Actual source code: ex52.c

petsc-master 2020-10-26
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  1: static char help[] = "Simple Advection-diffusion equation solved using FVM in DMPLEX\n";

  3: /*
  4:    Solves the simple advection equation given by

  6:    q_t + u (q_x) + v (q_y) - D (q_xx + q_yy) = 0 using FVM and First Order Upwind discretization.

  8:    with a user defined initial condition.

 10:    with dirichlet/neumann conditions on the four boundaries of the domain.

 12:    User can define the mesh parameters either in the command line or inside
 13:    the ProcessOptions() routine.

 15:    Contributed by: Mukkund Sunjii, Domenico Lahaye
 16: */

 18: #include <petscdmplex.h>
 19: #include <petscts.h>
 20: #include <petscblaslapack.h>

 22: #if defined(PETSC_HAVE_CGNS)
 23: #undef I
 24: #include <cgnslib.h>
 25: #endif
 26: /*
 27:    User-defined routines
 28: */
 29: extern PetscErrorCode FormFunction(TS, PetscReal, Vec, Vec, void *), FormInitialSolution(DM, Vec);
 30: extern PetscErrorCode MyTSMonitor(TS, PetscInt, PetscReal, Vec, void *);
 31: extern PetscErrorCode MySNESMonitor(SNES, PetscInt, PetscReal, PetscViewerAndFormat *);

 33: /* Defining the usr defined context */
 34: typedef struct {
 35:     DM          da;
 36:     PetscBool   interpolate;                  /* Generate intermediate mesh elements */
 37:     char        filename[PETSC_MAX_PATH_LEN]; /* Mesh filename */
 38:     PetscInt    dim;
 39:     PetscScalar diffusion;
 40:     PetscReal   u, v;
 41:     PetscScalar delta_x, delta_y;
 42:     PetscInt    cells[2];
 43: } AppCtx;

 45: /* Options for the scenario */
 46: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
 47: {

 51:     options->interpolate = PETSC_TRUE;
 52:     options->filename[0] = '\0';
 53:     options->dim = 2;
 54:     options->u = 2.5;
 55:     options->v = 0.0;
 56:     options->cells[0] = 20;
 57:     options->cells[1] = 20;
 58:     options->diffusion = 0.0;

 60:     PetscOptionsBegin(comm, "", "Meshing Problem Options", "DMPLEX");
 61:     PetscOptionsBool("-interpolate", "Generate intermediate mesh elements", "advection_DMPLEX.c",options->interpolate, &options->interpolate, NULL);
 62:     PetscOptionsString("-filename", "The mesh file", "advection_DMPLEX.c", options->filename, options->filename, sizeof(options->filename), NULL);
 63:     PetscOptionsRangeInt("-dim", "Problem dimension used for the non-file mesh.", "ex7.c", options->dim, &options->dim, NULL,1,3);
 64:     PetscOptionsReal("-u", "The x component of the convective coefficient", "advection_DMPLEX.c", options->u, &options->u, NULL);
 65:     PetscOptionsReal("-v", "The y component of the convective coefficient", "advection_DMPLEX.c", options->v, &options->v, NULL);
 66:     PetscOptionsScalar("-diffus", "The diffusive coefficient", "advection_DMPLEX.c", options->diffusion, &options->diffusion, NULL);
 67:     PetscOptionsEnd();
 68:     return(0);
 69: }

 71: /*
 72:   User can provide the file containing the mesh.
 73:   Or can generate the mesh using DMPlexCreateBoxMesh with the specified options.
 74: */
 75: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
 76: {
 77:     size_t len;
 80:     PetscStrlen(user->filename, &len);
 81:     if (!len) {
 82:         DMLabel label;
 83:         DMPlexCreateBoxMesh(comm, user->dim, PETSC_FALSE, user->cells, NULL, NULL, NULL, user->interpolate, dm);
 84:         /* Mark boundary and set BC */
 85:         DMCreateLabel(*dm, "boundary");
 86:         DMGetLabel(*dm, "boundary", &label);
 87:         DMPlexMarkBoundaryFaces(*dm, 1, label);
 88:         DMPlexLabelComplete(*dm, label);
 89:     } else {
 90:         DMPlexCreateFromFile(comm, user->filename, user->interpolate, dm);
 91:     }
 92:     PetscObjectSetName((PetscObject) * dm, "Mesh");
 93:     DMSetFromOptions(*dm);
 94:     DMViewFromOptions(*dm, NULL, "-dm_view");
 95:     return(0);
 96: }

 98:     /* This routine is responsible for defining the local solution vector x
 99:     with a given initial solution.
100:     The initial solution can be modified accordingly inside the loops.
101:     No need for a local vector because there is exchange of information
102:     across the processors. Unlike for FormFunction which depends on the neighbours */
103: PetscErrorCode FormInitialSolution(DM da, Vec U)
104: {
106:     PetscScalar    *u;
107:     PetscInt       cell, cStart, cEnd;
108:     PetscReal      cellvol, centroid[3], normal[3];

111:     /* Get pointers to vector data */
112:     VecGetArray(U, &u);
113:     /* Get local grid boundaries */
114:     DMPlexGetHeightStratum(da, 0, &cStart, &cEnd);
115:     /* Assigning the values at the cell centers based on x and y directions */
116:     for (cell = cStart; cell < cEnd; cell++) {
117:         DMPlexComputeCellGeometryFVM(da, cell, &cellvol, centroid, normal);
118:         if (centroid[0] > 0.9 && centroid[0] < 0.95) {
119:             if (centroid[1] > 0.9 && centroid[1] < 0.95) u[cell] = 2.0;
120:         }
121:         else u[cell] = 0;
122:     }
123:     VecRestoreArray(U, &u);
124:     return(0);
125: }

127: PetscErrorCode MyTSMonitor(TS ts, PetscInt step, PetscReal ptime, Vec v, void *ctx)
128: {
130:     PetscReal      norm;
131:     MPI_Comm       comm;

134:     if (step < 0) return(0); /* step of -1 indicates an interpolated solution */
135:     VecNorm(v, NORM_2, &norm);
136:     PetscObjectGetComm((PetscObject) ts, &comm);
137:     PetscPrintf(comm, "timestep %D time %g norm %g\n", step, (double) ptime, (double) norm);
138:     return(0);
139: }

141: /*
142:    MySNESMonitor - illustrate how to set user-defined monitoring routine for SNES.
143:    Input Parameters:
144:      snes - the SNES context
145:      its - iteration number
146:      fnorm - 2-norm function value (may be estimated)
147:      ctx - optional user-defined context for private data for the
148:          monitor routine, as set by SNESMonitorSet()
149: */
150: PetscErrorCode MySNESMonitor(SNES snes, PetscInt its, PetscReal fnorm, PetscViewerAndFormat *vf)
151: {

155:     SNESMonitorDefaultShort(snes, its, fnorm, vf);
156:     return(0);
157: }

159: /*
160:    FormFunction - Evaluates nonlinear function, F(x).

162:    Input Parameters:
163: .  ts - the TS context
164: .  X - input vector
165: .  ctx - optional user-defined context, as set by SNESSetFunction()

167:    Output Parameter:
168: .  F - function vector
169:  */
170: PetscErrorCode FormFunction(TS ts, PetscReal ftime, Vec X, Vec F, void *ctx)
171: {
172:     AppCtx *user = (AppCtx *) ctx;
173:     DM da = (DM) user->da;
175:     PetscScalar *x, *f;
176:     Vec localX;
177:     PetscInt fStart, fEnd, nF;
178:     PetscInt cell, cStart, cEnd, nC;
179:     DM dmFace;      /* DMPLEX for face geometry */
180:     PetscFV fvm;                /* specify type of FVM discretization */
181:     Vec cellGeom, faceGeom; /* vector of structs related to cell/face geometry*/
182:     const PetscScalar *fgeom;             /* values stored in the vector facegeom */
183:     PetscFVFaceGeom *fgA;               /* struct with face geometry information */
184:     const PetscInt *cellcone, *cellsupport;
185:     PetscScalar flux_east, flux_west, flux_north, flux_south, flux_centre;
186:     PetscScalar centroid_x[2], centroid_y[2], boundary = 0.0;
187:     PetscScalar boundary_left = 0.0;
188:     PetscReal u_plus, u_minus, v_plus, v_minus, zero = 0.0;
189:     PetscScalar delta_x, delta_y;

191:     /* Get the local vector from the DM object. */
193:     DMGetLocalVector(da, &localX);

195:     /* Scatter ghost points to local vector,using the 2-step process
196:        DMGlobalToLocalBegin(),DMGlobalToLocalEnd(). */
197:     DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX);
198:     DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX);
199:     /* Get pointers to vector data. */
200:     VecGetArray(localX, &x);
201:     VecGetArray(F, &f);

203:     /* Obtaining local cell and face ownership */
204:     DMPlexGetHeightStratum(da, 0, &cStart, &cEnd);
205:     DMPlexGetHeightStratum(da, 1, &fStart, &fEnd);

207:     /* Creating the PetscFV object to obtain face and cell geometry.
208:     Later to be used to compute face centroid to find cell widths. */

210:     PetscFVCreate(PETSC_COMM_WORLD, &fvm);
211:     PetscFVSetType(fvm, PETSCFVUPWIND);
212:     /*....Retrieve precomputed cell geometry....*/
213:     DMPlexGetDataFVM(da, fvm, &cellGeom, &faceGeom, NULL);
214:     VecGetDM(faceGeom, &dmFace);
215:     VecGetArrayRead(faceGeom, &fgeom);

217:     /* Spanning through all the cells and an inner loop through the faces. Find the
218:     face neighbors and pick the upwinded cell value for flux. */

220:     u_plus = PetscMax(user->u, zero);
221:     u_minus = PetscMin(user->u, zero);
222:     v_plus = PetscMax(user->v, zero);
223:     v_minus = PetscMin(user->v, zero);

225:     for (cell = cStart; cell < cEnd; cell++) {
226:         /* Obtaining the faces of the cell */
227:         DMPlexGetConeSize(da, cell, &nF);
228:         DMPlexGetCone(da, cell, &cellcone);

230:         /* south */
231:         DMPlexPointLocalRead(dmFace, cellcone[0], fgeom, &fgA);
232:         centroid_y[0] = fgA->centroid[1];
233:         /* North */
234:         DMPlexPointLocalRead(dmFace, cellcone[2], fgeom, &fgA);
235:         centroid_y[1] = fgA->centroid[1];
236:         /* West */
237:         DMPlexPointLocalRead(dmFace, cellcone[3], fgeom, &fgA);
238:         centroid_x[0] = fgA->centroid[0];
239:         /* East */
240:         DMPlexPointLocalRead(dmFace, cellcone[1], fgeom, &fgA);
241:         centroid_x[1] = fgA->centroid[0];

243:         /* Computing the cell widths in the x and y direction */
244:         delta_x = centroid_x[1] - centroid_x[0];
245:         delta_y = centroid_y[1] - centroid_y[0];

247:         /* Getting the neighbors of each face
248:            Going through the faces by the order (cellcone) */

250:         /* cellcone[0] - south */
251:         DMPlexGetSupportSize(da, cellcone[0], &nC);
252:         DMPlexGetSupport(da, cellcone[0], &cellsupport);
253:         if (nC == 2) flux_south = (x[cellsupport[0]] * (-v_plus - user->diffusion * delta_x)) / delta_y;
254:         else flux_south = (boundary * (-v_plus - user->diffusion * delta_x)) / delta_y;

256:         /* cellcone[1] - east */
257:         DMPlexGetSupportSize(da, cellcone[1], &nC);
258:         DMPlexGetSupport(da, cellcone[1], &cellsupport);
259:         if (nC == 2) flux_east = (x[cellsupport[1]] * (u_minus - user->diffusion * delta_y)) / delta_x;
260:         else flux_east = (boundary * (u_minus - user->diffusion * delta_y)) / delta_x;

262:         /* cellcone[2] - north */
263:         DMPlexGetSupportSize(da, cellcone[2], &nC);
264:         DMPlexGetSupport(da, cellcone[2], &cellsupport);
265:         if (nC == 2) flux_north = (x[cellsupport[1]] * (v_minus - user->diffusion * delta_x)) / delta_y;
266:         else flux_north = (boundary * (v_minus - user->diffusion * delta_x)) / delta_y;

268:         /* cellcone[3] - west */
269:         DMPlexGetSupportSize(da, cellcone[3], &nC);
270:         DMPlexGetSupport(da, cellcone[3], &cellsupport);
271:         if (nC == 2) flux_west = (x[cellsupport[0]] * (-u_plus - user->diffusion * delta_y)) / delta_x;
272:         else flux_west = (boundary_left * (-u_plus - user->diffusion * delta_y)) / delta_x;

274:         /* Contribution by the cell to the fluxes */
275:         flux_centre = x[cell] * ((u_plus - u_minus + 2 * user->diffusion * delta_y) / delta_x +
276:                                  (v_plus - v_minus + 2 * user->diffusion * delta_x) / delta_y);

278:         /* Calculating the net flux for each cell
279:            and computing the RHS time derivative f[.] */
280:         f[cell] = -(flux_centre + flux_east + flux_west + flux_north + flux_south);
281:     }
282:     PetscFVDestroy(&fvm);
283:     VecRestoreArray(localX, &x);
284:     VecRestoreArray(F, &f);
285:     DMRestoreLocalVector(da, &localX);
286:     return(0);
287: }

289: int main(int argc, char **argv)
290: {
291:     TS                   ts;                         /* time integrator */
292:     SNES                 snes;
293:     Vec                  x, r;                        /* solution, residual vectors */
294:     PetscErrorCode       ierr;
295:     DM                   da;
296:     PetscMPIInt          rank;
297:     PetscViewerAndFormat *vf;
298:     AppCtx               user;                             /* mesh context */
299:     PetscInt             numFields = 1, numBC, i;
300:     PetscInt             numComp[1];
301:     PetscInt             numDof[12];
302:     PetscInt             bcField[1];
303:     PetscSection         section;
304:     IS                   bcPointIS[1];

306:     /* Initialize program */
307:     PetscInitialize(&argc, &argv, (char *) 0, help);if (ierr) return ierr;
308:     MPI_Comm_rank(PETSC_COMM_WORLD, &rank);
309:     /* Create distributed array (DMPLEX) to manage parallel grid and vectors */
310:     ProcessOptions(PETSC_COMM_WORLD, &user);
311:     CreateMesh(PETSC_COMM_WORLD, &user, &da);

313:     /* Specifying the fields and dof for the formula through PETSc Section
314:     Create a scalar field u with 1 component on cells, faces and edges.
315:     Alternatively, the field information could be added through a PETSCFV object
316:     using DMAddField(...).*/
317:     numComp[0] = 1;

319:     for (i = 0; i < numFields * (user.dim + 1); ++i) numDof[i] = 0;

321:     numDof[0 * (user.dim + 1)] = 1;
322:     numDof[0 * (user.dim + 1) + user.dim - 1] = 1;
323:     numDof[0 * (user.dim + 1) + user.dim] = 1;

325:     /* Setup boundary conditions */
326:     numBC = 1;
327:     /* Prescribe a Dirichlet condition on u on the boundary
328:        Label "marker" is made by the mesh creation routine  */
329:     bcField[0] = 0;
330:     DMGetStratumIS(da, "marker", 1, &bcPointIS[0]);

332:     /* Create a PetscSection with this data layout */
333:     DMSetNumFields(da, numFields);
334:     DMPlexCreateSection(da, NULL, numComp, numDof, numBC, bcField, NULL, bcPointIS, NULL, &section);

336:     /* Name the Field variables */
337:     PetscSectionSetFieldName(section, 0, "u");

339:     /* Tell the DM to use this section (with the specified fields and dof) */
340:     DMSetLocalSection(da, section);
341:     user.da = da;

343:     /* Extract global vectors from DMDA; then duplicate for remaining
344:        vectors that are the same types */

346:     /* Create a Vec with this layout and view it */
347:     DMGetGlobalVector(da, &x);
348:     VecDuplicate(x, &r);

350:     /* Create timestepping solver context */
351:     TSCreate(PETSC_COMM_WORLD, &ts);
352:     TSSetProblemType(ts, TS_NONLINEAR);
353:     TSSetRHSFunction(ts, NULL, FormFunction, &user);

355:     TSSetMaxTime(ts, 1.0);
356:     TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER);
357:     TSMonitorSet(ts, MyTSMonitor, PETSC_VIEWER_STDOUT_WORLD, NULL);
358:     TSSetDM(ts, da);

360:     /* Customize nonlinear solver */
361:     TSSetType(ts, TSEULER);
362:     TSGetSNES(ts, &snes);
363:     PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD, PETSC_VIEWER_DEFAULT, &vf);
364:     SNESMonitorSet(snes, (PetscErrorCode (*)(SNES, PetscInt, PetscReal, void *)) MySNESMonitor, vf,(PetscErrorCode (*)(void **)) PetscViewerAndFormatDestroy);

366:      /* Set initial conditions */
367:     FormInitialSolution(da, x);
368:     TSSetTimeStep(ts, .0001);
369:     TSSetSolution(ts, x);
370:     /* Set runtime options */
371:     TSSetFromOptions(ts);
372:     /* Solve nonlinear system */
373:     TSSolve(ts, x);

375:     /* Clean up routine */
376:     DMRestoreGlobalVector(da, &x);
377:     ISDestroy(&bcPointIS[0]);
378:     PetscSectionDestroy(&section);
379:     VecDestroy(&r);
380:     TSDestroy(&ts);
381:     DMDestroy(&da);
382:     PetscFinalize();
383:     return ierr;
384: }

386: /*TEST

388:     test:
389:       suffix: 0
390:       args: -ts_max_steps 5 -ts_type rk
391:       requires: !single !complex triangle ctetgen

393: TEST*/