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(¶m,&grid);
150: ReportParams(¶m,&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 = ¶m;
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: }
965: if (param->output_ivisc != param->ivisc) {
966: PetscPrintf(PETSC_COMM_WORLD," Output viscosity: -ivisc %D\n",param->output_ivisc);
967: }
969: PetscPrintf(PETSC_COMM_WORLD,"---------------------END ex30 PARAM REPORT---------------------\n");
970: }
971: if (param->param_test) PetscEnd();
972: return ierr_out;
973: }
975: /* ------------------------------------------------------------------- */
976: /* generates an initial guess using the analytic solution for isoviscous
977: corner flow */
978: PetscErrorCode Initialize(DM da)
979: /* ------------------------------------------------------------------- */
980: {
981: AppCtx *user;
982: Parameter *param;
983: GridInfo *grid;
984: PetscInt i,j,is,js,im,jm;
986: Field **x;
987: Vec Xguess;
989: /* Get the fine grid */
990: DMGetApplicationContext(da,&user);
991: Xguess = user->Xguess;
992: param = user->param;
993: grid = user->grid;
994: DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
995: DMDAVecGetArray(da,Xguess,(void**)&x);
997: /* Compute initial guess */
998: for (j=js; j<js+jm; j++) {
999: for (i=is; i<is+im; i++) {
1000: if (i<j) x[j][i].u = param->cb;
1001: else if (j<=grid->jlid) x[j][i].u = 0.0;
1002: else x[j][i].u = HorizVelocity(i,j,user);
1004: if (i<=j) x[j][i].w = param->sb;
1005: else if (j<=grid->jlid) x[j][i].w = 0.0;
1006: else x[j][i].w = VertVelocity(i,j,user);
1008: if (i<j || j<=grid->jlid) x[j][i].p = 0.0;
1009: else x[j][i].p = Pressure(i,j,user);
1011: x[j][i].T = PetscMin(grid->dz*(j-0.5),1.0);
1012: }
1013: }
1015: /* Restore x to Xguess */
1016: DMDAVecRestoreArray(da,Xguess,(void**)&x);
1018: return 0;
1019: }
1021: /*---------------------------------------------------------------------*/
1022: /* controls output to a file */
1023: PetscErrorCode DoOutput(SNES snes, PetscInt its)
1024: /*---------------------------------------------------------------------*/
1025: {
1026: AppCtx *user;
1027: Parameter *param;
1028: GridInfo *grid;
1029: PetscInt ivt;
1031: PetscMPIInt rank;
1032: PetscViewer viewer;
1033: Vec res, pars;
1034: MPI_Comm comm;
1035: DM da;
1037: SNESGetDM(snes,&da);
1038: DMGetApplicationContext(da,&user);
1039: param = user->param;
1040: grid = user->grid;
1041: ivt = param->ivisc;
1043: param->ivisc = param->output_ivisc;
1045: /* compute final residual and final viscosity/strain rate fields */
1046: SNESGetFunction(snes, &res, NULL, NULL);
1047: ViscosityField(da, user->x, user->Xguess);
1049: /* get the communicator and the rank of the processor */
1050: PetscObjectGetComm((PetscObject)snes, &comm);
1051: MPI_Comm_rank(comm, &rank);
1053: if (param->output_to_file) { /* send output to binary file */
1054: VecCreate(comm, &pars);
1055: if (rank == 0) { /* on processor 0 */
1056: VecSetSizes(pars, 20, PETSC_DETERMINE);
1057: VecSetFromOptions(pars);
1058: VecSetValue(pars,0, (PetscScalar)(grid->ni),INSERT_VALUES);
1059: VecSetValue(pars,1, (PetscScalar)(grid->nj),INSERT_VALUES);
1060: VecSetValue(pars,2, (PetscScalar)(grid->dx),INSERT_VALUES);
1061: VecSetValue(pars,3, (PetscScalar)(grid->dz),INSERT_VALUES);
1062: VecSetValue(pars,4, (PetscScalar)(param->L),INSERT_VALUES);
1063: VecSetValue(pars,5, (PetscScalar)(param->V),INSERT_VALUES);
1064: /* skipped 6 intentionally */
1065: VecSetValue(pars,7, (PetscScalar)(param->slab_dip),INSERT_VALUES);
1066: VecSetValue(pars,8, (PetscScalar)(grid->jlid),INSERT_VALUES);
1067: VecSetValue(pars,9, (PetscScalar)(param->lid_depth),INSERT_VALUES);
1068: VecSetValue(pars,10,(PetscScalar)(grid->jfault),INSERT_VALUES);
1069: VecSetValue(pars,11,(PetscScalar)(param->fault_depth),INSERT_VALUES);
1070: VecSetValue(pars,12,(PetscScalar)(param->potentialT),INSERT_VALUES);
1071: VecSetValue(pars,13,(PetscScalar)(param->ivisc),INSERT_VALUES);
1072: VecSetValue(pars,14,(PetscScalar)(param->visc_cutoff),INSERT_VALUES);
1073: VecSetValue(pars,15,(PetscScalar)(param->ibound),INSERT_VALUES);
1074: VecSetValue(pars,16,(PetscScalar)(its),INSERT_VALUES);
1075: } else { /* on some other processor */
1076: VecSetSizes(pars, 0, PETSC_DETERMINE);
1077: VecSetFromOptions(pars);
1078: }
1079: VecAssemblyBegin(pars); VecAssemblyEnd(pars);
1081: /* create viewer */
1082: #if defined(PETSC_HAVE_MATLAB_ENGINE)
1083: PetscViewerMatlabOpen(PETSC_COMM_WORLD,param->filename,FILE_MODE_WRITE,&viewer);
1084: #else
1085: PetscViewerBinaryOpen(PETSC_COMM_WORLD,param->filename,FILE_MODE_WRITE,&viewer);
1086: #endif
1088: /* send vectors to viewer */
1089: PetscObjectSetName((PetscObject)res,"res");
1090: VecView(res,viewer);
1091: PetscObjectSetName((PetscObject)user->x,"out");
1092: VecView(user->x, viewer);
1093: PetscObjectSetName((PetscObject)(user->Xguess),"aux");
1094: VecView(user->Xguess, viewer);
1095: StressField(da); /* compute stress fields */
1096: PetscObjectSetName((PetscObject)(user->Xguess),"str");
1097: VecView(user->Xguess, viewer);
1098: PetscObjectSetName((PetscObject)pars,"par");
1099: VecView(pars, viewer);
1101: /* destroy viewer and vector */
1102: PetscViewerDestroy(&viewer);
1103: VecDestroy(&pars);
1104: }
1106: param->ivisc = ivt;
1107: return 0;
1108: }
1110: /* ------------------------------------------------------------------- */
1111: /* Compute both the second invariant of the strain rate tensor and the viscosity, at both cell centers and cell corners */
1112: PetscErrorCode ViscosityField(DM da, Vec X, Vec V)
1113: /* ------------------------------------------------------------------- */
1114: {
1115: AppCtx *user;
1116: Parameter *param;
1117: GridInfo *grid;
1118: Vec localX;
1119: Field **v, **x;
1120: PetscReal eps, /* dx,*/ dz, T, epsC, TC;
1121: PetscInt i,j,is,js,im,jm,ilim,jlim,ivt;
1125: DMGetApplicationContext(da,&user);
1126: param = user->param;
1127: grid = user->grid;
1128: ivt = param->ivisc;
1129: param->ivisc = param->output_ivisc;
1131: DMGetLocalVector(da, &localX);
1132: DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX);
1133: DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX);
1134: DMDAVecGetArray(da,localX,(void**)&x);
1135: DMDAVecGetArray(da,V,(void**)&v);
1137: /* Parameters */
1138: /* dx = grid->dx; */ dz = grid->dz;
1140: ilim = grid->ni-1; jlim = grid->nj-1;
1142: /* Compute real temperature, strain rate and viscosity */
1143: DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1144: for (j=js; j<js+jm; j++) {
1145: for (i=is; i<is+im; i++) {
1146: T = PetscRealPart(param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*param->z_scale));
1147: if (i<ilim && j<jlim) {
1148: TC = PetscRealPart(param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*param->z_scale));
1149: } else {
1150: TC = T;
1151: }
1152: eps = PetscRealPart((CalcSecInv(x,i,j,CELL_CENTER,user)));
1153: epsC = PetscRealPart(CalcSecInv(x,i,j,CELL_CORNER,user));
1155: v[j][i].u = eps;
1156: v[j][i].w = epsC;
1157: v[j][i].p = Viscosity(T,eps,dz*(j-0.5),param);
1158: v[j][i].T = Viscosity(TC,epsC,dz*j,param);
1159: }
1160: }
1161: DMDAVecRestoreArray(da,V,(void**)&v);
1162: DMDAVecRestoreArray(da,localX,(void**)&x);
1163: DMRestoreLocalVector(da, &localX);
1165: param->ivisc = ivt;
1166: return(0);
1167: }
1169: /* ------------------------------------------------------------------- */
1170: /* post-processing: compute stress everywhere */
1171: PetscErrorCode StressField(DM da)
1172: /* ------------------------------------------------------------------- */
1173: {
1174: AppCtx *user;
1175: PetscInt i,j,is,js,im,jm;
1177: Vec locVec;
1178: Field **x, **y;
1180: DMGetApplicationContext(da,&user);
1182: /* Get the fine grid of Xguess and X */
1183: DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1184: DMDAVecGetArray(da,user->Xguess,(void**)&x);
1186: DMGetLocalVector(da, &locVec);
1187: DMGlobalToLocalBegin(da, user->x, INSERT_VALUES, locVec);
1188: DMGlobalToLocalEnd(da, user->x, INSERT_VALUES, locVec);
1189: DMDAVecGetArray(da,locVec,(void**)&y);
1191: /* Compute stress on the corner points */
1192: for (j=js; j<js+jm; j++) {
1193: for (i=is; i<is+im; i++) {
1194: x[j][i].u = ShearStress(y,i,j,CELL_CENTER,user);
1195: x[j][i].w = ShearStress(y,i,j,CELL_CORNER,user);
1196: x[j][i].p = XNormalStress(y,i,j,CELL_CENTER,user);
1197: x[j][i].T = ZNormalStress(y,i,j,CELL_CENTER,user);
1198: }
1199: }
1201: /* Restore the fine grid of Xguess and X */
1202: DMDAVecRestoreArray(da,user->Xguess,(void**)&x);
1203: DMDAVecRestoreArray(da,locVec,(void**)&y);
1204: DMRestoreLocalVector(da, &locVec);
1205: return 0;
1206: }
1208: /*=====================================================================
1209: UTILITY FUNCTIONS
1210: =====================================================================*/
1212: /*---------------------------------------------------------------------*/
1213: /* returns the velocity of the subducting slab and handles fault nodes
1214: for BC */
1215: PETSC_STATIC_INLINE PetscScalar SlabVel(char c, PetscInt i, PetscInt j, AppCtx *user)
1216: /*---------------------------------------------------------------------*/
1217: {
1218: Parameter *param = user->param;
1219: GridInfo *grid = user->grid;
1221: if (c=='U' || c=='u') {
1222: if (i<j-1) return param->cb;
1223: else if (j<=grid->jfault) return 0.0;
1224: else return param->cb;
1226: } else {
1227: if (i<j) return param->sb;
1228: else if (j<=grid->jfault) return 0.0;
1229: else return param->sb;
1230: }
1231: }
1233: /*---------------------------------------------------------------------*/
1234: /* solution to diffusive half-space cooling model for BC */
1235: PETSC_STATIC_INLINE PetscScalar PlateModel(PetscInt j, PetscInt plate, AppCtx *user)
1236: /*---------------------------------------------------------------------*/
1237: {
1238: Parameter *param = user->param;
1239: PetscScalar z;
1240: if (plate==PLATE_LID) z = (j-0.5)*user->grid->dz;
1241: else z = (j-0.5)*user->grid->dz*param->cb; /* PLATE_SLAB */
1242: #if defined(PETSC_HAVE_ERF)
1243: return (PetscReal)(erf((double)PetscRealPart(z*param->L/2.0/param->skt)));
1244: #else
1245: (*PetscErrorPrintf)("erf() not available on this machine\n");
1246: MPI_Abort(PETSC_COMM_SELF,1);
1247: #endif
1248: }
1250: /*=====================================================================
1251: INTERACTIVE SIGNAL HANDLING
1252: =====================================================================*/
1254: /* ------------------------------------------------------------------- */
1255: PetscErrorCode SNESConverged_Interactive(SNES snes, PetscInt it,PetscReal xnorm, PetscReal snorm, PetscReal fnorm, SNESConvergedReason *reason, void *ctx)
1256: /* ------------------------------------------------------------------- */
1257: {
1258: AppCtx *user = (AppCtx*) ctx;
1259: Parameter *param = user->param;
1260: KSP ksp;
1264: if (param->interrupted) {
1265: param->interrupted = PETSC_FALSE;
1266: PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: exiting SNES solve. \n");
1267: *reason = SNES_CONVERGED_FNORM_ABS;
1268: return(0);
1269: } else if (param->toggle_kspmon) {
1270: param->toggle_kspmon = PETSC_FALSE;
1272: SNESGetKSP(snes, &ksp);
1274: if (param->kspmon) {
1275: KSPMonitorCancel(ksp);
1277: param->kspmon = PETSC_FALSE;
1278: PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: deactivating ksp singular value monitor. \n");
1279: } else {
1280: PetscViewerAndFormat *vf;
1281: PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_DEFAULT,&vf);
1282: KSPMonitorSet(ksp,(PetscErrorCode (*)(KSP,PetscInt,PetscReal,void*))KSPMonitorSingularValue,vf,(PetscErrorCode (*)(void**))PetscViewerAndFormatDestroy);
1284: param->kspmon = PETSC_TRUE;
1285: PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: activating ksp singular value monitor. \n");
1286: }
1287: }
1288: PetscFunctionReturn(SNESConvergedDefault(snes,it,xnorm,snorm,fnorm,reason,ctx));
1289: }
1291: /* ------------------------------------------------------------------- */
1292: #include <signal.h>
1293: PetscErrorCode InteractiveHandler(int signum, void *ctx)
1294: /* ------------------------------------------------------------------- */
1295: {
1296: AppCtx *user = (AppCtx*) ctx;
1297: Parameter *param = user->param;
1299: if (signum == SIGILL) {
1300: param->toggle_kspmon = PETSC_TRUE;
1301: #if !defined(PETSC_MISSING_SIGCONT)
1302: } else if (signum == SIGCONT) {
1303: param->interrupted = PETSC_TRUE;
1304: #endif
1305: #if !defined(PETSC_MISSING_SIGURG)
1306: } else if (signum == SIGURG) {
1307: param->stop_solve = PETSC_TRUE;
1308: #endif
1309: }
1310: return 0;
1311: }
1313: /*---------------------------------------------------------------------*/
1314: /* main call-back function that computes the processor-local piece
1315: of the residual */
1316: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,Field **x,Field **f,void *ptr)
1317: /*---------------------------------------------------------------------*/
1318: {
1319: AppCtx *user = (AppCtx*)ptr;
1320: Parameter *param = user->param;
1321: GridInfo *grid = user->grid;
1322: PetscScalar mag_w, mag_u;
1323: PetscInt i,j,mx,mz,ilim,jlim;
1324: PetscInt is,ie,js,je,ibound; /* ,ivisc */
1327: /* Define global and local grid parameters */
1328: mx = info->mx; mz = info->my;
1329: ilim = mx-1; jlim = mz-1;
1330: is = info->xs; ie = info->xs+info->xm;
1331: js = info->ys; je = info->ys+info->ym;
1333: /* Define geometric and numeric parameters */
1334: /* ivisc = param->ivisc; */ ibound = param->ibound;
1336: for (j=js; j<je; j++) {
1337: for (i=is; i<ie; i++) {
1339: /************* X-MOMENTUM/VELOCITY *************/
1340: if (i<j) f[j][i].u = x[j][i].u - SlabVel('U',i,j,user);
1341: else if (j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1342: /* in the lithospheric lid */
1343: f[j][i].u = x[j][i].u - 0.0;
1344: } else if (i==ilim) {
1345: /* on the right side boundary */
1346: if (ibound==BC_ANALYTIC) {
1347: f[j][i].u = x[j][i].u - HorizVelocity(i,j,user);
1348: } else {
1349: f[j][i].u = XNormalStress(x,i,j,CELL_CENTER,user) - EPS_ZERO;
1350: }
1352: } else if (j==jlim) {
1353: /* on the bottom boundary */
1354: if (ibound==BC_ANALYTIC) {
1355: f[j][i].u = x[j][i].u - HorizVelocity(i,j,user);
1356: } else if (ibound==BC_NOSTRESS) {
1357: f[j][i].u = XMomentumResidual(x,i,j,user);
1358: } else {
1359: /* experimental boundary condition */
1360: }
1362: } else {
1363: /* in the mantle wedge */
1364: f[j][i].u = XMomentumResidual(x,i,j,user);
1365: }
1367: /************* Z-MOMENTUM/VELOCITY *************/
1368: if (i<=j) {
1369: f[j][i].w = x[j][i].w - SlabVel('W',i,j,user);
1371: } else if (j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1372: /* in the lithospheric lid */
1373: f[j][i].w = x[j][i].w - 0.0;
1375: } else if (j==jlim) {
1376: /* on the bottom boundary */
1377: if (ibound==BC_ANALYTIC) {
1378: f[j][i].w = x[j][i].w - VertVelocity(i,j,user);
1379: } else {
1380: f[j][i].w = ZNormalStress(x,i,j,CELL_CENTER,user) - EPS_ZERO;
1381: }
1383: } else if (i==ilim) {
1384: /* on the right side boundary */
1385: if (ibound==BC_ANALYTIC) {
1386: f[j][i].w = x[j][i].w - VertVelocity(i,j,user);
1387: } else if (ibound==BC_NOSTRESS) {
1388: f[j][i].w = ZMomentumResidual(x,i,j,user);
1389: } else {
1390: /* experimental boundary condition */
1391: }
1393: } else {
1394: /* in the mantle wedge */
1395: f[j][i].w = ZMomentumResidual(x,i,j,user);
1396: }
1398: /************* CONTINUITY/PRESSURE *************/
1399: if (i<j || j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1400: /* in the lid or slab */
1401: f[j][i].p = x[j][i].p;
1403: } else if ((i==ilim || j==jlim) && ibound==BC_ANALYTIC) {
1404: /* on an analytic boundary */
1405: f[j][i].p = x[j][i].p - Pressure(i,j,user);
1407: } else {
1408: /* in the mantle wedge */
1409: f[j][i].p = ContinuityResidual(x,i,j,user);
1410: }
1412: /************* TEMPERATURE *************/
1413: if (j==0) {
1414: /* on the surface */
1415: f[j][i].T = x[j][i].T + x[j+1][i].T + PetscMax(PetscRealPart(x[j][i].T),0.0);
1417: } else if (i==0) {
1418: /* slab inflow boundary */
1419: f[j][i].T = x[j][i].T - PlateModel(j,PLATE_SLAB,user);
1421: } else if (i==ilim) {
1422: /* right side boundary */
1423: mag_u = 1.0 - PetscPowRealInt((1.0-PetscMax(PetscMin(PetscRealPart(x[j][i-1].u)/param->cb,1.0),0.0)), 5);
1424: 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);
1426: } else if (j==jlim) {
1427: /* bottom boundary */
1428: mag_w = 1.0 - PetscPowRealInt((1.0-PetscMax(PetscMin(PetscRealPart(x[j-1][i].w)/param->sb,1.0),0.0)), 5);
1429: f[j][i].T = x[j][i].T - mag_w*x[j-1][i-1].T - (1.0-mag_w);
1431: } else {
1432: /* in the mantle wedge */
1433: f[j][i].T = EnergyResidual(x,i,j,user);
1434: }
1435: }
1436: }
1437: return(0);
1438: }
1440: /*TEST
1442: build:
1443: requires: !complex erf
1445: test:
1446: args: -ni 18
1447: filter: grep -v Destination
1448: requires: !single
1450: TEST*/