Actual source code: ex76.c
1: static char help[] = "Low Mach Flow in 2d and 3d channels with finite elements.\n\
2: We solve the Low Mach flow problem in a rectangular\n\
3: domain, using a parallel unstructured mesh (DMPLEX) to discretize it.\n\n\n";
5: /*F
6: This Low Mach flow is a steady-state isoviscous Navier-Stokes flow. We discretize using the
7: finite element method on an unstructured mesh. The weak form equations are
9: \begin{align*}
10: < q, \nabla\cdot u > = 0
11: <v, u \cdot \nabla u> + < \nabla v, \nu (\nabla u + {\nabla u}^T) > - < \nabla\cdot v, p > - < v, f > = 0
12: < w, u \cdot \nabla T > - < \nabla w, \alpha \nabla T > - < w, Q > = 0
13: \end{align*}
15: where $\nu$ is the kinematic viscosity and $\alpha$ is thermal diffusivity.
17: For visualization, use
19: -dm_view hdf5:$PWD/sol.h5 -sol_vec_view hdf5:$PWD/sol.h5::append -exact_vec_view hdf5:$PWD/sol.h5::append
20: F*/
22: #include <petscdmplex.h>
23: #include <petscsnes.h>
24: #include <petscds.h>
25: #include <petscbag.h>
27: typedef enum {
28: SOL_QUADRATIC,
29: SOL_CUBIC,
30: NUM_SOL_TYPES
31: } SolType;
32: const char *solTypes[NUM_SOL_TYPES + 1] = {"quadratic", "cubic", "unknown"};
34: typedef struct {
35: PetscReal nu; /* Kinematic viscosity */
36: PetscReal theta; /* Angle of pipe wall to x-axis */
37: PetscReal alpha; /* Thermal diffusivity */
38: PetscReal T_in; /* Inlet temperature*/
39: } Parameter;
41: typedef struct {
42: PetscBool showError;
43: PetscBag bag;
44: SolType solType;
45: } AppCtx;
47: static PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
48: {
49: PetscInt d;
50: for (d = 0; d < Nc; ++d) u[d] = 0.0;
51: return PETSC_SUCCESS;
52: }
54: static PetscErrorCode constant(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
55: {
56: PetscInt d;
57: for (d = 0; d < Nc; ++d) u[d] = 1.0;
58: return PETSC_SUCCESS;
59: }
61: /*
62: CASE: quadratic
63: In 2D we use exact solution:
65: u = x^2 + y^2
66: v = 2x^2 - 2xy
67: p = x + y - 1
68: T = x + y
69: f = <2x^3 + 4x^2y - 2xy^2 -4\nu + 1, 4xy^2 + 2x^2y - 2y^3 -4\nu + 1>
70: Q = 3x^2 + y^2 - 2xy
72: so that
74: (1) \nabla \cdot u = 2x - 2x = 0
76: (2) u \cdot \nabla u - \nu \Delta u + \nabla p - f
77: = <2x^3 + 4x^2y -2xy^2, 4xy^2 + 2x^2y - 2y^3> -\nu <4, 4> + <1, 1> - <2x^3 + 4x^2y - 2xy^2 -4\nu + 1, 4xy^2 + 2x^2y - 2y^3 - 4\nu + 1> = 0
79: (3) u \cdot \nabla T - \alpha \Delta T - Q = 3x^2 + y^2 - 2xy - \alpha*0 - 3x^2 - y^2 + 2xy = 0
80: */
82: static PetscErrorCode quadratic_u(PetscInt Dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *u, void *ctx)
83: {
84: u[0] = X[0] * X[0] + X[1] * X[1];
85: u[1] = 2.0 * X[0] * X[0] - 2.0 * X[0] * X[1];
86: return PETSC_SUCCESS;
87: }
89: static PetscErrorCode linear_p(PetscInt Dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *p, void *ctx)
90: {
91: p[0] = X[0] + X[1] - 1.0;
92: return PETSC_SUCCESS;
93: }
95: static PetscErrorCode linear_T(PetscInt Dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *T, void *ctx)
96: {
97: T[0] = X[0] + X[1];
98: return PETSC_SUCCESS;
99: }
101: static void f0_quadratic_v(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal X[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
102: {
103: PetscInt c, d;
104: PetscInt Nc = dim;
105: const PetscReal nu = PetscRealPart(constants[0]);
107: for (c = 0; c < Nc; ++c) {
108: for (d = 0; d < dim; ++d) f0[c] += u[d] * u_x[c * dim + d];
109: }
110: f0[0] -= (2 * X[0] * X[0] * X[0] + 4 * X[0] * X[0] * X[1] - 2 * X[0] * X[1] * X[1] - 4.0 * nu + 1);
111: f0[1] -= (4 * X[0] * X[1] * X[1] + 2 * X[0] * X[0] * X[1] - 2 * X[1] * X[1] * X[1] - 4.0 * nu + 1);
112: }
114: static void f0_quadratic_w(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal X[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
115: {
116: PetscInt d;
117: for (d = 0, f0[0] = 0; d < dim; ++d) f0[0] += u[uOff[0] + d] * u_x[uOff_x[2] + d];
118: f0[0] -= (3 * X[0] * X[0] + X[1] * X[1] - 2 * X[0] * X[1]);
119: }
121: /*
122: CASE: cubic
123: In 2D we use exact solution:
125: u = x^3 + y^3
126: v = 2x^3 - 3x^2y
127: p = 3/2 x^2 + 3/2 y^2 - 1
128: T = 1/2 x^2 + 1/2 y^2
129: f = <3x^5 + 6x^3y^2 - 6x^2y^3 - \nu(6x + 6y), 6x^2y^3 + 3x^4y - 6xy^4 - \nu(12x - 6y) + 3y>
130: Q = x^4 + xy^3 + 2x^3y - 3x^2y^2 - 2
132: so that
134: \nabla \cdot u = 3x^2 - 3x^2 = 0
136: u \cdot \nabla u - \nu \Delta u + \nabla p - f
137: = <3x^5 + 6x^3y^2 - 6x^2y^3, 6x^2y^3 + 3x^4y - 6xy^4> - \nu<6x + 6y, 12x - 6y> + <3x, 3y> - <3x^5 + 6x^3y^2 - 6x^2y^3 - \nu(6x + 6y), 6x^2y^3 + 3x^4y - 6xy^4 - \nu(12x - 6y) + 3y> = 0
139: u \cdot \nabla T - \alpha\Delta T - Q = (x^3 + y^3) x + (2x^3 - 3x^2y) y - 2*\alpha - (x^4 + xy^3 + 2x^3y - 3x^2y^2 - 2) = 0
140: */
142: static PetscErrorCode cubic_u(PetscInt Dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *u, void *ctx)
143: {
144: u[0] = X[0] * X[0] * X[0] + X[1] * X[1] * X[1];
145: u[1] = 2.0 * X[0] * X[0] * X[0] - 3.0 * X[0] * X[0] * X[1];
146: return PETSC_SUCCESS;
147: }
149: static PetscErrorCode quadratic_p(PetscInt Dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *p, void *ctx)
150: {
151: p[0] = 3.0 * X[0] * X[0] / 2.0 + 3.0 * X[1] * X[1] / 2.0 - 1.0;
152: return PETSC_SUCCESS;
153: }
155: static PetscErrorCode quadratic_T(PetscInt Dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *T, void *ctx)
156: {
157: T[0] = X[0] * X[0] / 2.0 + X[1] * X[1] / 2.0;
158: return PETSC_SUCCESS;
159: }
161: static void f0_cubic_v(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal X[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
162: {
163: PetscInt c, d;
164: PetscInt Nc = dim;
165: const PetscReal nu = PetscRealPart(constants[0]);
167: for (c = 0; c < Nc; ++c) {
168: for (d = 0; d < dim; ++d) f0[c] += u[d] * u_x[c * dim + d];
169: }
170: f0[0] -= (3 * X[0] * X[0] * X[0] * X[0] * X[0] + 6 * X[0] * X[0] * X[0] * X[1] * X[1] - 6 * X[0] * X[0] * X[1] * X[1] * X[1] - (6 * X[0] + 6 * X[1]) * nu + 3 * X[0]);
171: f0[1] -= (6 * X[0] * X[0] * X[1] * X[1] * X[1] + 3 * X[0] * X[0] * X[0] * X[0] * X[1] - 6 * X[0] * X[1] * X[1] * X[1] * X[1] - (12 * X[0] - 6 * X[1]) * nu + 3 * X[1]);
172: }
174: static void f0_cubic_w(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal X[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
175: {
176: const PetscReal alpha = PetscRealPart(constants[1]);
177: PetscInt d;
179: for (d = 0, f0[0] = 0; d < dim; ++d) f0[0] += u[uOff[0] + d] * u_x[uOff_x[2] + d];
180: f0[0] -= (X[0] * X[0] * X[0] * X[0] + X[0] * X[1] * X[1] * X[1] + 2.0 * X[0] * X[0] * X[0] * X[1] - 3.0 * X[0] * X[0] * X[1] * X[1] - 2.0 * alpha);
181: }
183: static void f0_q(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal X[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
184: {
185: PetscInt d;
186: for (d = 0, f0[0] = 0.0; d < dim; ++d) f0[0] += u_x[d * dim + d];
187: }
189: static void f1_v(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal X[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
190: {
191: const PetscReal nu = PetscRealPart(constants[0]);
192: const PetscInt Nc = dim;
193: PetscInt c, d;
195: for (c = 0; c < Nc; ++c) {
196: for (d = 0; d < dim; ++d) {
197: f1[c * dim + d] = nu * (u_x[c * dim + d] + u_x[d * dim + c]);
198: //f1[c*dim+d] = nu*u_x[c*dim+d];
199: }
200: f1[c * dim + c] -= u[uOff[1]];
201: }
202: }
204: static void f1_w(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal X[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
205: {
206: const PetscReal alpha = PetscRealPart(constants[1]);
207: PetscInt d;
208: for (d = 0; d < dim; ++d) f1[d] = alpha * u_x[uOff_x[2] + d];
209: }
211: /* Jacobians */
212: static void g1_qu(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
213: {
214: PetscInt d;
215: for (d = 0; d < dim; ++d) g1[d * dim + d] = 1.0;
216: }
218: static void g0_vu(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
219: {
220: const PetscInt Nc = dim;
221: PetscInt c, d;
223: for (c = 0; c < Nc; ++c) {
224: for (d = 0; d < dim; ++d) g0[c * Nc + d] = u_x[c * Nc + d];
225: }
226: }
228: static void g1_vu(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
229: {
230: PetscInt NcI = dim;
231: PetscInt NcJ = dim;
232: PetscInt c, d, e;
234: for (c = 0; c < NcI; ++c) {
235: for (d = 0; d < NcJ; ++d) {
236: for (e = 0; e < dim; ++e) {
237: if (c == d) g1[(c * NcJ + d) * dim + e] = u[e];
238: }
239: }
240: }
241: }
243: static void g2_vp(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[])
244: {
245: PetscInt d;
246: for (d = 0; d < dim; ++d) g2[d * dim + d] = -1.0;
247: }
249: static void g3_vu(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
250: {
251: const PetscReal nu = PetscRealPart(constants[0]);
252: const PetscInt Nc = dim;
253: PetscInt c, d;
255: for (c = 0; c < Nc; ++c) {
256: for (d = 0; d < dim; ++d) {
257: g3[((c * Nc + c) * dim + d) * dim + d] += nu; // gradU
258: g3[((c * Nc + d) * dim + d) * dim + c] += nu; // gradU transpose
259: }
260: }
261: }
263: static void g0_wu(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
264: {
265: PetscInt d;
266: for (d = 0; d < dim; ++d) g0[d] = u_x[uOff_x[2] + d];
267: }
269: static void g1_wT(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
270: {
271: PetscInt d;
272: for (d = 0; d < dim; ++d) g1[d] = u[uOff[0] + d];
273: }
275: static void g3_wT(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
276: {
277: const PetscReal alpha = PetscRealPart(constants[1]);
278: PetscInt d;
280: for (d = 0; d < dim; ++d) g3[d * dim + d] = alpha;
281: }
283: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
284: {
285: PetscInt sol;
287: PetscFunctionBeginUser;
288: options->solType = SOL_QUADRATIC;
289: options->showError = PETSC_FALSE;
290: PetscOptionsBegin(comm, "", "Stokes Problem Options", "DMPLEX");
291: sol = options->solType;
292: PetscCall(PetscOptionsEList("-sol_type", "The solution type", "ex62.c", solTypes, NUM_SOL_TYPES, solTypes[options->solType], &sol, NULL));
293: options->solType = (SolType)sol;
294: PetscCall(PetscOptionsBool("-show_error", "Output the error for verification", "ex62.c", options->showError, &options->showError, NULL));
295: PetscOptionsEnd();
296: PetscFunctionReturn(PETSC_SUCCESS);
297: }
299: static PetscErrorCode SetupParameters(AppCtx *user)
300: {
301: PetscBag bag;
302: Parameter *p;
304: PetscFunctionBeginUser;
305: /* setup PETSc parameter bag */
306: PetscCall(PetscBagGetData(user->bag, (void **)&p));
307: PetscCall(PetscBagSetName(user->bag, "par", "Poiseuille flow parameters"));
308: bag = user->bag;
309: PetscCall(PetscBagRegisterReal(bag, &p->nu, 1.0, "nu", "Kinematic viscosity"));
310: PetscCall(PetscBagRegisterReal(bag, &p->alpha, 1.0, "alpha", "Thermal diffusivity"));
311: PetscCall(PetscBagRegisterReal(bag, &p->theta, 0.0, "theta", "Angle of pipe wall to x-axis"));
312: PetscFunctionReturn(PETSC_SUCCESS);
313: }
315: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
316: {
317: PetscFunctionBeginUser;
318: PetscCall(DMCreate(comm, dm));
319: PetscCall(DMSetType(*dm, DMPLEX));
320: PetscCall(DMSetFromOptions(*dm));
321: {
322: Parameter *param;
323: Vec coordinates;
324: PetscScalar *coords;
325: PetscReal theta;
326: PetscInt cdim, N, bs, i;
328: PetscCall(DMGetCoordinateDim(*dm, &cdim));
329: PetscCall(DMGetCoordinates(*dm, &coordinates));
330: PetscCall(VecGetLocalSize(coordinates, &N));
331: PetscCall(VecGetBlockSize(coordinates, &bs));
332: PetscCheck(bs == cdim, comm, PETSC_ERR_ARG_WRONG, "Invalid coordinate blocksize %" PetscInt_FMT " != embedding dimension %" PetscInt_FMT, bs, cdim);
333: PetscCall(VecGetArray(coordinates, &coords));
334: PetscCall(PetscBagGetData(user->bag, (void **)¶m));
335: theta = param->theta;
336: for (i = 0; i < N; i += cdim) {
337: PetscScalar x = coords[i + 0];
338: PetscScalar y = coords[i + 1];
340: coords[i + 0] = PetscCosReal(theta) * x - PetscSinReal(theta) * y;
341: coords[i + 1] = PetscSinReal(theta) * x + PetscCosReal(theta) * y;
342: }
343: PetscCall(VecRestoreArray(coordinates, &coords));
344: PetscCall(DMSetCoordinates(*dm, coordinates));
345: }
346: PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view"));
347: PetscFunctionReturn(PETSC_SUCCESS);
348: }
350: static PetscErrorCode SetupProblem(DM dm, AppCtx *user)
351: {
352: PetscErrorCode (*exactFuncs[3])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
353: PetscDS prob;
354: DMLabel label;
355: Parameter *ctx;
356: PetscInt id;
358: PetscFunctionBeginUser;
359: PetscCall(DMGetLabel(dm, "marker", &label));
360: PetscCall(DMGetDS(dm, &prob));
361: switch (user->solType) {
362: case SOL_QUADRATIC:
363: PetscCall(PetscDSSetResidual(prob, 0, f0_quadratic_v, f1_v));
364: PetscCall(PetscDSSetResidual(prob, 2, f0_quadratic_w, f1_w));
366: exactFuncs[0] = quadratic_u;
367: exactFuncs[1] = linear_p;
368: exactFuncs[2] = linear_T;
369: break;
370: case SOL_CUBIC:
371: PetscCall(PetscDSSetResidual(prob, 0, f0_cubic_v, f1_v));
372: PetscCall(PetscDSSetResidual(prob, 2, f0_cubic_w, f1_w));
374: exactFuncs[0] = cubic_u;
375: exactFuncs[1] = quadratic_p;
376: exactFuncs[2] = quadratic_T;
377: break;
378: default:
379: SETERRQ(PetscObjectComm((PetscObject)prob), PETSC_ERR_ARG_WRONG, "Unsupported solution type: %s (%d)", solTypes[PetscMin(user->solType, NUM_SOL_TYPES)], user->solType);
380: }
382: PetscCall(PetscDSSetResidual(prob, 1, f0_q, NULL));
384: PetscCall(PetscDSSetJacobian(prob, 0, 0, g0_vu, g1_vu, NULL, g3_vu));
385: PetscCall(PetscDSSetJacobian(prob, 0, 1, NULL, NULL, g2_vp, NULL));
386: PetscCall(PetscDSSetJacobian(prob, 1, 0, NULL, g1_qu, NULL, NULL));
387: PetscCall(PetscDSSetJacobian(prob, 2, 0, g0_wu, NULL, NULL, NULL));
388: PetscCall(PetscDSSetJacobian(prob, 2, 2, NULL, g1_wT, NULL, g3_wT));
389: /* Setup constants */
390: {
391: Parameter *param;
392: PetscScalar constants[3];
394: PetscCall(PetscBagGetData(user->bag, (void **)¶m));
396: constants[0] = param->nu;
397: constants[1] = param->alpha;
398: constants[2] = param->theta;
399: PetscCall(PetscDSSetConstants(prob, 3, constants));
400: }
401: /* Setup Boundary Conditions */
402: PetscCall(PetscBagGetData(user->bag, (void **)&ctx));
403: id = 3;
404: PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "top wall velocity", label, 1, &id, 0, 0, NULL, (void (*)(void))exactFuncs[0], NULL, ctx, NULL));
405: id = 1;
406: PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "bottom wall velocity", label, 1, &id, 0, 0, NULL, (void (*)(void))exactFuncs[0], NULL, ctx, NULL));
407: id = 2;
408: PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "right wall velocity", label, 1, &id, 0, 0, NULL, (void (*)(void))exactFuncs[0], NULL, ctx, NULL));
409: id = 4;
410: PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "left wall velocity", label, 1, &id, 0, 0, NULL, (void (*)(void))exactFuncs[0], NULL, ctx, NULL));
411: id = 3;
412: PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "top wall temp", label, 1, &id, 2, 0, NULL, (void (*)(void))exactFuncs[2], NULL, ctx, NULL));
413: id = 1;
414: PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "bottom wall temp", label, 1, &id, 2, 0, NULL, (void (*)(void))exactFuncs[2], NULL, ctx, NULL));
415: id = 2;
416: PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "right wall temp", label, 1, &id, 2, 0, NULL, (void (*)(void))exactFuncs[2], NULL, ctx, NULL));
417: id = 4;
418: PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "left wall temp", label, 1, &id, 2, 0, NULL, (void (*)(void))exactFuncs[2], NULL, ctx, NULL));
420: /*setup exact solution.*/
421: PetscCall(PetscDSSetExactSolution(prob, 0, exactFuncs[0], ctx));
422: PetscCall(PetscDSSetExactSolution(prob, 1, exactFuncs[1], ctx));
423: PetscCall(PetscDSSetExactSolution(prob, 2, exactFuncs[2], ctx));
424: PetscFunctionReturn(PETSC_SUCCESS);
425: }
427: static PetscErrorCode SetupDiscretization(DM dm, AppCtx *user)
428: {
429: DM cdm = dm;
430: PetscFE fe[3];
431: Parameter *param;
432: MPI_Comm comm;
433: PetscInt dim;
434: PetscBool simplex;
436: PetscFunctionBeginUser;
437: PetscCall(DMGetDimension(dm, &dim));
438: PetscCall(DMPlexIsSimplex(dm, &simplex));
439: /* Create finite element */
440: PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
441: PetscCall(PetscFECreateDefault(comm, dim, dim, simplex, "vel_", PETSC_DEFAULT, &fe[0]));
442: PetscCall(PetscObjectSetName((PetscObject)fe[0], "velocity"));
444: PetscCall(PetscFECreateDefault(comm, dim, 1, simplex, "pres_", PETSC_DEFAULT, &fe[1]));
445: PetscCall(PetscFECopyQuadrature(fe[0], fe[1]));
446: PetscCall(PetscObjectSetName((PetscObject)fe[1], "pressure"));
448: PetscCall(PetscFECreateDefault(comm, dim, 1, simplex, "temp_", PETSC_DEFAULT, &fe[2]));
449: PetscCall(PetscFECopyQuadrature(fe[0], fe[2]));
450: PetscCall(PetscObjectSetName((PetscObject)fe[2], "temperature"));
452: /* Set discretization and boundary conditions for each mesh */
453: PetscCall(DMSetField(dm, 0, NULL, (PetscObject)fe[0]));
454: PetscCall(DMSetField(dm, 1, NULL, (PetscObject)fe[1]));
455: PetscCall(DMSetField(dm, 2, NULL, (PetscObject)fe[2]));
456: PetscCall(DMCreateDS(dm));
457: PetscCall(SetupProblem(dm, user));
458: PetscCall(PetscBagGetData(user->bag, (void **)¶m));
459: while (cdm) {
460: PetscCall(DMCopyDisc(dm, cdm));
461: PetscCall(DMPlexCreateBasisRotation(cdm, param->theta, 0.0, 0.0));
462: PetscCall(DMGetCoarseDM(cdm, &cdm));
463: }
464: PetscCall(PetscFEDestroy(&fe[0]));
465: PetscCall(PetscFEDestroy(&fe[1]));
466: PetscCall(PetscFEDestroy(&fe[2]));
467: PetscFunctionReturn(PETSC_SUCCESS);
468: }
470: static PetscErrorCode CreatePressureNullSpace(DM dm, PetscInt ofield, PetscInt nfield, MatNullSpace *nullSpace)
471: {
472: Vec vec;
473: PetscErrorCode (*funcs[3])(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *) = {zero, zero, zero};
475: PetscFunctionBeginUser;
476: PetscCheck(ofield == 1, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Nullspace must be for pressure field at index 1, not %" PetscInt_FMT, ofield);
477: funcs[nfield] = constant;
478: PetscCall(DMCreateGlobalVector(dm, &vec));
479: PetscCall(DMProjectFunction(dm, 0.0, funcs, NULL, INSERT_ALL_VALUES, vec));
480: PetscCall(VecNormalize(vec, NULL));
481: PetscCall(PetscObjectSetName((PetscObject)vec, "Pressure Null Space"));
482: PetscCall(VecViewFromOptions(vec, NULL, "-pressure_nullspace_view"));
483: PetscCall(MatNullSpaceCreate(PetscObjectComm((PetscObject)dm), PETSC_FALSE, 1, &vec, nullSpace));
484: PetscCall(VecDestroy(&vec));
485: PetscFunctionReturn(PETSC_SUCCESS);
486: }
488: int main(int argc, char **argv)
489: {
490: SNES snes; /* nonlinear solver */
491: DM dm; /* problem definition */
492: Vec u, r; /* solution, residual vectors */
493: AppCtx user; /* user-defined work context */
495: PetscFunctionBeginUser;
496: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
497: PetscCall(ProcessOptions(PETSC_COMM_WORLD, &user));
498: PetscCall(PetscBagCreate(PETSC_COMM_WORLD, sizeof(Parameter), &user.bag));
499: PetscCall(SetupParameters(&user));
500: PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes));
501: PetscCall(CreateMesh(PETSC_COMM_WORLD, &user, &dm));
502: PetscCall(SNESSetDM(snes, dm));
503: PetscCall(DMSetApplicationContext(dm, &user));
504: /* Setup problem */
505: PetscCall(SetupDiscretization(dm, &user));
506: PetscCall(DMPlexCreateClosureIndex(dm, NULL));
508: PetscCall(DMCreateGlobalVector(dm, &u));
509: PetscCall(PetscObjectSetName((PetscObject)u, "Solution"));
510: PetscCall(VecDuplicate(u, &r));
512: PetscCall(DMSetNullSpaceConstructor(dm, 1, CreatePressureNullSpace));
513: PetscCall(DMPlexSetSNESLocalFEM(dm, PETSC_FALSE, &user));
515: PetscCall(SNESSetFromOptions(snes));
516: {
517: PetscDS ds;
518: PetscErrorCode (*exactFuncs[3])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
519: void *ctxs[3];
521: PetscCall(DMGetDS(dm, &ds));
522: PetscCall(PetscDSGetExactSolution(ds, 0, &exactFuncs[0], &ctxs[0]));
523: PetscCall(PetscDSGetExactSolution(ds, 1, &exactFuncs[1], &ctxs[1]));
524: PetscCall(PetscDSGetExactSolution(ds, 2, &exactFuncs[2], &ctxs[2]));
525: PetscCall(DMProjectFunction(dm, 0.0, exactFuncs, ctxs, INSERT_ALL_VALUES, u));
526: PetscCall(PetscObjectSetName((PetscObject)u, "Exact Solution"));
527: PetscCall(VecViewFromOptions(u, NULL, "-exact_vec_view"));
528: }
529: PetscCall(DMSNESCheckFromOptions(snes, u));
530: PetscCall(VecSet(u, 0.0));
531: PetscCall(SNESSolve(snes, NULL, u));
533: if (user.showError) {
534: PetscDS ds;
535: Vec r;
536: PetscErrorCode (*exactFuncs[3])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
537: void *ctxs[3];
539: PetscCall(DMGetDS(dm, &ds));
540: PetscCall(PetscDSGetExactSolution(ds, 0, &exactFuncs[0], &ctxs[0]));
541: PetscCall(PetscDSGetExactSolution(ds, 1, &exactFuncs[1], &ctxs[1]));
542: PetscCall(PetscDSGetExactSolution(ds, 2, &exactFuncs[2], &ctxs[2]));
543: PetscCall(DMGetGlobalVector(dm, &r));
544: PetscCall(DMProjectFunction(dm, 0.0, exactFuncs, ctxs, INSERT_ALL_VALUES, r));
545: PetscCall(VecAXPY(r, -1.0, u));
546: PetscCall(PetscObjectSetName((PetscObject)r, "Solution Error"));
547: PetscCall(VecViewFromOptions(r, NULL, "-error_vec_view"));
548: PetscCall(DMRestoreGlobalVector(dm, &r));
549: }
550: PetscCall(PetscObjectSetName((PetscObject)u, "Numerical Solution"));
551: PetscCall(VecViewFromOptions(u, NULL, "-sol_vec_view"));
553: PetscCall(VecDestroy(&u));
554: PetscCall(VecDestroy(&r));
555: PetscCall(DMDestroy(&dm));
556: PetscCall(SNESDestroy(&snes));
557: PetscCall(PetscBagDestroy(&user.bag));
558: PetscCall(PetscFinalize());
559: return 0;
560: }
562: /*TEST
564: test:
565: suffix: 2d_tri_p2_p1_p1
566: requires: triangle !single
567: args: -dm_plex_separate_marker -sol_type quadratic -dm_refine 0 \
568: -vel_petscspace_degree 2 -pres_petscspace_degree 1 -temp_petscspace_degree 1 \
569: -dmsnes_check .001 -snes_error_if_not_converged \
570: -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
571: -pc_type fieldsplit -pc_fieldsplit_0_fields 0,2 -pc_fieldsplit_1_fields 1 -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
572: -fieldsplit_0_pc_type lu \
573: -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
575: test:
576: # Using -dm_refine 2 -convest_num_refine 3 gives L_2 convergence rate: [2.9, 2.3, 1.9]
577: suffix: 2d_tri_p2_p1_p1_conv
578: requires: triangle !single
579: args: -dm_plex_separate_marker -sol_type cubic -dm_refine 0 \
580: -vel_petscspace_degree 2 -pres_petscspace_degree 1 -temp_petscspace_degree 1 \
581: -snes_error_if_not_converged -snes_convergence_test correct_pressure -snes_convergence_estimate -convest_num_refine 1 \
582: -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
583: -pc_type fieldsplit -pc_fieldsplit_0_fields 0,2 -pc_fieldsplit_1_fields 1 -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
584: -fieldsplit_0_pc_type lu \
585: -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
587: test:
588: suffix: 2d_tri_p3_p2_p2
589: requires: triangle !single
590: args: -dm_plex_separate_marker -sol_type cubic -dm_refine 0 \
591: -vel_petscspace_degree 3 -pres_petscspace_degree 2 -temp_petscspace_degree 2 \
592: -dmsnes_check .001 -snes_error_if_not_converged \
593: -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
594: -pc_type fieldsplit -pc_fieldsplit_0_fields 0,2 -pc_fieldsplit_1_fields 1 -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
595: -fieldsplit_0_pc_type lu \
596: -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
598: TEST*/