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:
-------$w_{ij}$------
$u_{i-1j}$ $P,T_{ij}$ $u_{ij}$
------$w_{ij-1}$-----
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*);
124: /*-----------------------------------------------------------------------*/
125: int main(int argc,char **argv)
126: /*-----------------------------------------------------------------------*/
127: {
128: SNES snes;
129: AppCtx *user; /* user-defined work context */
130: Parameter param;
131: GridInfo grid;
132: PetscInt nits;
134: MPI_Comm comm;
135: DM da;
137: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
138: PetscOptionsSetValue(NULL,"-file","ex30_output");
139: PetscOptionsSetValue(NULL,"-snes_monitor_short",NULL);
140: PetscOptionsSetValue(NULL,"-snes_max_it","20");
141: PetscOptionsSetValue(NULL,"-ksp_max_it","1500");
142: PetscOptionsSetValue(NULL,"-ksp_gmres_restart","300");
143: PetscOptionsInsert(NULL,&argc,&argv,NULL);
145: comm = PETSC_COMM_WORLD;
147: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148: Set up the problem parameters.
149: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
150: SetParams(¶m,&grid);
151: ReportParams(¶m,&grid);
153: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
154: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
155: SNESCreate(comm,&snes);
156: DMDACreate2d(comm,grid.bx,grid.by,grid.stencil,grid.ni,grid.nj,PETSC_DECIDE,PETSC_DECIDE,grid.dof,grid.stencil_width,0,0,&da);
157: DMSetFromOptions(da);
158: DMSetUp(da);
159: SNESSetDM(snes,da);
160: DMDASetFieldName(da,0,"x-velocity");
161: DMDASetFieldName(da,1,"y-velocity");
162: DMDASetFieldName(da,2,"pressure");
163: DMDASetFieldName(da,3,"temperature");
166: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
167: Create user context, set problem data, create vector data structures.
168: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
169: PetscNew(&user);
170: user->param = ¶m;
171: user->grid = &grid;
172: DMSetApplicationContext(da,user);
173: DMCreateGlobalVector(da,&(user->Xguess));
176: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
177: Set up the SNES solver with callback functions.
178: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
179: DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,(void*)user);
180: SNESSetFromOptions(snes);
183: SNESSetConvergenceTest(snes,SNESConverged_Interactive,(void*)user,NULL);
184: PetscPushSignalHandler(InteractiveHandler,(void*)user);
186: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
187: Initialize and solve the nonlinear system
188: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
189: Initialize(da);
190: UpdateSolution(snes,user,&nits);
192: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193: Output variables.
194: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
195: DoOutput(snes,nits);
197: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
198: Free work space.
199: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
200: VecDestroy(&user->Xguess);
201: VecDestroy(&user->x);
202: PetscFree(user);
203: SNESDestroy(&snes);
204: DMDestroy(&da);
205: PetscPopSignalHandler();
206: PetscFinalize();
207: return ierr;
208: }
210: /*=====================================================================
211: PETSc INTERACTION FUNCTIONS (initialize & call SNESSolve)
212: =====================================================================*/
214: /*---------------------------------------------------------------------*/
215: /* manages solve: adaptive continuation method */
216: PetscErrorCode UpdateSolution(SNES snes, AppCtx *user, PetscInt *nits)
217: {
218: KSP ksp;
219: PC pc;
220: SNESConvergedReason reason = SNES_CONVERGED_ITERATING;
221: Parameter *param = user->param;
222: PetscReal cont_incr=0.3;
223: PetscInt its;
224: PetscErrorCode ierr;
225: PetscBool q = PETSC_FALSE;
226: DM dm;
229: SNESGetDM(snes,&dm);
230: DMCreateGlobalVector(dm,&user->x);
231: SNESGetKSP(snes,&ksp);
232: KSPGetPC(ksp, &pc);
233: KSPSetComputeSingularValues(ksp, PETSC_TRUE);
235: *nits=0;
237: /* Isoviscous solve */
238: if (param->ivisc == VISC_CONST && !param->stop_solve) {
239: param->ivisc = VISC_CONST;
241: SNESSolve(snes,0,user->x);
242: SNESGetConvergedReason(snes,&reason);
243: SNESGetIterationNumber(snes,&its);
244: *nits += its;
245: VecCopy(user->x,user->Xguess);
246: if (param->stop_solve) goto done;
247: }
249: /* Olivine diffusion creep */
250: if (param->ivisc >= VISC_DIFN && !param->stop_solve) {
251: if (!q) {PetscPrintf(PETSC_COMM_WORLD,"Computing Variable Viscosity Solution\n");}
253: /* continuation method on viscosity cutoff */
254: for (param->continuation=0.0;; param->continuation+=cont_incr) {
255: if (!q) {PetscPrintf(PETSC_COMM_WORLD," Continuation parameter = %g\n", (double)param->continuation);}
257: /* solve the non-linear system */
258: VecCopy(user->Xguess,user->x);
259: SNESSolve(snes,0,user->x);
260: SNESGetConvergedReason(snes,&reason);
261: SNESGetIterationNumber(snes,&its);
262: *nits += its;
263: if (!q) {PetscPrintf(PETSC_COMM_WORLD," SNES iterations: %D, Cumulative: %D\n", its, *nits);}
264: if (param->stop_solve) goto done;
266: if (reason<0) {
267: /* NOT converged */
268: cont_incr = -PetscAbsReal(cont_incr)/2.0;
269: if (PetscAbsReal(cont_incr)<0.01) goto done;
271: } else {
272: /* converged */
273: VecCopy(user->x,user->Xguess);
274: if (param->continuation >= 1.0) goto done;
275: if (its<=3) cont_incr = 0.30001;
276: else if (its<=8) cont_incr = 0.15001;
277: else cont_incr = 0.10001;
279: if (param->continuation+cont_incr > 1.0) cont_incr = 1.0 - param->continuation;
280: } /* endif reason<0 */
281: }
282: }
283: done:
284: if (param->stop_solve && !q) {PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: stopping solve.\n");}
285: if (reason<0 && !q) {PetscPrintf(PETSC_COMM_WORLD,"FAILED TO CONVERGE: stopping solve.\n");}
286: return(0);
287: }
290: /*=====================================================================
291: PHYSICS FUNCTIONS (compute the discrete residual)
292: =====================================================================*/
295: /*---------------------------------------------------------------------*/
296: PETSC_STATIC_INLINE PetscScalar UInterp(Field **x, PetscInt i, PetscInt j)
297: /*---------------------------------------------------------------------*/
298: {
299: return 0.25*(x[j][i].u+x[j+1][i].u+x[j][i+1].u+x[j+1][i+1].u);
300: }
302: /*---------------------------------------------------------------------*/
303: PETSC_STATIC_INLINE PetscScalar WInterp(Field **x, PetscInt i, PetscInt j)
304: /*---------------------------------------------------------------------*/
305: {
306: return 0.25*(x[j][i].w+x[j+1][i].w+x[j][i+1].w+x[j+1][i+1].w);
307: }
309: /*---------------------------------------------------------------------*/
310: PETSC_STATIC_INLINE PetscScalar PInterp(Field **x, PetscInt i, PetscInt j)
311: /*---------------------------------------------------------------------*/
312: {
313: return 0.25*(x[j][i].p+x[j+1][i].p+x[j][i+1].p+x[j+1][i+1].p);
314: }
316: /*---------------------------------------------------------------------*/
317: PETSC_STATIC_INLINE PetscScalar TInterp(Field **x, PetscInt i, PetscInt j)
318: /*---------------------------------------------------------------------*/
319: {
320: return 0.25*(x[j][i].T+x[j+1][i].T+x[j][i+1].T+x[j+1][i+1].T);
321: }
323: /*---------------------------------------------------------------------*/
324: /* isoviscous analytic solution for IC */
325: PETSC_STATIC_INLINE PetscScalar HorizVelocity(PetscInt i, PetscInt j, AppCtx *user)
326: /*---------------------------------------------------------------------*/
327: {
328: Parameter *param = user->param;
329: GridInfo *grid = user->grid;
330: PetscScalar st, ct, th, c=param->c, d=param->d;
331: PetscReal x, z,r;
333: x = (i - grid->jlid)*grid->dx; z = (j - grid->jlid - 0.5)*grid->dz;
334: r = PetscSqrtReal(x*x+z*z);
335: st = z/r;
336: ct = x/r;
337: th = PetscAtanReal(z/x);
338: return ct*(c*th*st+d*(st+th*ct)) + st*(c*(st-th*ct)+d*th*st);
339: }
341: /*---------------------------------------------------------------------*/
342: /* isoviscous analytic solution for IC */
343: PETSC_STATIC_INLINE PetscScalar VertVelocity(PetscInt i, PetscInt j, AppCtx *user)
344: /*---------------------------------------------------------------------*/
345: {
346: Parameter *param = user->param;
347: GridInfo *grid = user->grid;
348: PetscScalar st, ct, th, c=param->c, d=param->d;
349: PetscReal x, z, r;
351: x = (i - grid->jlid - 0.5)*grid->dx; z = (j - grid->jlid)*grid->dz;
352: r = PetscSqrtReal(x*x+z*z); st = z/r; ct = x/r; th = PetscAtanReal(z/x);
353: return st*(c*th*st+d*(st+th*ct)) - ct*(c*(st-th*ct)+d*th*st);
354: }
356: /*---------------------------------------------------------------------*/
357: /* isoviscous analytic solution for IC */
358: PETSC_STATIC_INLINE PetscScalar Pressure(PetscInt i, PetscInt j, AppCtx *user)
359: /*---------------------------------------------------------------------*/
360: {
361: Parameter *param = user->param;
362: GridInfo *grid = user->grid;
363: PetscScalar x, z, r, st, ct, c=param->c, d=param->d;
365: x = (i - grid->jlid - 0.5)*grid->dx; z = (j - grid->jlid - 0.5)*grid->dz;
366: r = PetscSqrtReal(x*x+z*z); st = z/r; ct = x/r;
367: return (-2.0*(c*ct-d*st)/r);
368: }
370: /* computes the second invariant of the strain rate tensor */
371: PETSC_STATIC_INLINE PetscScalar CalcSecInv(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
372: /*---------------------------------------------------------------------*/
373: {
374: Parameter *param = user->param;
375: GridInfo *grid = user->grid;
376: PetscInt ilim =grid->ni-1, jlim=grid->nj-1;
377: PetscScalar uN,uS,uE,uW,wN,wS,wE,wW;
378: PetscScalar eps11, eps12, eps22;
380: if (i<j) return EPS_ZERO;
381: if (i==ilim) i--;
382: if (j==jlim) j--;
384: if (ipos==CELL_CENTER) { /* on cell center */
385: if (j<=grid->jlid) return EPS_ZERO;
387: uE = x[j][i].u; uW = x[j][i-1].u;
388: wN = x[j][i].w; wS = x[j-1][i].w;
389: wE = WInterp(x,i,j-1);
390: if (i==j) {
391: uN = param->cb; wW = param->sb;
392: } else {
393: uN = UInterp(x,i-1,j); wW = WInterp(x,i-1,j-1);
394: }
396: if (j==grid->jlid+1) uS = 0.0;
397: else uS = UInterp(x,i-1,j-1);
399: } else { /* on CELL_CORNER */
400: if (j<grid->jlid) return EPS_ZERO;
402: uN = x[j+1][i].u; uS = x[j][i].u;
403: wE = x[j][i+1].w; wW = x[j][i].w;
404: if (i==j) {
405: wN = param->sb;
406: uW = param->cb;
407: } else {
408: wN = WInterp(x,i,j);
409: uW = UInterp(x,i-1,j);
410: }
412: if (j==grid->jlid) {
413: uE = 0.0; uW = 0.0;
414: uS = -uN;
415: wS = -wN;
416: } else {
417: uE = UInterp(x,i,j);
418: wS = WInterp(x,i,j-1);
419: }
420: }
422: eps11 = (uE-uW)/grid->dx; eps22 = (wN-wS)/grid->dz;
423: eps12 = 0.5*((uN-uS)/grid->dz + (wE-wW)/grid->dx);
425: return PetscSqrtReal(0.5*(eps11*eps11 + 2.0*eps12*eps12 + eps22*eps22));
426: }
428: /*---------------------------------------------------------------------*/
429: /* computes the shear viscosity */
430: PETSC_STATIC_INLINE PetscScalar Viscosity(PetscScalar T, PetscScalar eps, PetscScalar z, Parameter *param)
431: /*---------------------------------------------------------------------*/
432: {
433: PetscReal result =0.0;
434: ViscParam difn =param->diffusion, disl=param->dislocation;
435: PetscInt iVisc =param->ivisc;
436: PetscScalar eps_scale=param->V/(param->L*1000.0);
437: PetscScalar strain_power, v1, v2, P;
438: PetscScalar rho_g = 32340.0, R=8.3144;
440: P = rho_g*(z*param->L*1000.0); /* Pa */
442: if (iVisc==VISC_CONST) {
443: /* constant viscosity */
444: return 1.0;
445: } else if (iVisc==VISC_DIFN) {
446: /* diffusion creep rheology */
447: result = PetscRealPart((difn.A*PetscExpScalar((difn.Estar + P*difn.Vstar)/R/(T+273.0))/param->eta0));
448: } else if (iVisc==VISC_DISL) {
449: /* dislocation creep rheology */
450: strain_power = PetscPowScalar(eps*eps_scale, (1.0-disl.n)/disl.n);
452: result = PetscRealPart(disl.A*PetscExpScalar((disl.Estar + P*disl.Vstar)/disl.n/R/(T+273.0))*strain_power/param->eta0);
453: } else if (iVisc==VISC_FULL) {
454: /* dislocation/diffusion creep rheology */
455: strain_power = PetscPowScalar(eps*eps_scale, (1.0-disl.n)/disl.n);
457: v1 = difn.A*PetscExpScalar((difn.Estar + P*difn.Vstar)/R/(T+273.0))/param->eta0;
458: v2 = disl.A*PetscExpScalar((disl.Estar + P*disl.Vstar)/disl.n/R/(T+273.0))*strain_power/param->eta0;
460: result = PetscRealPart(1.0/(1.0/v1 + 1.0/v2));
461: }
463: /* max viscosity is param->eta0 */
464: result = PetscMin(result, 1.0);
465: /* min viscosity is param->visc_cutoff */
466: result = PetscMax(result, param->visc_cutoff);
467: /* continuation method */
468: result = PetscPowReal(result,param->continuation);
469: return result;
470: }
472: /*---------------------------------------------------------------------*/
473: /* computes the residual of the x-component of eqn (1) above */
474: PETSC_STATIC_INLINE PetscScalar XMomentumResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
475: /*---------------------------------------------------------------------*/
476: {
477: Parameter *param=user->param;
478: GridInfo *grid =user->grid;
479: PetscScalar dx = grid->dx, dz=grid->dz;
480: PetscScalar etaN,etaS,etaE,etaW,epsN=0.0,epsS=0.0,epsE=0.0,epsW=0.0;
481: PetscScalar TE=0.0,TN=0.0,TS=0.0,TW=0.0, dPdx, residual, z_scale;
482: PetscScalar dudxW,dudxE,dudzN,dudzS,dwdxN,dwdxS;
483: PetscInt jlim = grid->nj-1;
485: z_scale = param->z_scale;
487: if (param->ivisc==VISC_DIFN || param->ivisc>=VISC_DISL) { /* viscosity is T-dependent */
488: TS = param->potentialT * TInterp(x,i,j-1) * PetscExpScalar((j-1.0)*dz*z_scale);
489: if (j==jlim) TN = TS;
490: else TN = param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*z_scale);
491: TW = param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*z_scale);
492: TE = param->potentialT * x[j][i+1].T * PetscExpScalar((j-0.5)*dz*z_scale);
493: if (param->ivisc>=VISC_DISL) { /* olivine dislocation creep */
494: epsN = CalcSecInv(x,i,j, CELL_CORNER,user);
495: epsS = CalcSecInv(x,i,j-1,CELL_CORNER,user);
496: epsE = CalcSecInv(x,i+1,j,CELL_CENTER,user);
497: epsW = CalcSecInv(x,i,j, CELL_CENTER,user);
498: }
499: }
500: etaN = Viscosity(TN,epsN,dz*(j+0.5),param);
501: etaS = Viscosity(TS,epsS,dz*(j-0.5),param);
502: etaW = Viscosity(TW,epsW,dz*j,param);
503: etaE = Viscosity(TE,epsE,dz*j,param);
505: dPdx = (x[j][i+1].p - x[j][i].p)/dx;
506: if (j==jlim) dudzN = etaN * (x[j][i].w - x[j][i+1].w)/dx;
507: else dudzN = etaN * (x[j+1][i].u - x[j][i].u) /dz;
508: dudzS = etaS * (x[j][i].u - x[j-1][i].u)/dz;
509: dudxE = etaE * (x[j][i+1].u - x[j][i].u) /dx;
510: dudxW = etaW * (x[j][i].u - x[j][i-1].u)/dx;
512: residual = -dPdx /* X-MOMENTUM EQUATION*/
513: +(dudxE - dudxW)/dx
514: +(dudzN - dudzS)/dz;
516: if (param->ivisc!=VISC_CONST) {
517: dwdxN = etaN * (x[j][i+1].w - x[j][i].w) /dx;
518: dwdxS = etaS * (x[j-1][i+1].w - x[j-1][i].w)/dx;
520: residual += (dudxE - dudxW)/dx + (dwdxN - dwdxS)/dz;
521: }
523: return residual;
524: }
526: /*---------------------------------------------------------------------*/
527: /* computes the residual of the z-component of eqn (1) above */
528: PETSC_STATIC_INLINE PetscScalar ZMomentumResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
529: /*---------------------------------------------------------------------*/
530: {
531: Parameter *param=user->param;
532: GridInfo *grid =user->grid;
533: PetscScalar dx = grid->dx, dz=grid->dz;
534: 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;
535: PetscScalar TE =0.0,TN=0.0,TS=0.0,TW=0.0, dPdz, residual,z_scale;
536: PetscScalar dudzE,dudzW,dwdxW,dwdxE,dwdzN,dwdzS;
537: PetscInt ilim = grid->ni-1;
539: /* geometric and other parameters */
540: z_scale = param->z_scale;
542: /* viscosity */
543: if (param->ivisc==VISC_DIFN || param->ivisc>=VISC_DISL) { /* viscosity is T-dependent */
544: TN = param->potentialT * x[j+1][i].T * PetscExpScalar((j+0.5)*dz*z_scale);
545: TS = param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*z_scale);
546: TW = param->potentialT * TInterp(x,i-1,j) * PetscExpScalar(j*dz*z_scale);
547: if (i==ilim) TE = TW;
548: else TE = param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*z_scale);
549: if (param->ivisc>=VISC_DISL) { /* olivine dislocation creep */
550: epsN = CalcSecInv(x,i,j+1,CELL_CENTER,user);
551: epsS = CalcSecInv(x,i,j, CELL_CENTER,user);
552: epsE = CalcSecInv(x,i,j, CELL_CORNER,user);
553: epsW = CalcSecInv(x,i-1,j,CELL_CORNER,user);
554: }
555: }
556: etaN = Viscosity(TN,epsN,dz*(j+1.0),param);
557: etaS = Viscosity(TS,epsS,dz*(j+0.0),param);
558: etaW = Viscosity(TW,epsW,dz*(j+0.5),param);
559: etaE = Viscosity(TE,epsE,dz*(j+0.5),param);
561: dPdz = (x[j+1][i].p - x[j][i].p)/dz;
562: dwdzN = etaN * (x[j+1][i].w - x[j][i].w)/dz;
563: dwdzS = etaS * (x[j][i].w - x[j-1][i].w)/dz;
564: if (i==ilim) dwdxE = etaE * (x[j][i].u - x[j+1][i].u)/dz;
565: else dwdxE = etaE * (x[j][i+1].w - x[j][i].w) /dx;
566: dwdxW = 2.0*etaW * (x[j][i].w - x[j][i-1].w)/dx;
568: /* Z-MOMENTUM */
569: residual = -dPdz /* constant viscosity terms */
570: +(dwdzN - dwdzS)/dz
571: +(dwdxE - dwdxW)/dx;
573: if (param->ivisc!=VISC_CONST) {
574: dudzE = etaE * (x[j+1][i].u - x[j][i].u)/dz;
575: dudzW = etaW * (x[j+1][i-1].u - x[j][i-1].u)/dz;
577: residual += (dwdzN - dwdzS)/dz + (dudzE - dudzW)/dx;
578: }
580: return residual;
581: }
583: /*---------------------------------------------------------------------*/
584: /* computes the residual of eqn (2) above */
585: PETSC_STATIC_INLINE PetscScalar ContinuityResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
586: /*---------------------------------------------------------------------*/
587: {
588: GridInfo *grid =user->grid;
589: PetscScalar uE,uW,wN,wS,dudx,dwdz;
591: uW = x[j][i-1].u; uE = x[j][i].u; dudx = (uE - uW)/grid->dx;
592: wS = x[j-1][i].w; wN = x[j][i].w; dwdz = (wN - wS)/grid->dz;
594: return dudx + dwdz;
595: }
597: /*---------------------------------------------------------------------*/
598: /* computes the residual of eqn (3) above */
599: PETSC_STATIC_INLINE PetscScalar EnergyResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
600: /*---------------------------------------------------------------------*/
601: {
602: Parameter *param=user->param;
603: GridInfo *grid =user->grid;
604: PetscScalar dx = grid->dx, dz=grid->dz;
605: PetscInt ilim =grid->ni-1, jlim=grid->nj-1, jlid=grid->jlid;
606: PetscScalar TE, TN, TS, TW, residual;
607: PetscScalar uE,uW,wN,wS;
608: PetscScalar fN,fS,fE,fW,dTdxW,dTdxE,dTdzN,dTdzS;
610: dTdzN = (x[j+1][i].T - x[j][i].T) /dz;
611: dTdzS = (x[j][i].T - x[j-1][i].T)/dz;
612: dTdxE = (x[j][i+1].T - x[j][i].T) /dx;
613: dTdxW = (x[j][i].T - x[j][i-1].T)/dx;
615: residual = ((dTdzN - dTdzS)/dz + /* diffusion term */
616: (dTdxE - dTdxW)/dx)*dx*dz/param->peclet;
618: if (j<=jlid && i>=j) {
619: /* don't advect in the lid */
620: return residual;
621: } else if (i<j) {
622: /* beneath the slab sfc */
623: uW = uE = param->cb;
624: wS = wN = param->sb;
625: } else {
626: /* advect in the slab and wedge */
627: uW = x[j][i-1].u; uE = x[j][i].u;
628: wS = x[j-1][i].w; wN = x[j][i].w;
629: }
631: if (param->adv_scheme==ADVECT_FV || i==ilim-1 || j==jlim-1 || i==1 || j==1) {
632: /* finite volume advection */
633: TS = (x[j][i].T + x[j-1][i].T)/2.0;
634: TN = (x[j][i].T + x[j+1][i].T)/2.0;
635: TE = (x[j][i].T + x[j][i+1].T)/2.0;
636: TW = (x[j][i].T + x[j][i-1].T)/2.0;
637: fN = wN*TN*dx; fS = wS*TS*dx;
638: fE = uE*TE*dz; fW = uW*TW*dz;
640: } else {
641: /* Fromm advection scheme */
642: 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
643: - 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;
644: 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
645: - 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;
646: 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
647: - 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;
648: 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
649: - 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;
650: }
652: residual -= (fE - fW + fN - fS);
654: return residual;
655: }
657: /*---------------------------------------------------------------------*/
658: /* computes the shear stress---used on the boundaries */
659: PETSC_STATIC_INLINE PetscScalar ShearStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
660: /*---------------------------------------------------------------------*/
661: {
662: Parameter *param=user->param;
663: GridInfo *grid =user->grid;
664: PetscInt ilim =grid->ni-1, jlim=grid->nj-1;
665: PetscScalar uN, uS, wE, wW;
667: if (j<=grid->jlid || i<j || i==ilim || j==jlim) return EPS_ZERO;
669: if (ipos==CELL_CENTER) { /* on cell center */
671: wE = WInterp(x,i,j-1);
672: if (i==j) {
673: wW = param->sb;
674: uN = param->cb;
675: } else {
676: wW = WInterp(x,i-1,j-1);
677: uN = UInterp(x,i-1,j);
678: }
679: if (j==grid->jlid+1) uS = 0.0;
680: else uS = UInterp(x,i-1,j-1);
682: } else { /* on cell corner */
684: uN = x[j+1][i].u; uS = x[j][i].u;
685: wW = x[j][i].w; wE = x[j][i+1].w;
687: }
689: return (uN-uS)/grid->dz + (wE-wW)/grid->dx;
690: }
692: /*---------------------------------------------------------------------*/
693: /* computes the normal stress---used on the boundaries */
694: PETSC_STATIC_INLINE PetscScalar XNormalStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
695: /*---------------------------------------------------------------------*/
696: {
697: Parameter *param=user->param;
698: GridInfo *grid =user->grid;
699: PetscScalar dx = grid->dx, dz=grid->dz;
700: PetscInt ilim =grid->ni-1, jlim=grid->nj-1, ivisc;
701: PetscScalar epsC =0.0, etaC, TC, uE, uW, pC, z_scale;
702: if (i<j || j<=grid->jlid) return EPS_ZERO;
704: ivisc=param->ivisc; z_scale = param->z_scale;
706: if (ipos==CELL_CENTER) { /* on cell center */
708: TC = param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*z_scale);
709: if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CENTER,user);
710: etaC = Viscosity(TC,epsC,dz*j,param);
712: uW = x[j][i-1].u; uE = x[j][i].u;
713: pC = x[j][i].p;
715: } else { /* on cell corner */
716: if (i==ilim || j==jlim) return EPS_ZERO;
718: TC = param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*z_scale);
719: if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CORNER,user);
720: etaC = Viscosity(TC,epsC,dz*(j+0.5),param);
722: if (i==j) uW = param->sb;
723: else uW = UInterp(x,i-1,j);
724: uE = UInterp(x,i,j); pC = PInterp(x,i,j);
725: }
727: return 2.0*etaC*(uE-uW)/dx - pC;
728: }
730: /*---------------------------------------------------------------------*/
731: /* computes the normal stress---used on the boundaries */
732: PETSC_STATIC_INLINE PetscScalar ZNormalStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
733: /*---------------------------------------------------------------------*/
734: {
735: Parameter *param=user->param;
736: GridInfo *grid =user->grid;
737: PetscScalar dz =grid->dz;
738: PetscInt ilim =grid->ni-1, jlim=grid->nj-1, ivisc;
739: PetscScalar epsC =0.0, etaC, TC;
740: PetscScalar pC, wN, wS, z_scale;
741: if (i<j || j<=grid->jlid) return EPS_ZERO;
743: ivisc=param->ivisc; z_scale = param->z_scale;
745: if (ipos==CELL_CENTER) { /* on cell center */
747: TC = param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*z_scale);
748: if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CENTER,user);
749: etaC = Viscosity(TC,epsC,dz*j,param);
750: wN = x[j][i].w; wS = x[j-1][i].w; pC = x[j][i].p;
752: } else { /* on cell corner */
753: if ((i==ilim) || (j==jlim)) return EPS_ZERO;
755: TC = param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*z_scale);
756: if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CORNER,user);
757: etaC = Viscosity(TC,epsC,dz*(j+0.5),param);
758: if (i==j) wN = param->sb;
759: else wN = WInterp(x,i,j);
760: wS = WInterp(x,i,j-1); pC = PInterp(x,i,j);
761: }
763: return 2.0*etaC*(wN-wS)/dz - pC;
764: }
766: /*---------------------------------------------------------------------*/
768: /*=====================================================================
769: INITIALIZATION, POST-PROCESSING AND OUTPUT FUNCTIONS
770: =====================================================================*/
772: /*---------------------------------------------------------------------*/
773: /* initializes the problem parameters and checks for
774: command line changes */
775: PetscErrorCode SetParams(Parameter *param, GridInfo *grid)
776: /*---------------------------------------------------------------------*/
777: {
778: PetscErrorCode ierr, ierr_out=0;
779: PetscReal SEC_PER_YR = 3600.00*24.00*365.2500;
780: PetscReal alpha_g_on_cp_units_inverse_km=4.0e-5*9.8;
782: /* domain geometry */
783: param->slab_dip = 45.0;
784: param->width = 320.0; /* km */
785: param->depth = 300.0; /* km */
786: param->lid_depth = 35.0; /* km */
787: param->fault_depth = 35.0; /* km */
789: PetscOptionsGetReal(NULL,NULL,"-slab_dip",&(param->slab_dip),NULL);
790: PetscOptionsGetReal(NULL,NULL,"-width",&(param->width),NULL);
791: PetscOptionsGetReal(NULL,NULL,"-depth",&(param->depth),NULL);
792: PetscOptionsGetReal(NULL,NULL,"-lid_depth",&(param->lid_depth),NULL);
793: PetscOptionsGetReal(NULL,NULL,"-fault_depth",&(param->fault_depth),NULL);
795: param->slab_dip = param->slab_dip*PETSC_PI/180.0; /* radians */
797: /* grid information */
798: PetscOptionsGetInt(NULL,NULL, "-jfault",&(grid->jfault),NULL);
799: grid->ni = 82;
800: PetscOptionsGetInt(NULL,NULL, "-ni",&(grid->ni),NULL);
802: grid->dx = param->width/((PetscReal)(grid->ni-2)); /* km */
803: grid->dz = grid->dx*PetscTanReal(param->slab_dip); /* km */
804: grid->nj = (PetscInt)(param->depth/grid->dz + 3.0); /* gridpoints*/
805: param->depth = grid->dz*(grid->nj-2); /* km */
806: grid->inose = 0; /* gridpoints*/
807: PetscOptionsGetInt(NULL,NULL,"-inose",&(grid->inose),NULL);
808: grid->bx = DM_BOUNDARY_NONE;
809: grid->by = DM_BOUNDARY_NONE;
810: grid->stencil = DMDA_STENCIL_BOX;
811: grid->dof = 4;
812: grid->stencil_width = 2;
813: grid->mglevels = 1;
815: /* boundary conditions */
816: param->pv_analytic = PETSC_FALSE;
817: param->ibound = BC_NOSTRESS;
818: PetscOptionsGetInt(NULL,NULL,"-ibound",&(param->ibound),NULL);
820: /* physical constants */
821: param->slab_velocity = 5.0; /* cm/yr */
822: param->slab_age = 50.0; /* Ma */
823: param->lid_age = 50.0; /* Ma */
824: param->kappa = 0.7272e-6; /* m^2/sec */
825: param->potentialT = 1300.0; /* degrees C */
827: PetscOptionsGetReal(NULL,NULL,"-slab_velocity",&(param->slab_velocity),NULL);
828: PetscOptionsGetReal(NULL,NULL,"-slab_age",&(param->slab_age),NULL);
829: PetscOptionsGetReal(NULL,NULL,"-lid_age",&(param->lid_age),NULL);
830: PetscOptionsGetReal(NULL,NULL,"-kappa",&(param->kappa),NULL);
831: PetscOptionsGetReal(NULL,NULL,"-potentialT",&(param->potentialT),NULL);
833: /* viscosity */
834: param->ivisc = 3; /* 0=isovisc, 1=difn creep, 2=disl creep, 3=full */
835: param->eta0 = 1e24; /* Pa-s */
836: param->visc_cutoff = 0.0; /* factor of eta_0 */
837: param->continuation = 1.0;
839: /* constants for diffusion creep */
840: param->diffusion.A = 1.8e7; /* Pa-s */
841: param->diffusion.n = 1.0; /* dim'less */
842: param->diffusion.Estar = 375e3; /* J/mol */
843: param->diffusion.Vstar = 5e-6; /* m^3/mol */
845: /* constants for param->dislocationocation creep */
846: param->dislocation.A = 2.8969e4; /* Pa-s */
847: param->dislocation.n = 3.5; /* dim'less */
848: param->dislocation.Estar = 530e3; /* J/mol */
849: param->dislocation.Vstar = 14e-6; /* m^3/mol */
851: PetscOptionsGetInt(NULL,NULL, "-ivisc",&(param->ivisc),NULL);
852: PetscOptionsGetReal(NULL,NULL,"-visc_cutoff",&(param->visc_cutoff),NULL);
854: param->output_ivisc = param->ivisc;
856: PetscOptionsGetInt(NULL,NULL,"-output_ivisc",&(param->output_ivisc),NULL);
857: PetscOptionsGetReal(NULL,NULL,"-vstar",&(param->dislocation.Vstar),NULL);
859: /* output options */
860: param->quiet = PETSC_FALSE;
861: param->param_test = PETSC_FALSE;
863: PetscOptionsHasName(NULL,NULL,"-quiet",&(param->quiet));
864: PetscOptionsHasName(NULL,NULL,"-test",&(param->param_test));
865: PetscOptionsGetString(NULL,NULL,"-file",param->filename,sizeof(param->filename),&(param->output_to_file));
867: /* advection */
868: param->adv_scheme = ADVECT_FROMM; /* advection scheme: 0=finite vol, 1=Fromm */
870: PetscOptionsGetInt(NULL,NULL,"-adv_scheme",&(param->adv_scheme),NULL);
872: /* misc. flags */
873: param->stop_solve = PETSC_FALSE;
874: param->interrupted = PETSC_FALSE;
875: param->kspmon = PETSC_FALSE;
876: param->toggle_kspmon = PETSC_FALSE;
878: /* derived parameters for slab angle */
879: param->sb = PetscSinReal(param->slab_dip);
880: param->cb = PetscCosReal(param->slab_dip);
881: param->c = param->slab_dip*param->sb/(param->slab_dip*param->slab_dip-param->sb*param->sb);
882: param->d = (param->slab_dip*param->cb-param->sb)/(param->slab_dip*param->slab_dip-param->sb*param->sb);
884: /* length, velocity and time scale for non-dimensionalization */
885: param->L = PetscMin(param->width,param->depth); /* km */
886: param->V = param->slab_velocity/100.0/SEC_PER_YR; /* m/sec */
888: /* other unit conversions and derived parameters */
889: param->scaled_width = param->width/param->L; /* dim'less */
890: param->scaled_depth = param->depth/param->L; /* dim'less */
891: param->lid_depth = param->lid_depth/param->L; /* dim'less */
892: param->fault_depth = param->fault_depth/param->L; /* dim'less */
893: grid->dx = grid->dx/param->L; /* dim'less */
894: grid->dz = grid->dz/param->L; /* dim'less */
895: grid->jlid = (PetscInt)(param->lid_depth/grid->dz); /* gridcells */
896: grid->jfault = (PetscInt)(param->fault_depth/grid->dz); /* gridcells */
897: param->lid_depth = grid->jlid*grid->dz; /* dim'less */
898: param->fault_depth = grid->jfault*grid->dz; /* dim'less */
899: grid->corner = grid->jlid+1; /* gridcells */
900: param->peclet = param->V /* m/sec */
901: * param->L*1000.0 /* m */
902: / param->kappa; /* m^2/sec */
903: param->z_scale = param->L * alpha_g_on_cp_units_inverse_km;
904: param->skt = PetscSqrtReal(param->kappa*param->slab_age*SEC_PER_YR);
905: PetscOptionsGetReal(NULL,NULL,"-peclet",&(param->peclet),NULL);
907: return ierr_out;
908: }
910: /*---------------------------------------------------------------------*/
911: /* prints a report of the problem parameters to stdout */
912: PetscErrorCode ReportParams(Parameter *param, GridInfo *grid)
913: /*---------------------------------------------------------------------*/
914: {
915: PetscErrorCode ierr, ierr_out=0;
916: char date[30];
918: PetscGetDate(date,30);
920: if (!(param->quiet)) {
921: PetscPrintf(PETSC_COMM_WORLD,"---------------------BEGIN ex30 PARAM REPORT-------------------\n");
922: PetscPrintf(PETSC_COMM_WORLD,"Domain: \n");
923: PetscPrintf(PETSC_COMM_WORLD," Width = %g km, Depth = %g km\n",(double)param->width,(double)param->depth);
924: 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);
925: 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));
927: PetscPrintf(PETSC_COMM_WORLD,"\nGrid: \n");
928: 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));
929: PetscPrintf(PETSC_COMM_WORLD," jlid = %3D jfault = %3D \n",grid->jlid,grid->jfault);
930: PetscPrintf(PETSC_COMM_WORLD," Pe = %g\n",(double)param->peclet);
932: PetscPrintf(PETSC_COMM_WORLD,"\nRheology:");
933: if (param->ivisc==VISC_CONST) {
934: PetscPrintf(PETSC_COMM_WORLD," Isoviscous \n");
935: if (param->pv_analytic) {
936: PetscPrintf(PETSC_COMM_WORLD," Pressure and Velocity prescribed! \n");
937: }
938: } else if (param->ivisc==VISC_DIFN) {
939: PetscPrintf(PETSC_COMM_WORLD," Diffusion Creep (T-Dependent Newtonian) \n");
940: PetscPrintf(PETSC_COMM_WORLD," Viscosity range: %g--%g Pa-sec \n",(double)param->eta0,(double)(param->visc_cutoff*param->eta0));
941: } else if (param->ivisc==VISC_DISL) {
942: PetscPrintf(PETSC_COMM_WORLD," Dislocation Creep (T-Dependent Non-Newtonian) \n");
943: PetscPrintf(PETSC_COMM_WORLD," Viscosity range: %g--%g Pa-sec \n",(double)param->eta0,(double)(param->visc_cutoff*param->eta0));
944: } else if (param->ivisc==VISC_FULL) {
945: PetscPrintf(PETSC_COMM_WORLD," Full Rheology \n");
946: PetscPrintf(PETSC_COMM_WORLD," Viscosity range: %g--%g Pa-sec \n",(double)param->eta0,(double)(param->visc_cutoff*param->eta0));
947: } else {
948: PetscPrintf(PETSC_COMM_WORLD," Invalid! \n");
949: ierr_out = 1;
950: }
952: PetscPrintf(PETSC_COMM_WORLD,"Boundary condition:");
953: if (param->ibound==BC_ANALYTIC) {
954: PetscPrintf(PETSC_COMM_WORLD," Isoviscous Analytic Dirichlet \n");
955: } else if (param->ibound==BC_NOSTRESS) {
956: PetscPrintf(PETSC_COMM_WORLD," Stress-Free (normal & shear stress)\n");
957: } else if (param->ibound==BC_EXPERMNT) {
958: PetscPrintf(PETSC_COMM_WORLD," Experimental boundary condition \n");
959: } else {
960: PetscPrintf(PETSC_COMM_WORLD," Invalid! \n");
961: ierr_out = 1;
962: }
964: if (param->output_to_file)
965: #if defined(PETSC_HAVE_MATLAB_ENGINE)
966: PetscPrintf(PETSC_COMM_WORLD,"Output Destination: Mat file \"%s\"\n",param->filename);
967: #else
968: PetscPrintf(PETSC_COMM_WORLD,"Output Destination: PETSc binary file \"%s\"\n",param->filename);
969: #endif
970: if (param->output_ivisc != param->ivisc) {
971: PetscPrintf(PETSC_COMM_WORLD," Output viscosity: -ivisc %D\n",param->output_ivisc);
972: }
974: PetscPrintf(PETSC_COMM_WORLD,"---------------------END ex30 PARAM REPORT---------------------\n");
975: }
976: if (param->param_test) PetscEnd();
977: return ierr_out;
978: }
980: /* ------------------------------------------------------------------- */
981: /* generates an inital guess using the analytic solution for isoviscous
982: corner flow */
983: PetscErrorCode Initialize(DM da)
984: /* ------------------------------------------------------------------- */
985: {
986: AppCtx *user;
987: Parameter *param;
988: GridInfo *grid;
989: PetscInt i,j,is,js,im,jm;
991: Field **x;
992: Vec Xguess;
994: /* Get the fine grid */
995: DMGetApplicationContext(da,&user);
996: Xguess = user->Xguess;
997: param = user->param;
998: grid = user->grid;
999: DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1000: DMDAVecGetArray(da,Xguess,(void**)&x);
1002: /* Compute initial guess */
1003: for (j=js; j<js+jm; j++) {
1004: for (i=is; i<is+im; i++) {
1005: if (i<j) x[j][i].u = param->cb;
1006: else if (j<=grid->jlid) x[j][i].u = 0.0;
1007: else x[j][i].u = HorizVelocity(i,j,user);
1009: if (i<=j) x[j][i].w = param->sb;
1010: else if (j<=grid->jlid) x[j][i].w = 0.0;
1011: else x[j][i].w = VertVelocity(i,j,user);
1013: if (i<j || j<=grid->jlid) x[j][i].p = 0.0;
1014: else x[j][i].p = Pressure(i,j,user);
1016: x[j][i].T = PetscMin(grid->dz*(j-0.5),1.0);
1017: }
1018: }
1020: /* Restore x to Xguess */
1021: DMDAVecRestoreArray(da,Xguess,(void**)&x);
1023: return 0;
1024: }
1026: /*---------------------------------------------------------------------*/
1027: /* controls output to a file */
1028: PetscErrorCode DoOutput(SNES snes, PetscInt its)
1029: /*---------------------------------------------------------------------*/
1030: {
1031: AppCtx *user;
1032: Parameter *param;
1033: GridInfo *grid;
1034: PetscInt ivt;
1036: PetscMPIInt rank;
1037: PetscViewer viewer;
1038: Vec res, pars;
1039: MPI_Comm comm;
1040: DM da;
1042: SNESGetDM(snes,&da);
1043: DMGetApplicationContext(da,&user);
1044: param = user->param;
1045: grid = user->grid;
1046: ivt = param->ivisc;
1048: param->ivisc = param->output_ivisc;
1050: /* compute final residual and final viscosity/strain rate fields */
1051: SNESGetFunction(snes, &res, NULL, NULL);
1052: ViscosityField(da, user->x, user->Xguess);
1054: /* get the communicator and the rank of the processor */
1055: PetscObjectGetComm((PetscObject)snes, &comm);
1056: MPI_Comm_rank(comm, &rank);
1058: if (param->output_to_file) { /* send output to binary file */
1059: VecCreate(comm, &pars);
1060: if (!rank) { /* on processor 0 */
1061: VecSetSizes(pars, 20, PETSC_DETERMINE);
1062: VecSetFromOptions(pars);
1063: VecSetValue(pars,0, (PetscScalar)(grid->ni),INSERT_VALUES);
1064: VecSetValue(pars,1, (PetscScalar)(grid->nj),INSERT_VALUES);
1065: VecSetValue(pars,2, (PetscScalar)(grid->dx),INSERT_VALUES);
1066: VecSetValue(pars,3, (PetscScalar)(grid->dz),INSERT_VALUES);
1067: VecSetValue(pars,4, (PetscScalar)(param->L),INSERT_VALUES);
1068: VecSetValue(pars,5, (PetscScalar)(param->V),INSERT_VALUES);
1069: /* skipped 6 intentionally */
1070: VecSetValue(pars,7, (PetscScalar)(param->slab_dip),INSERT_VALUES);
1071: VecSetValue(pars,8, (PetscScalar)(grid->jlid),INSERT_VALUES);
1072: VecSetValue(pars,9, (PetscScalar)(param->lid_depth),INSERT_VALUES);
1073: VecSetValue(pars,10,(PetscScalar)(grid->jfault),INSERT_VALUES);
1074: VecSetValue(pars,11,(PetscScalar)(param->fault_depth),INSERT_VALUES);
1075: VecSetValue(pars,12,(PetscScalar)(param->potentialT),INSERT_VALUES);
1076: VecSetValue(pars,13,(PetscScalar)(param->ivisc),INSERT_VALUES);
1077: VecSetValue(pars,14,(PetscScalar)(param->visc_cutoff),INSERT_VALUES);
1078: VecSetValue(pars,15,(PetscScalar)(param->ibound),INSERT_VALUES);
1079: VecSetValue(pars,16,(PetscScalar)(its),INSERT_VALUES);
1080: } else { /* on some other processor */
1081: VecSetSizes(pars, 0, PETSC_DETERMINE);
1082: VecSetFromOptions(pars);
1083: }
1084: VecAssemblyBegin(pars); VecAssemblyEnd(pars);
1086: /* create viewer */
1087: #if defined(PETSC_HAVE_MATLAB_ENGINE)
1088: PetscViewerMatlabOpen(PETSC_COMM_WORLD,param->filename,FILE_MODE_WRITE,&viewer);
1089: #else
1090: PetscViewerBinaryOpen(PETSC_COMM_WORLD,param->filename,FILE_MODE_WRITE,&viewer);
1091: #endif
1093: /* send vectors to viewer */
1094: PetscObjectSetName((PetscObject)res,"res");
1095: VecView(res,viewer);
1096: PetscObjectSetName((PetscObject)user->x,"out");
1097: VecView(user->x, viewer);
1098: PetscObjectSetName((PetscObject)(user->Xguess),"aux");
1099: VecView(user->Xguess, viewer);
1100: StressField(da); /* compute stress fields */
1101: PetscObjectSetName((PetscObject)(user->Xguess),"str");
1102: VecView(user->Xguess, viewer);
1103: PetscObjectSetName((PetscObject)pars,"par");
1104: VecView(pars, viewer);
1106: /* destroy viewer and vector */
1107: PetscViewerDestroy(&viewer);
1108: VecDestroy(&pars);
1109: }
1111: param->ivisc = ivt;
1112: return 0;
1113: }
1115: /* ------------------------------------------------------------------- */
1116: /* Compute both the second invariant of the strain rate tensor and the viscosity, at both cell centers and cell corners */
1117: PetscErrorCode ViscosityField(DM da, Vec X, Vec V)
1118: /* ------------------------------------------------------------------- */
1119: {
1120: AppCtx *user;
1121: Parameter *param;
1122: GridInfo *grid;
1123: Vec localX;
1124: Field **v, **x;
1125: PetscReal eps, /* dx,*/ dz, T, epsC, TC;
1126: PetscInt i,j,is,js,im,jm,ilim,jlim,ivt;
1130: DMGetApplicationContext(da,&user);
1131: param = user->param;
1132: grid = user->grid;
1133: ivt = param->ivisc;
1134: param->ivisc = param->output_ivisc;
1136: DMGetLocalVector(da, &localX);
1137: DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX);
1138: DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX);
1139: DMDAVecGetArray(da,localX,(void**)&x);
1140: DMDAVecGetArray(da,V,(void**)&v);
1142: /* Parameters */
1143: /* dx = grid->dx; */ dz = grid->dz;
1145: ilim = grid->ni-1; jlim = grid->nj-1;
1147: /* Compute real temperature, strain rate and viscosity */
1148: DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1149: for (j=js; j<js+jm; j++) {
1150: for (i=is; i<is+im; i++) {
1151: T = PetscRealPart(param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*param->z_scale));
1152: if (i<ilim && j<jlim) {
1153: TC = PetscRealPart(param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*param->z_scale));
1154: } else {
1155: TC = T;
1156: }
1157: eps = PetscRealPart((CalcSecInv(x,i,j,CELL_CENTER,user)));
1158: epsC = PetscRealPart(CalcSecInv(x,i,j,CELL_CORNER,user));
1160: v[j][i].u = eps;
1161: v[j][i].w = epsC;
1162: v[j][i].p = Viscosity(T,eps,dz*(j-0.5),param);
1163: v[j][i].T = Viscosity(TC,epsC,dz*j,param);
1164: }
1165: }
1166: DMDAVecRestoreArray(da,V,(void**)&v);
1167: DMDAVecRestoreArray(da,localX,(void**)&x);
1168: DMRestoreLocalVector(da, &localX);
1170: param->ivisc = ivt;
1171: return(0);
1172: }
1174: /* ------------------------------------------------------------------- */
1175: /* post-processing: compute stress everywhere */
1176: PetscErrorCode StressField(DM da)
1177: /* ------------------------------------------------------------------- */
1178: {
1179: AppCtx *user;
1180: PetscInt i,j,is,js,im,jm;
1182: Vec locVec;
1183: Field **x, **y;
1185: DMGetApplicationContext(da,&user);
1187: /* Get the fine grid of Xguess and X */
1188: DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1189: DMDAVecGetArray(da,user->Xguess,(void**)&x);
1191: DMGetLocalVector(da, &locVec);
1192: DMGlobalToLocalBegin(da, user->x, INSERT_VALUES, locVec);
1193: DMGlobalToLocalEnd(da, user->x, INSERT_VALUES, locVec);
1194: DMDAVecGetArray(da,locVec,(void**)&y);
1196: /* Compute stress on the corner points */
1197: for (j=js; j<js+jm; j++) {
1198: for (i=is; i<is+im; i++) {
1199: x[j][i].u = ShearStress(y,i,j,CELL_CENTER,user);
1200: x[j][i].w = ShearStress(y,i,j,CELL_CORNER,user);
1201: x[j][i].p = XNormalStress(y,i,j,CELL_CENTER,user);
1202: x[j][i].T = ZNormalStress(y,i,j,CELL_CENTER,user);
1203: }
1204: }
1206: /* Restore the fine grid of Xguess and X */
1207: DMDAVecRestoreArray(da,user->Xguess,(void**)&x);
1208: DMDAVecRestoreArray(da,locVec,(void**)&y);
1209: DMRestoreLocalVector(da, &locVec);
1210: return 0;
1211: }
1213: /*=====================================================================
1214: UTILITY FUNCTIONS
1215: =====================================================================*/
1217: /*---------------------------------------------------------------------*/
1218: /* returns the velocity of the subducting slab and handles fault nodes
1219: for BC */
1220: PETSC_STATIC_INLINE PetscScalar SlabVel(char c, PetscInt i, PetscInt j, AppCtx *user)
1221: /*---------------------------------------------------------------------*/
1222: {
1223: Parameter *param = user->param;
1224: GridInfo *grid = user->grid;
1226: if (c=='U' || c=='u') {
1227: if (i<j-1) return param->cb;
1228: else if (j<=grid->jfault) return 0.0;
1229: else return param->cb;
1231: } else {
1232: if (i<j) return param->sb;
1233: else if (j<=grid->jfault) return 0.0;
1234: else return param->sb;
1235: }
1236: }
1238: /*---------------------------------------------------------------------*/
1239: /* solution to diffusive half-space cooling model for BC */
1240: PETSC_STATIC_INLINE PetscScalar PlateModel(PetscInt j, PetscInt plate, AppCtx *user)
1241: /*---------------------------------------------------------------------*/
1242: {
1243: Parameter *param = user->param;
1244: PetscScalar z;
1245: if (plate==PLATE_LID) z = (j-0.5)*user->grid->dz;
1246: else z = (j-0.5)*user->grid->dz*param->cb; /* PLATE_SLAB */
1247: #if defined(PETSC_HAVE_ERF)
1248: return (PetscReal)(erf((double)PetscRealPart(z*param->L/2.0/param->skt)));
1249: #else
1250: (*PetscErrorPrintf)("erf() not available on this machine\n");
1251: MPI_Abort(PETSC_COMM_SELF,1);
1252: #endif
1253: }
1255: /*=====================================================================
1256: INTERACTIVE SIGNAL HANDLING
1257: =====================================================================*/
1259: /* ------------------------------------------------------------------- */
1260: PetscErrorCode SNESConverged_Interactive(SNES snes, PetscInt it,PetscReal xnorm, PetscReal snorm, PetscReal fnorm, SNESConvergedReason *reason, void *ctx)
1261: /* ------------------------------------------------------------------- */
1262: {
1263: AppCtx *user = (AppCtx*) ctx;
1264: Parameter *param = user->param;
1265: KSP ksp;
1269: if (param->interrupted) {
1270: param->interrupted = PETSC_FALSE;
1271: PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: exiting SNES solve. \n");
1272: *reason = SNES_CONVERGED_FNORM_ABS;
1273: return(0);
1274: } else if (param->toggle_kspmon) {
1275: param->toggle_kspmon = PETSC_FALSE;
1277: SNESGetKSP(snes, &ksp);
1279: if (param->kspmon) {
1280: KSPMonitorCancel(ksp);
1282: param->kspmon = PETSC_FALSE;
1283: PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: deactivating ksp singular value monitor. \n");
1284: } else {
1285: PetscViewerAndFormat *vf;
1286: PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_DEFAULT,&vf);
1287: KSPMonitorSet(ksp,(PetscErrorCode (*)(KSP,PetscInt,PetscReal,void*))KSPMonitorSingularValue,vf,(PetscErrorCode (*)(void**))PetscViewerAndFormatDestroy);
1289: param->kspmon = PETSC_TRUE;
1290: PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: activating ksp singular value monitor. \n");
1291: }
1292: }
1293: PetscFunctionReturn(SNESConvergedDefault(snes,it,xnorm,snorm,fnorm,reason,ctx));
1294: }
1296: /* ------------------------------------------------------------------- */
1297: #include <signal.h>
1298: PetscErrorCode InteractiveHandler(int signum, void *ctx)
1299: /* ------------------------------------------------------------------- */
1300: {
1301: AppCtx *user = (AppCtx*) ctx;
1302: Parameter *param = user->param;
1304: if (signum == SIGILL) {
1305: param->toggle_kspmon = PETSC_TRUE;
1306: #if !defined(PETSC_MISSING_SIGCONT)
1307: } else if (signum == SIGCONT) {
1308: param->interrupted = PETSC_TRUE;
1309: #endif
1310: #if !defined(PETSC_MISSING_SIGURG)
1311: } else if (signum == SIGURG) {
1312: param->stop_solve = PETSC_TRUE;
1313: #endif
1314: }
1315: return 0;
1316: }
1318: /*---------------------------------------------------------------------*/
1319: /* main call-back function that computes the processor-local piece
1320: of the residual */
1321: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,Field **x,Field **f,void *ptr)
1322: /*---------------------------------------------------------------------*/
1323: {
1324: AppCtx *user = (AppCtx*)ptr;
1325: Parameter *param = user->param;
1326: GridInfo *grid = user->grid;
1327: PetscScalar mag_w, mag_u;
1328: PetscInt i,j,mx,mz,ilim,jlim;
1329: PetscInt is,ie,js,je,ibound; /* ,ivisc */
1332: /* Define global and local grid parameters */
1333: mx = info->mx; mz = info->my;
1334: ilim = mx-1; jlim = mz-1;
1335: is = info->xs; ie = info->xs+info->xm;
1336: js = info->ys; je = info->ys+info->ym;
1338: /* Define geometric and numeric parameters */
1339: /* ivisc = param->ivisc; */ ibound = param->ibound;
1341: for (j=js; j<je; j++) {
1342: for (i=is; i<ie; i++) {
1344: /************* X-MOMENTUM/VELOCITY *************/
1345: if (i<j) f[j][i].u = x[j][i].u - SlabVel('U',i,j,user);
1346: else if (j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1347: /* in the lithospheric lid */
1348: f[j][i].u = x[j][i].u - 0.0;
1349: } else if (i==ilim) {
1350: /* on the right side boundary */
1351: if (ibound==BC_ANALYTIC) {
1352: f[j][i].u = x[j][i].u - HorizVelocity(i,j,user);
1353: } else {
1354: f[j][i].u = XNormalStress(x,i,j,CELL_CENTER,user) - EPS_ZERO;
1355: }
1357: } else if (j==jlim) {
1358: /* on the bottom boundary */
1359: if (ibound==BC_ANALYTIC) {
1360: f[j][i].u = x[j][i].u - HorizVelocity(i,j,user);
1361: } else if (ibound==BC_NOSTRESS) {
1362: f[j][i].u = XMomentumResidual(x,i,j,user);
1363: } else {
1364: /* experimental boundary condition */
1365: }
1367: } else {
1368: /* in the mantle wedge */
1369: f[j][i].u = XMomentumResidual(x,i,j,user);
1370: }
1372: /************* Z-MOMENTUM/VELOCITY *************/
1373: if (i<=j) {
1374: f[j][i].w = x[j][i].w - SlabVel('W',i,j,user);
1376: } else if (j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1377: /* in the lithospheric lid */
1378: f[j][i].w = x[j][i].w - 0.0;
1380: } else if (j==jlim) {
1381: /* on the bottom boundary */
1382: if (ibound==BC_ANALYTIC) {
1383: f[j][i].w = x[j][i].w - VertVelocity(i,j,user);
1384: } else {
1385: f[j][i].w = ZNormalStress(x,i,j,CELL_CENTER,user) - EPS_ZERO;
1386: }
1388: } else if (i==ilim) {
1389: /* on the right side boundary */
1390: if (ibound==BC_ANALYTIC) {
1391: f[j][i].w = x[j][i].w - VertVelocity(i,j,user);
1392: } else if (ibound==BC_NOSTRESS) {
1393: f[j][i].w = ZMomentumResidual(x,i,j,user);
1394: } else {
1395: /* experimental boundary condition */
1396: }
1398: } else {
1399: /* in the mantle wedge */
1400: f[j][i].w = ZMomentumResidual(x,i,j,user);
1401: }
1403: /************* CONTINUITY/PRESSURE *************/
1404: if (i<j || j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1405: /* in the lid or slab */
1406: f[j][i].p = x[j][i].p;
1408: } else if ((i==ilim || j==jlim) && ibound==BC_ANALYTIC) {
1409: /* on an analytic boundary */
1410: f[j][i].p = x[j][i].p - Pressure(i,j,user);
1412: } else {
1413: /* in the mantle wedge */
1414: f[j][i].p = ContinuityResidual(x,i,j,user);
1415: }
1417: /************* TEMPERATURE *************/
1418: if (j==0) {
1419: /* on the surface */
1420: f[j][i].T = x[j][i].T + x[j+1][i].T + PetscMax(PetscRealPart(x[j][i].T),0.0);
1422: } else if (i==0) {
1423: /* slab inflow boundary */
1424: f[j][i].T = x[j][i].T - PlateModel(j,PLATE_SLAB,user);
1426: } else if (i==ilim) {
1427: /* right side boundary */
1428: mag_u = 1.0 - PetscPowRealInt((1.0-PetscMax(PetscMin(PetscRealPart(x[j][i-1].u)/param->cb,1.0),0.0)), 5);
1429: 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);
1431: } else if (j==jlim) {
1432: /* bottom boundary */
1433: mag_w = 1.0 - PetscPowRealInt((1.0-PetscMax(PetscMin(PetscRealPart(x[j-1][i].w)/param->sb,1.0),0.0)), 5);
1434: f[j][i].T = x[j][i].T - mag_w*x[j-1][i-1].T - (1.0-mag_w);
1436: } else {
1437: /* in the mantle wedge */
1438: f[j][i].T = EnergyResidual(x,i,j,user);
1439: }
1440: }
1441: }
1442: return(0);
1443: }
1446: /*TEST
1448: build:
1449: requires: !complex erf
1451: test:
1452: args: -ni 18
1453: filter: grep -v Destination
1454: requires: !single
1456: TEST*/