Actual source code: ex52.c
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: PetscScalar diffusion;
36: PetscReal u, v;
37: PetscScalar delta_x, delta_y;
38: } AppCtx;
40: /* Options for the scenario */
41: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
42: {
46: options->u = 2.5;
47: options->v = 0.0;
48: options->diffusion = 0.0;
50: PetscOptionsBegin(comm, "", "Meshing Problem Options", "DMPLEX");
51: PetscOptionsReal("-u", "The x component of the convective coefficient", "advection_DMPLEX.c", options->u, &options->u, NULL);
52: PetscOptionsReal("-v", "The y component of the convective coefficient", "advection_DMPLEX.c", options->v, &options->v, NULL);
53: PetscOptionsScalar("-diffus", "The diffusive coefficient", "advection_DMPLEX.c", options->diffusion, &options->diffusion, NULL);
54: PetscOptionsEnd();
55: return 0;
56: }
58: /*
59: User can provide the file containing the mesh.
60: Or can generate the mesh using DMPlexCreateBoxMesh with the specified options.
61: */
62: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
63: {
65: DMCreate(comm, dm);
66: DMSetType(*dm, DMPLEX);
67: DMSetFromOptions(*dm);
68: DMViewFromOptions(*dm, NULL, "-dm_view");
69: {
70: DMLabel label;
71: DMGetLabel(*dm, "boundary", &label);
72: DMPlexLabelComplete(*dm, label);
73: }
74: return 0;
75: }
77: /* This routine is responsible for defining the local solution vector x
78: with a given initial solution.
79: The initial solution can be modified accordingly inside the loops.
80: No need for a local vector because there is exchange of information
81: across the processors. Unlike for FormFunction which depends on the neighbours */
82: PetscErrorCode FormInitialSolution(DM da, Vec U)
83: {
84: PetscScalar *u;
85: PetscInt cell, cStart, cEnd;
86: PetscReal cellvol, centroid[3], normal[3];
89: /* Get pointers to vector data */
90: VecGetArray(U, &u);
91: /* Get local grid boundaries */
92: DMPlexGetHeightStratum(da, 0, &cStart, &cEnd);
93: /* Assigning the values at the cell centers based on x and y directions */
94: for (cell = cStart; cell < cEnd; cell++) {
95: DMPlexComputeCellGeometryFVM(da, cell, &cellvol, centroid, normal);
96: if (centroid[0] > 0.9 && centroid[0] < 0.95) {
97: if (centroid[1] > 0.9 && centroid[1] < 0.95) u[cell] = 2.0;
98: }
99: else u[cell] = 0;
100: }
101: VecRestoreArray(U, &u);
102: return 0;
103: }
105: PetscErrorCode MyTSMonitor(TS ts, PetscInt step, PetscReal ptime, Vec v, void *ctx)
106: {
107: PetscReal norm;
108: MPI_Comm comm;
111: if (step < 0) return 0; /* step of -1 indicates an interpolated solution */
112: VecNorm(v, NORM_2, &norm);
113: PetscObjectGetComm((PetscObject) ts, &comm);
114: PetscPrintf(comm, "timestep %D time %g norm %g\n", step, (double) ptime, (double) norm);
115: return 0;
116: }
118: /*
119: MySNESMonitor - illustrate how to set user-defined monitoring routine for SNES.
120: Input Parameters:
121: snes - the SNES context
122: its - iteration number
123: fnorm - 2-norm function value (may be estimated)
124: ctx - optional user-defined context for private data for the
125: monitor routine, as set by SNESMonitorSet()
126: */
127: PetscErrorCode MySNESMonitor(SNES snes, PetscInt its, PetscReal fnorm, PetscViewerAndFormat *vf)
128: {
130: SNESMonitorDefaultShort(snes, its, fnorm, vf);
131: return 0;
132: }
134: /*
135: FormFunction - Evaluates nonlinear function, F(x).
137: Input Parameters:
138: . ts - the TS context
139: . X - input vector
140: . ctx - optional user-defined context, as set by SNESSetFunction()
142: Output Parameter:
143: . F - function vector
144: */
145: PetscErrorCode FormFunction(TS ts, PetscReal ftime, Vec X, Vec F, void *ctx)
146: {
147: AppCtx *user = (AppCtx *) ctx;
148: DM da;
149: PetscScalar *x, *f;
150: Vec localX;
151: PetscInt fStart, fEnd, nF;
152: PetscInt cell, cStart, cEnd, nC;
153: DM dmFace; /* DMPLEX for face geometry */
154: PetscFV fvm; /* specify type of FVM discretization */
155: Vec cellGeom, faceGeom; /* vector of structs related to cell/face geometry*/
156: const PetscScalar *fgeom; /* values stored in the vector facegeom */
157: PetscFVFaceGeom *fgA; /* struct with face geometry information */
158: const PetscInt *cellcone, *cellsupport;
159: PetscScalar flux_east, flux_west, flux_north, flux_south, flux_centre;
160: PetscScalar centroid_x[2], centroid_y[2], boundary = 0.0;
161: PetscScalar boundary_left = 0.0;
162: PetscReal u_plus, u_minus, v_plus, v_minus, zero = 0.0;
163: PetscScalar delta_x, delta_y;
165: /* Get the local vector from the DM object. */
167: TSGetDM(ts, &da);
168: DMGetLocalVector(da, &localX);
170: /* Scatter ghost points to local vector,using the 2-step process
171: DMGlobalToLocalBegin(),DMGlobalToLocalEnd(). */
172: DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX);
173: DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX);
174: /* Get pointers to vector data. */
175: VecGetArray(localX, &x);
176: VecGetArray(F, &f);
178: /* Obtaining local cell and face ownership */
179: DMPlexGetHeightStratum(da, 0, &cStart, &cEnd);
180: DMPlexGetHeightStratum(da, 1, &fStart, &fEnd);
182: /* Creating the PetscFV object to obtain face and cell geometry.
183: Later to be used to compute face centroid to find cell widths. */
185: PetscFVCreate(PETSC_COMM_WORLD, &fvm);
186: PetscFVSetType(fvm, PETSCFVUPWIND);
187: /*....Retrieve precomputed cell geometry....*/
188: DMPlexGetDataFVM(da, fvm, &cellGeom, &faceGeom, NULL);
189: VecGetDM(faceGeom, &dmFace);
190: VecGetArrayRead(faceGeom, &fgeom);
192: /* Spanning through all the cells and an inner loop through the faces. Find the
193: face neighbors and pick the upwinded cell value for flux. */
195: u_plus = PetscMax(user->u, zero);
196: u_minus = PetscMin(user->u, zero);
197: v_plus = PetscMax(user->v, zero);
198: v_minus = PetscMin(user->v, zero);
200: for (cell = cStart; cell < cEnd; cell++) {
201: /* Obtaining the faces of the cell */
202: DMPlexGetConeSize(da, cell, &nF);
203: DMPlexGetCone(da, cell, &cellcone);
205: /* south */
206: DMPlexPointLocalRead(dmFace, cellcone[0], fgeom, &fgA);
207: centroid_y[0] = fgA->centroid[1];
208: /* North */
209: DMPlexPointLocalRead(dmFace, cellcone[2], fgeom, &fgA);
210: centroid_y[1] = fgA->centroid[1];
211: /* West */
212: DMPlexPointLocalRead(dmFace, cellcone[3], fgeom, &fgA);
213: centroid_x[0] = fgA->centroid[0];
214: /* East */
215: DMPlexPointLocalRead(dmFace, cellcone[1], fgeom, &fgA);
216: centroid_x[1] = fgA->centroid[0];
218: /* Computing the cell widths in the x and y direction */
219: delta_x = centroid_x[1] - centroid_x[0];
220: delta_y = centroid_y[1] - centroid_y[0];
222: /* Getting the neighbors of each face
223: Going through the faces by the order (cellcone) */
225: /* cellcone[0] - south */
226: DMPlexGetSupportSize(da, cellcone[0], &nC);
227: DMPlexGetSupport(da, cellcone[0], &cellsupport);
228: if (nC == 2) flux_south = (x[cellsupport[0]] * (-v_plus - user->diffusion * delta_x)) / delta_y;
229: else flux_south = (boundary * (-v_plus - user->diffusion * delta_x)) / delta_y;
231: /* cellcone[1] - east */
232: DMPlexGetSupportSize(da, cellcone[1], &nC);
233: DMPlexGetSupport(da, cellcone[1], &cellsupport);
234: if (nC == 2) flux_east = (x[cellsupport[1]] * (u_minus - user->diffusion * delta_y)) / delta_x;
235: else flux_east = (boundary * (u_minus - user->diffusion * delta_y)) / delta_x;
237: /* cellcone[2] - north */
238: DMPlexGetSupportSize(da, cellcone[2], &nC);
239: DMPlexGetSupport(da, cellcone[2], &cellsupport);
240: if (nC == 2) flux_north = (x[cellsupport[1]] * (v_minus - user->diffusion * delta_x)) / delta_y;
241: else flux_north = (boundary * (v_minus - user->diffusion * delta_x)) / delta_y;
243: /* cellcone[3] - west */
244: DMPlexGetSupportSize(da, cellcone[3], &nC);
245: DMPlexGetSupport(da, cellcone[3], &cellsupport);
246: if (nC == 2) flux_west = (x[cellsupport[0]] * (-u_plus - user->diffusion * delta_y)) / delta_x;
247: else flux_west = (boundary_left * (-u_plus - user->diffusion * delta_y)) / delta_x;
249: /* Contribution by the cell to the fluxes */
250: flux_centre = x[cell] * ((u_plus - u_minus + 2 * user->diffusion * delta_y) / delta_x +
251: (v_plus - v_minus + 2 * user->diffusion * delta_x) / delta_y);
253: /* Calculating the net flux for each cell
254: and computing the RHS time derivative f[.] */
255: f[cell] = -(flux_centre + flux_east + flux_west + flux_north + flux_south);
256: }
257: PetscFVDestroy(&fvm);
258: VecRestoreArray(localX, &x);
259: VecRestoreArray(F, &f);
260: DMRestoreLocalVector(da, &localX);
261: return 0;
262: }
264: int main(int argc, char **argv)
265: {
266: TS ts; /* time integrator */
267: SNES snes;
268: Vec x, r; /* solution, residual vectors */
269: DM da;
270: PetscMPIInt rank;
271: PetscViewerAndFormat *vf;
272: AppCtx user; /* mesh context */
273: PetscInt dim, numFields = 1, numBC, i;
274: PetscInt numComp[1];
275: PetscInt numDof[12];
276: PetscInt bcField[1];
277: PetscSection section;
278: IS bcPointIS[1];
280: /* Initialize program */
281: PetscInitialize(&argc, &argv, (char *) 0, help);
282: MPI_Comm_rank(PETSC_COMM_WORLD, &rank);
283: /* Create distributed array (DMPLEX) to manage parallel grid and vectors */
284: ProcessOptions(PETSC_COMM_WORLD, &user);
285: CreateMesh(PETSC_COMM_WORLD, &user, &da);
286: DMGetDimension(da, &dim);
288: /* Specifying the fields and dof for the formula through PETSc Section
289: Create a scalar field u with 1 component on cells, faces and edges.
290: Alternatively, the field information could be added through a PETSCFV object
291: using DMAddField(...).*/
292: numComp[0] = 1;
294: for (i = 0; i < numFields * (dim + 1); ++i) numDof[i] = 0;
296: numDof[0 * (dim + 1)] = 1;
297: numDof[0 * (dim + 1) + dim - 1] = 1;
298: numDof[0 * (dim + 1) + dim] = 1;
300: /* Setup boundary conditions */
301: numBC = 1;
302: /* Prescribe a Dirichlet condition on u on the boundary
303: Label "marker" is made by the mesh creation routine */
304: bcField[0] = 0;
305: DMGetStratumIS(da, "marker", 1, &bcPointIS[0]);
307: /* Create a PetscSection with this data layout */
308: DMSetNumFields(da, numFields);
309: DMPlexCreateSection(da, NULL, numComp, numDof, numBC, bcField, NULL, bcPointIS, NULL, §ion);
311: /* Name the Field variables */
312: PetscSectionSetFieldName(section, 0, "u");
314: /* Tell the DM to use this section (with the specified fields and dof) */
315: DMSetLocalSection(da, section);
317: /* Extract global vectors from DMDA; then duplicate for remaining
318: vectors that are the same types */
320: /* Create a Vec with this layout and view it */
321: DMGetGlobalVector(da, &x);
322: VecDuplicate(x, &r);
324: /* Create timestepping solver context */
325: TSCreate(PETSC_COMM_WORLD, &ts);
326: TSSetProblemType(ts, TS_NONLINEAR);
327: TSSetRHSFunction(ts, NULL, FormFunction, &user);
329: TSSetMaxTime(ts, 1.0);
330: TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER);
331: TSMonitorSet(ts, MyTSMonitor, PETSC_VIEWER_STDOUT_WORLD, NULL);
332: TSSetDM(ts, da);
334: /* Customize nonlinear solver */
335: TSSetType(ts, TSEULER);
336: TSGetSNES(ts, &snes);
337: PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD, PETSC_VIEWER_DEFAULT, &vf);
338: SNESMonitorSet(snes, (PetscErrorCode (*)(SNES, PetscInt, PetscReal, void *)) MySNESMonitor, vf,(PetscErrorCode (*)(void **)) PetscViewerAndFormatDestroy);
340: /* Set initial conditions */
341: FormInitialSolution(da, x);
342: TSSetTimeStep(ts, .0001);
343: TSSetSolution(ts, x);
344: /* Set runtime options */
345: TSSetFromOptions(ts);
346: /* Solve nonlinear system */
347: TSSolve(ts, x);
349: /* Clean up routine */
350: DMRestoreGlobalVector(da, &x);
351: ISDestroy(&bcPointIS[0]);
352: PetscSectionDestroy(§ion);
353: VecDestroy(&r);
354: TSDestroy(&ts);
355: DMDestroy(&da);
356: PetscFinalize();
357: return 0;
358: }
360: /*TEST
362: test:
363: suffix: 0
364: args: -dm_plex_simplex 0 -dm_plex_box_faces 20,20 -dm_plex_boundary_label boundary -ts_max_steps 5 -ts_type rk
365: requires: !single !complex triangle ctetgen
367: TEST*/