param->kspmon) {
1348: KSPMonitorCancel(ksp);
1350: param->kspmon = PETSC_FALSE;
1351: PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: deactivating ksp singular value monitor. \n");
1352: } else {
1353: KSPMonitorSet(ksp,KSPMonitorSingularValue,NULL,NULL);
1355: param->kspmon = PETSC_TRUE;
1356: PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: activating ksp singular value monitor. \n");
1357: }
1358: }
1359: PetscFunctionReturn(SNESConvergedDefault(snes,it,xnorm,snorm,fnorm,reason,ctx));
1360: }
1362: /* ------------------------------------------------------------------- */
1363: #include <signal.h>
1366: PetscErrorCode InteractiveHandler(int signum, void *ctx)
1367: /* ------------------------------------------------------------------- */
1368: {
1369: AppCtx *user = (AppCtx*) ctx;
1370: Parameter *param = user->param;
1372: if (signum == SIGILL) {
1373: param->toggle_kspmon = PETSC_TRUE;
1374: #if !defined(PETSC_MISSING_SIGCONT)
1375: } else if (signum == SIGCONT) {
1376: param->interrupted = PETSC_TRUE;
1377: #endif
1378: #if !defined(PETSC_MISSING_SIGURG)
1379: } else if (signum == SIGURG) {
1380: param->stop_solve = PETSC_TRUE;
1381: #endif
1382: }
1383: return 0;
1384: }
1386: /*---------------------------------------------------------------------*/
1389: /* main call-back function that computes the processor-local piece
1390: of the residual */
1391: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,Field **x,Field **f,void *ptr)
1392: /*---------------------------------------------------------------------*/
1393: {
1394: AppCtx *user = (AppCtx*)ptr;
1395: Parameter *param = user->param;
1396: GridInfo *grid = user->grid;
1397: PetscScalar mag_w, mag_u;
1398: PetscInt i,j,mx,mz,ilim,jlim;
1399: PetscInt is,ie,js,je,ibound; /* ,ivisc */
1402: /* Define global and local grid parameters */
1403: mx = info->mx; mz = info->my;
1404: ilim = mx-1; jlim = mz-1;
1405: is = info->xs; ie = info->xs+info->xm;
1406: js = info->ys; je = info->ys+info->ym;
1408: /* Define geometric and numeric parameters */
1409: /* ivisc = param->ivisc; */ ibound = param->ibound;
1411: for (j=js; j<je; j++) {
1412: for (i=is; i<ie; i++) {
1414: /************* X-MOMENTUM/VELOCITY *************/
1415: if (i<j) f[j][i].u = x[j][i].u - SlabVel('U',i,j,user);
1416: else if (j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1417: /* in the lithospheric lid */
1418: f[j][i].u = x[j][i].u - 0.0;
1419: } else if (i==ilim) {
1420: /* on the right side boundary */
1421: if (ibound==BC_ANALYTIC) {
1422: f[j][i].u = x[j][i].u - HorizVelocity(i,j,user);
1423: } else {
1424: f[j][i].u = XNormalStress(x,i,j,CELL_CENTER,user) - EPS_ZERO;
1425: }
1427: } else if (j==jlim) {
1428: /* on the bottom boundary */
1429: if (ibound==BC_ANALYTIC) {
1430: f[j][i].u = x[j][i].u - HorizVelocity(i,j,user);
1431: } else if (ibound==BC_NOSTRESS) {
1432: f[j][i].u = XMomentumResidual(x,i,j,user);
1433: } else {
1434: /* experimental boundary condition */
1435: }
1437: } else {
1438: /* in the mantle wedge */
1439: f[j][i].u = XMomentumResidual(x,i,j,user);
1440: }
1442: /************* Z-MOMENTUM/VELOCITY *************/
1443: if (i<=j) {
1444: f[j][i].w = x[j][i].w - SlabVel('W',i,j,user);
1446: } else if (j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1447: /* in the lithospheric lid */
1448: f[j][i].w = x[j][i].w - 0.0;
1450: } else if (j==jlim) {
1451: /* on the bottom boundary */
1452: if (ibound==BC_ANALYTIC) {
1453: f[j][i].w = x[j][i].w - VertVelocity(i,j,user);
1454: } else {
1455: f[j][i].w = ZNormalStress(x,i,j,CELL_CENTER,user) - EPS_ZERO;
1456: }
1458: } else if (i==ilim) {
1459: /* on the right side boundary */
1460: if (ibound==BC_ANALYTIC) {
1461: f[j][i].w = x[j][i].w - VertVelocity(i,j,user);
1462: } else if (ibound==BC_NOSTRESS) {
1463: f[j][i].w = ZMomentumResidual(x,i,j,user);
1464: } else {
1465: /* experimental boundary condition */
1466: }
1468: } else {
1469: /* in the mantle wedge */
1470: f[j][i].w = ZMomentumResidual(x,i,j,user);
1471: }
1473: /************* CONTINUITY/PRESSURE *************/
1474: if (i<j || j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1475: /* in the lid or slab */
1476: f[j][i].p = x[j][i].p;
1478: } else if ((i==ilim || j==jlim) && ibound==BC_ANALYTIC) {
1479: /* on an analytic boundary */
1480: f[j][i].p = x[j][i].p - Pressure(i,j,user);
1482: } else {
1483: /* in the mantle wedge */
1484: f[j][i].p = ContinuityResidual(x,i,j,user);
1485: }
1487: /************* TEMPERATURE *************/
1488: if (j==0) {
1489: /* on the surface */
1490: f[j][i].T = x[j][i].T + x[j+1][i].T + PetscMax(PetscRealPart(x[j][i].T),0.0);
1492: } else if (i==0) {
1493: /* slab inflow boundary */
1494: f[j][i].T = x[j][i].T - PlateModel(j,PLATE_SLAB,user);
1496: } else if (i==ilim) {
1497: /* right side boundary */
1498: mag_u = 1.0 - PetscPowRealInt((1.0-PetscMax(PetscMin(PetscRealPart(x[j][i-1].u)/param->cb,1.0),0.0)), 5);
1499: 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);
1501: } else if (j==jlim) {
1502: /* bottom boundary */
1503: mag_w = 1.0 - PetscPowRealInt((1.0-PetscMax(PetscMin(PetscRealPart(x[j-1][i].w)/param->sb,1.0),0.0)), 5);
1504: f[j][i].T = x[j][i].T - mag_w*x[j-1][i-1].T - (1.0-mag_w);
1506: } else {
1507: /* in the mantle wedge */
1508: f[j][i].T = EnergyResidual(x,i,j,user);
1509: }
1510: }
1511: }
1512: return(0);
1513: }