Actual source code: ex77.c

  1: static char help[] = "Time-dependent reactive low Mach Flow in 2d and 3d channels with finite elements.\n\
  2: We solve the reactive low Mach flow problem in a rectangular domain\n\
  3: using a parallel unstructured mesh (DMPLEX) to discretize the flow\n\
  4: and particles (DWSWARM) to discretize the chemical species.\n\n\n";

  6: /*F
  7: This low Mach flow is time-dependent isoviscous Navier-Stokes flow. We discretize using the
  8: finite element method on an unstructured mesh. The weak form equations are

 10: \begin{align*}
 11:     < q, \nabla\cdot u > = 0
 12:     <v, du/dt> + <v, u \cdot \nabla u> + < \nabla v, \nu (\nabla u + {\nabla u}^T) > - < \nabla\cdot v, p >  - < v, f  >  = 0
 13:     < w, u \cdot \nabla T > + < \nabla w, \alpha \nabla T > - < w, Q > = 0
 14: \end{align*}

 16: where $\nu$ is the kinematic viscosity and $\alpha$ is thermal diffusivity.

 18: For visualization, use

 20:   -dm_view hdf5:$PWD/sol.h5 -sol_vec_view hdf5:$PWD/sol.h5::append -exact_vec_view hdf5:$PWD/sol.h5::append

 22: The particles can be visualized using

 24:   -part_dm_view draw -part_dm_view_swarm_radius 0.03

 26: F*/

 28: #include <petscdmplex.h>
 29: #include <petscdmswarm.h>
 30: #include <petscts.h>
 31: #include <petscds.h>
 32: #include <petscbag.h>

 34: typedef enum {
 35:   SOL_TRIG_TRIG,
 36:   NUM_SOL_TYPES
 37: } SolType;
 38: const char *solTypes[NUM_SOL_TYPES + 1] = {"trig_trig", "unknown"};

 40: typedef enum {
 41:   PART_LAYOUT_CELL,
 42:   PART_LAYOUT_BOX,
 43:   NUM_PART_LAYOUT_TYPES
 44: } PartLayoutType;
 45: const char *partLayoutTypes[NUM_PART_LAYOUT_TYPES + 1] = {"cell", "box", "unknown"};

 47: typedef struct {
 48:   PetscReal nu;    /* Kinematic viscosity */
 49:   PetscReal alpha; /* Thermal diffusivity */
 50:   PetscReal T_in;  /* Inlet temperature*/
 51:   PetscReal omega; /* Rotation speed in MMS benchmark */
 52: } Parameter;

 54: typedef struct {
 55:   /* Problem definition */
 56:   PetscBag       bag;          /* Holds problem parameters */
 57:   SolType        solType;      /* MMS solution type */
 58:   PartLayoutType partLayout;   /* Type of particle distribution */
 59:   PetscInt       Npc;          /* The initial number of particles per cell */
 60:   PetscReal      partLower[3]; /* Lower left corner of particle box */
 61:   PetscReal      partUpper[3]; /* Upper right corner of particle box */
 62:   PetscInt       Npb;          /* The initial number of particles per box dimension */
 63: } AppCtx;

 65: typedef struct {
 66:   PetscReal ti; /* The time for ui, at the beginning of the advection solve */
 67:   PetscReal tf; /* The time for uf, at the end of the advection solve */
 68:   Vec       ui; /* The PDE solution field at ti */
 69:   Vec       uf; /* The PDE solution field at tf */
 70:   Vec       x0; /* The initial particle positions at t = 0 */
 71:   PetscErrorCode (*exact)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *);
 72:   AppCtx *ctx; /* Context for exact solution */
 73: } AdvCtx;

 75: static PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
 76: {
 77:   PetscInt d;
 78:   for (d = 0; d < Nc; ++d) u[d] = 0.0;
 79:   return PETSC_SUCCESS;
 80: }

 82: static PetscErrorCode constant(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
 83: {
 84:   PetscInt d;
 85:   for (d = 0; d < Nc; ++d) u[d] = 1.0;
 86:   return PETSC_SUCCESS;
 87: }

 89: /*
 90:   CASE: trigonometric-trigonometric
 91:   In 2D we use exact solution:

 93:     x = r0 cos(w t + theta0)  r0     = sqrt(x0^2 + y0^2)
 94:     y = r0 sin(w t + theta0)  theta0 = arctan(y0/x0)
 95:     u = -w r0 sin(theta0) = -w y
 96:     v =  w r0 cos(theta0) =  w x
 97:     p = x + y - 1
 98:     T = t + x + y
 99:     f = <1, 1>
100:     Q = 1 + w (x - y)/r

102:   so that

104:     \nabla \cdot u = 0 + 0 = 0

106:   f = du/dt + u \cdot \nabla u - \nu \Delta u + \nabla p
107:     = <0, 0> + u_i d_i u_j - \nu 0 + <1, 1>
108:     = <1, 1> + w^2 <-y, x> . <<0, 1>, <-1, 0>>
109:     = <1, 1> + w^2 <-x, -y>
110:     = <1, 1> - w^2 <x, y>

112:   Q = dT/dt + u \cdot \nabla T - \alpha \Delta T
113:     = 1 + <u, v> . <1, 1> - \alpha 0
114:     = 1 + u + v
115: */
116: static PetscErrorCode trig_trig_x(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *x, void *ctx)
117: {
118:   const PetscReal x0     = X[0];
119:   const PetscReal y0     = X[1];
120:   const PetscReal R0     = PetscSqrtReal(x0 * x0 + y0 * y0);
121:   const PetscReal theta0 = PetscAtan2Real(y0, x0);
122:   Parameter      *p      = (Parameter *)ctx;

124:   x[0] = R0 * PetscCosReal(p->omega * time + theta0);
125:   x[1] = R0 * PetscSinReal(p->omega * time + theta0);
126:   return PETSC_SUCCESS;
127: }
128: static PetscErrorCode trig_trig_u(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *u, void *ctx)
129: {
130:   Parameter *p = (Parameter *)ctx;

132:   u[0] = -p->omega * X[1];
133:   u[1] = p->omega * X[0];
134:   return PETSC_SUCCESS;
135: }
136: static PetscErrorCode trig_trig_u_t(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *u, void *ctx)
137: {
138:   u[0] = 0.0;
139:   u[1] = 0.0;
140:   return PETSC_SUCCESS;
141: }

143: static PetscErrorCode trig_trig_p(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *p, void *ctx)
144: {
145:   p[0] = X[0] + X[1] - 1.0;
146:   return PETSC_SUCCESS;
147: }

149: static PetscErrorCode trig_trig_T(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *T, void *ctx)
150: {
151:   T[0] = time + X[0] + X[1];
152:   return PETSC_SUCCESS;
153: }
154: static PetscErrorCode trig_trig_T_t(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *T, void *ctx)
155: {
156:   T[0] = 1.0;
157:   return PETSC_SUCCESS;
158: }

160: static void f0_trig_trig_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[])
161: {
162:   const PetscReal omega = PetscRealPart(constants[3]);
163:   PetscInt        Nc    = dim;
164:   PetscInt        c, d;

166:   for (d = 0; d < dim; ++d) f0[d] = u_t[uOff[0] + d];

168:   for (c = 0; c < Nc; ++c) {
169:     for (d = 0; d < dim; ++d) f0[c] += u[d] * u_x[c * dim + d];
170:   }
171:   f0[0] -= 1.0 - omega * omega * X[0];
172:   f0[1] -= 1.0 - omega * omega * X[1];
173: }

175: static void f0_trig_trig_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[])
176: {
177:   const PetscReal omega = PetscRealPart(constants[3]);
178:   PetscInt        d;

180:   for (d = 0, f0[0] = 0; d < dim; ++d) f0[0] += u[uOff[0] + d] * u_x[uOff_x[2] + d];
181:   f0[0] += u_t[uOff[2]] - (1.0 + omega * (X[0] - X[1]));
182: }

184: 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[])
185: {
186:   PetscInt d;
187:   for (d = 0, f0[0] = 0.0; d < dim; ++d) f0[0] += u_x[d * dim + d];
188: }

190: /*f1_v = \nu[grad(u) + grad(u)^T] - pI */
191: 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[])
192: {
193:   const PetscReal nu = PetscRealPart(constants[0]);
194:   const PetscInt  Nc = dim;
195:   PetscInt        c, d;

197:   for (c = 0; c < Nc; ++c) {
198:     for (d = 0; d < dim; ++d) f1[c * dim + d] = nu * (u_x[c * dim + d] + u_x[d * dim + c]);
199:     f1[c * dim + c] -= u[uOff[1]];
200:   }
201: }

203: 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[])
204: {
205:   const PetscReal alpha = PetscRealPart(constants[1]);
206:   PetscInt        d;
207:   for (d = 0; d < dim; ++d) f1[d] = alpha * u_x[uOff_x[2] + d];
208: }

210: /* Jacobians */
211: 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[])
212: {
213:   PetscInt d;
214:   for (d = 0; d < dim; ++d) g1[d * dim + d] = 1.0;
215: }

217: 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[])
218: {
219:   PetscInt       c, d;
220:   const PetscInt Nc = dim;

222:   for (d = 0; d < dim; ++d) g0[d * dim + d] = u_tShift;

224:   for (c = 0; c < Nc; ++c) {
225:     for (d = 0; d < dim; ++d) g0[c * Nc + d] += u_x[c * Nc + d];
226:   }
227: }

229: 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[])
230: {
231:   PetscInt NcI = dim;
232:   PetscInt NcJ = dim;
233:   PetscInt c, d, e;

235:   for (c = 0; c < NcI; ++c) {
236:     for (d = 0; d < NcJ; ++d) {
237:       for (e = 0; e < dim; ++e) {
238:         if (c == d) g1[(c * NcJ + d) * dim + e] += u[e];
239:       }
240:     }
241:   }
242: }

244: 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[])
245: {
246:   PetscInt d;
247:   for (d = 0; d < dim; ++d) g2[d * dim + d] = -1.0;
248: }

250: 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[])
251: {
252:   const PetscReal nu = PetscRealPart(constants[0]);
253:   const PetscInt  Nc = dim;
254:   PetscInt        c, d;

256:   for (c = 0; c < Nc; ++c) {
257:     for (d = 0; d < dim; ++d) {
258:       g3[((c * Nc + c) * dim + d) * dim + d] += nu; // gradU
259:       g3[((c * Nc + d) * dim + d) * dim + c] += nu; // gradU transpose
260:     }
261:   }
262: }

264: static void g0_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 g0[])
265: {
266:   PetscInt d;
267:   for (d = 0; d < dim; ++d) g0[d] = u_tShift;
268: }

270: 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[])
271: {
272:   PetscInt d;
273:   for (d = 0; d < dim; ++d) g0[d] = u_x[uOff_x[2] + d];
274: }

276: 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[])
277: {
278:   PetscInt d;
279:   for (d = 0; d < dim; ++d) g1[d] = u[uOff[0] + d];
280: }

282: 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[])
283: {
284:   const PetscReal alpha = PetscRealPart(constants[1]);
285:   PetscInt        d;

287:   for (d = 0; d < dim; ++d) g3[d * dim + d] = alpha;
288: }

290: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
291: {
292:   PetscInt sol, pl, n;

294:   PetscFunctionBeginUser;
295:   options->solType      = SOL_TRIG_TRIG;
296:   options->partLayout   = PART_LAYOUT_CELL;
297:   options->Npc          = 1;
298:   options->Npb          = 1;
299:   options->partLower[0] = options->partLower[1] = options->partLower[2] = 0.;
300:   options->partUpper[0] = options->partUpper[1] = options->partUpper[2] = 1.;
301:   PetscOptionsBegin(comm, "", "Low Mach flow Problem Options", "DMPLEX");
302:   sol = options->solType;
303:   PetscCall(PetscOptionsEList("-sol_type", "The solution type", "ex77.c", solTypes, NUM_SOL_TYPES, solTypes[options->solType], &sol, NULL));
304:   options->solType = (SolType)sol;
305:   pl               = options->partLayout;
306:   PetscCall(PetscOptionsEList("-part_layout_type", "The particle layout type", "ex77.c", partLayoutTypes, NUM_PART_LAYOUT_TYPES, partLayoutTypes[options->partLayout], &pl, NULL));
307:   options->partLayout = (PartLayoutType)pl;
308:   PetscCall(PetscOptionsInt("-Npc", "The initial number of particles per cell", "ex77.c", options->Npc, &options->Npc, NULL));
309:   n = 3;
310:   PetscCall(PetscOptionsRealArray("-part_lower", "The lower left corner of the particle box", "ex77.c", options->partLower, &n, NULL));
311:   n = 3;
312:   PetscCall(PetscOptionsRealArray("-part_upper", "The upper right corner of the particle box", "ex77.c", options->partUpper, &n, NULL));
313:   PetscCall(PetscOptionsInt("-Npb", "The initial number of particles per box dimension", "ex77.c", options->Npb, &options->Npb, NULL));
314:   PetscOptionsEnd();
315:   PetscFunctionReturn(PETSC_SUCCESS);
316: }

318: static PetscErrorCode SetupParameters(AppCtx *user)
319: {
320:   PetscBag   bag;
321:   Parameter *p;

323:   PetscFunctionBeginUser;
324:   /* setup PETSc parameter bag */
325:   PetscCall(PetscBagGetData(user->bag, (void **)&p));
326:   PetscCall(PetscBagSetName(user->bag, "par", "Low Mach flow parameters"));
327:   bag = user->bag;
328:   PetscCall(PetscBagRegisterReal(bag, &p->nu, 1.0, "nu", "Kinematic viscosity"));
329:   PetscCall(PetscBagRegisterReal(bag, &p->alpha, 1.0, "alpha", "Thermal diffusivity"));
330:   PetscCall(PetscBagRegisterReal(bag, &p->T_in, 1.0, "T_in", "Inlet temperature"));
331:   PetscCall(PetscBagRegisterReal(bag, &p->omega, 1.0, "omega", "Rotation speed in MMS benchmark"));
332:   PetscFunctionReturn(PETSC_SUCCESS);
333: }

335: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
336: {
337:   PetscFunctionBeginUser;
338:   PetscCall(DMCreate(comm, dm));
339:   PetscCall(DMSetType(*dm, DMPLEX));
340:   PetscCall(DMSetFromOptions(*dm));
341:   PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view"));
342:   PetscFunctionReturn(PETSC_SUCCESS);
343: }

345: static PetscErrorCode SetupProblem(DM dm, AppCtx *user)
346: {
347:   PetscErrorCode (*exactFuncs[3])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
348:   PetscErrorCode (*exactFuncs_t[3])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
349:   PetscDS    prob;
350:   DMLabel    label;
351:   Parameter *ctx;
352:   PetscInt   id;

354:   PetscFunctionBeginUser;
355:   PetscCall(DMGetLabel(dm, "marker", &label));
356:   PetscCall(DMGetDS(dm, &prob));
357:   switch (user->solType) {
358:   case SOL_TRIG_TRIG:
359:     PetscCall(PetscDSSetResidual(prob, 0, f0_trig_trig_v, f1_v));
360:     PetscCall(PetscDSSetResidual(prob, 2, f0_trig_trig_w, f1_w));

362:     exactFuncs[0]   = trig_trig_u;
363:     exactFuncs[1]   = trig_trig_p;
364:     exactFuncs[2]   = trig_trig_T;
365:     exactFuncs_t[0] = trig_trig_u_t;
366:     exactFuncs_t[1] = NULL;
367:     exactFuncs_t[2] = trig_trig_T_t;
368:     break;
369:   default:
370:     SETERRQ(PetscObjectComm((PetscObject)prob), PETSC_ERR_ARG_WRONG, "Unsupported solution type: %s (%d)", solTypes[PetscMin(user->solType, NUM_SOL_TYPES)], user->solType);
371:   }

373:   PetscCall(PetscDSSetResidual(prob, 1, f0_q, NULL));

375:   PetscCall(PetscDSSetJacobian(prob, 0, 0, g0_vu, g1_vu, NULL, g3_vu));
376:   PetscCall(PetscDSSetJacobian(prob, 0, 1, NULL, NULL, g2_vp, NULL));
377:   PetscCall(PetscDSSetJacobian(prob, 1, 0, NULL, g1_qu, NULL, NULL));
378:   PetscCall(PetscDSSetJacobian(prob, 2, 0, g0_wu, NULL, NULL, NULL));
379:   PetscCall(PetscDSSetJacobian(prob, 2, 2, g0_wT, g1_wT, NULL, g3_wT));
380:   /* Setup constants */
381:   {
382:     Parameter  *param;
383:     PetscScalar constants[4];

385:     PetscCall(PetscBagGetData(user->bag, (void **)&param));

387:     constants[0] = param->nu;
388:     constants[1] = param->alpha;
389:     constants[2] = param->T_in;
390:     constants[3] = param->omega;
391:     PetscCall(PetscDSSetConstants(prob, 4, constants));
392:   }
393:   /* Setup Boundary Conditions */
394:   PetscCall(PetscBagGetData(user->bag, (void **)&ctx));
395:   id = 3;
396:   PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "top wall velocity", label, 1, &id, 0, 0, NULL, (void (*)(void))exactFuncs[0], (void (*)(void))exactFuncs_t[0], ctx, NULL));
397:   id = 1;
398:   PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "bottom wall velocity", label, 1, &id, 0, 0, NULL, (void (*)(void))exactFuncs[0], (void (*)(void))exactFuncs_t[0], ctx, NULL));
399:   id = 2;
400:   PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "right wall velocity", label, 1, &id, 0, 0, NULL, (void (*)(void))exactFuncs[0], (void (*)(void))exactFuncs_t[0], ctx, NULL));
401:   id = 4;
402:   PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "left wall velocity", label, 1, &id, 0, 0, NULL, (void (*)(void))exactFuncs[0], (void (*)(void))exactFuncs_t[0], ctx, NULL));
403:   id = 3;
404:   PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "top wall temp", label, 1, &id, 2, 0, NULL, (void (*)(void))exactFuncs[2], (void (*)(void))exactFuncs_t[2], ctx, NULL));
405:   id = 1;
406:   PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "bottom wall temp", label, 1, &id, 2, 0, NULL, (void (*)(void))exactFuncs[2], (void (*)(void))exactFuncs_t[2], ctx, NULL));
407:   id = 2;
408:   PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "right wall temp", label, 1, &id, 2, 0, NULL, (void (*)(void))exactFuncs[2], (void (*)(void))exactFuncs_t[2], ctx, NULL));
409:   id = 4;
410:   PetscCall(PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "left wall temp", label, 1, &id, 2, 0, NULL, (void (*)(void))exactFuncs[2], (void (*)(void))exactFuncs_t[2], ctx, NULL));

412:   /*setup exact solution.*/
413:   PetscCall(PetscDSSetExactSolution(prob, 0, exactFuncs[0], ctx));
414:   PetscCall(PetscDSSetExactSolution(prob, 1, exactFuncs[1], ctx));
415:   PetscCall(PetscDSSetExactSolution(prob, 2, exactFuncs[2], ctx));
416:   PetscCall(PetscDSSetExactSolutionTimeDerivative(prob, 0, exactFuncs_t[0], ctx));
417:   PetscCall(PetscDSSetExactSolutionTimeDerivative(prob, 1, exactFuncs_t[1], ctx));
418:   PetscCall(PetscDSSetExactSolutionTimeDerivative(prob, 2, exactFuncs_t[2], ctx));
419:   PetscFunctionReturn(PETSC_SUCCESS);
420: }

422: /* x_t = v

424:    Note that here we use the velocity field at t_{n+1} to advect the particles from
425:    t_n to t_{n+1}. If we use both of these fields, we could use Crank-Nicholson or
426:    the method of characteristics.
427: */
428: static PetscErrorCode FreeStreaming(TS ts, PetscReal t, Vec X, Vec F, void *ctx)
429: {
430:   AdvCtx             *adv = (AdvCtx *)ctx;
431:   Vec                 u   = adv->ui;
432:   DM                  sdm, dm, vdm;
433:   Vec                 vel, locvel, pvel;
434:   IS                  vis;
435:   DMInterpolationInfo ictx;
436:   const PetscScalar  *coords, *v;
437:   PetscScalar        *f;
438:   PetscInt            vf[1] = {0};
439:   PetscInt            dim, Np;

441:   PetscFunctionBeginUser;
442:   PetscCall(TSGetDM(ts, &sdm));
443:   PetscCall(DMSwarmGetCellDM(sdm, &dm));
444:   PetscCall(DMGetGlobalVector(sdm, &pvel));
445:   PetscCall(DMSwarmGetLocalSize(sdm, &Np));
446:   PetscCall(DMGetDimension(dm, &dim));
447:   /* Get local velocity */
448:   PetscCall(DMCreateSubDM(dm, 1, vf, &vis, &vdm));
449:   PetscCall(VecGetSubVector(u, vis, &vel));
450:   PetscCall(DMGetLocalVector(vdm, &locvel));
451:   PetscCall(DMPlexInsertBoundaryValues(vdm, PETSC_TRUE, locvel, adv->ti, NULL, NULL, NULL));
452:   PetscCall(DMGlobalToLocalBegin(vdm, vel, INSERT_VALUES, locvel));
453:   PetscCall(DMGlobalToLocalEnd(vdm, vel, INSERT_VALUES, locvel));
454:   PetscCall(VecRestoreSubVector(u, vis, &vel));
455:   PetscCall(ISDestroy(&vis));
456:   /* Interpolate velocity */
457:   PetscCall(DMInterpolationCreate(PETSC_COMM_SELF, &ictx));
458:   PetscCall(DMInterpolationSetDim(ictx, dim));
459:   PetscCall(DMInterpolationSetDof(ictx, dim));
460:   PetscCall(VecGetArrayRead(X, &coords));
461:   PetscCall(DMInterpolationAddPoints(ictx, Np, (PetscReal *)coords));
462:   PetscCall(VecRestoreArrayRead(X, &coords));
463:   /* Particles that lie outside the domain should be dropped,
464:      whereas particles that move to another partition should trigger a migration */
465:   PetscCall(DMInterpolationSetUp(ictx, vdm, PETSC_FALSE, PETSC_TRUE));
466:   PetscCall(VecSet(pvel, 0.));
467:   PetscCall(DMInterpolationEvaluate(ictx, vdm, locvel, pvel));
468:   PetscCall(DMInterpolationDestroy(&ictx));
469:   PetscCall(DMRestoreLocalVector(vdm, &locvel));
470:   PetscCall(DMDestroy(&vdm));

472:   PetscCall(VecGetArray(F, &f));
473:   PetscCall(VecGetArrayRead(pvel, &v));
474:   PetscCall(PetscArraycpy(f, v, Np * dim));
475:   PetscCall(VecRestoreArrayRead(pvel, &v));
476:   PetscCall(VecRestoreArray(F, &f));
477:   PetscCall(DMRestoreGlobalVector(sdm, &pvel));
478:   PetscFunctionReturn(PETSC_SUCCESS);
479: }

481: static PetscErrorCode SetInitialParticleConditions(TS ts, Vec u)
482: {
483:   AppCtx      *user;
484:   void        *ctx;
485:   DM           dm;
486:   PetscScalar *coords;
487:   PetscReal    x[3], dx[3];
488:   PetscInt     n[3];
489:   PetscInt     dim, d, i, j, k;

491:   PetscFunctionBeginUser;
492:   PetscCall(TSGetApplicationContext(ts, &ctx));
493:   user = ((AdvCtx *)ctx)->ctx;
494:   PetscCall(TSGetDM(ts, &dm));
495:   PetscCall(DMGetDimension(dm, &dim));
496:   switch (user->partLayout) {
497:   case PART_LAYOUT_CELL:
498:     PetscCall(DMSwarmSetPointCoordinatesRandom(dm, user->Npc));
499:     break;
500:   case PART_LAYOUT_BOX:
501:     for (d = 0; d < dim; ++d) {
502:       n[d]  = user->Npb;
503:       dx[d] = (user->partUpper[d] - user->partLower[d]) / PetscMax(1, n[d] - 1);
504:     }
505:     PetscCall(VecGetArray(u, &coords));
506:     switch (dim) {
507:     case 2:
508:       x[0] = user->partLower[0];
509:       for (i = 0; i < n[0]; ++i, x[0] += dx[0]) {
510:         x[1] = user->partLower[1];
511:         for (j = 0; j < n[1]; ++j, x[1] += dx[1]) {
512:           const PetscInt p = j * n[0] + i;
513:           for (d = 0; d < dim; ++d) coords[p * dim + d] = x[d];
514:         }
515:       }
516:       break;
517:     case 3:
518:       x[0] = user->partLower[0];
519:       for (i = 0; i < n[0]; ++i, x[0] += dx[0]) {
520:         x[1] = user->partLower[1];
521:         for (j = 0; j < n[1]; ++j, x[1] += dx[1]) {
522:           x[2] = user->partLower[2];
523:           for (k = 0; k < n[2]; ++k, x[2] += dx[2]) {
524:             const PetscInt p = (k * n[1] + j) * n[0] + i;
525:             for (d = 0; d < dim; ++d) coords[p * dim + d] = x[d];
526:           }
527:         }
528:       }
529:       break;
530:     default:
531:       SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "Do not support particle layout in dimension %" PetscInt_FMT, dim);
532:     }
533:     PetscCall(VecRestoreArray(u, &coords));
534:     break;
535:   default:
536:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_WRONG, "Invalid particle layout type %s", partLayoutTypes[PetscMin(user->partLayout, NUM_PART_LAYOUT_TYPES)]);
537:   }
538:   PetscFunctionReturn(PETSC_SUCCESS);
539: }

541: static PetscErrorCode SetupDiscretization(DM dm, DM sdm, AppCtx *user)
542: {
543:   DM             cdm = dm;
544:   DMSwarmCellDM  celldm;
545:   PetscFE        fe[3];
546:   Parameter     *param;
547:   PetscInt      *swarm_cellid, n[3];
548:   PetscReal      x[3], dx[3];
549:   PetscScalar   *coords;
550:   DMPolytopeType ct;
551:   PetscInt       dim, d, cStart, cEnd, c, Np, p, i, j, k;
552:   PetscBool      simplex;
553:   MPI_Comm       comm;
554:   const char    *cellid;

556:   PetscFunctionBeginUser;
557:   PetscCall(DMGetDimension(dm, &dim));
558:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
559:   PetscCall(DMPlexGetCellType(dm, cStart, &ct));
560:   simplex = DMPolytopeTypeGetNumVertices(ct) == DMPolytopeTypeGetDim(ct) + 1 ? PETSC_TRUE : PETSC_FALSE;
561:   /* Create finite element */
562:   PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
563:   PetscCall(PetscFECreateDefault(comm, dim, dim, simplex, "vel_", PETSC_DEFAULT, &fe[0]));
564:   PetscCall(PetscObjectSetName((PetscObject)fe[0], "velocity"));

566:   PetscCall(PetscFECreateDefault(comm, dim, 1, simplex, "pres_", PETSC_DEFAULT, &fe[1]));
567:   PetscCall(PetscFECopyQuadrature(fe[0], fe[1]));
568:   PetscCall(PetscObjectSetName((PetscObject)fe[1], "pressure"));

570:   PetscCall(PetscFECreateDefault(comm, dim, 1, simplex, "temp_", PETSC_DEFAULT, &fe[2]));
571:   PetscCall(PetscFECopyQuadrature(fe[0], fe[2]));
572:   PetscCall(PetscObjectSetName((PetscObject)fe[2], "temperature"));

574:   /* Set discretization and boundary conditions for each mesh */
575:   PetscCall(DMSetField(dm, 0, NULL, (PetscObject)fe[0]));
576:   PetscCall(DMSetField(dm, 1, NULL, (PetscObject)fe[1]));
577:   PetscCall(DMSetField(dm, 2, NULL, (PetscObject)fe[2]));
578:   PetscCall(DMCreateDS(dm));
579:   PetscCall(SetupProblem(dm, user));
580:   PetscCall(PetscBagGetData(user->bag, (void **)&param));
581:   while (cdm) {
582:     PetscCall(DMCopyDisc(dm, cdm));
583:     PetscCall(DMGetCoarseDM(cdm, &cdm));
584:   }
585:   PetscCall(PetscFEDestroy(&fe[0]));
586:   PetscCall(PetscFEDestroy(&fe[1]));
587:   PetscCall(PetscFEDestroy(&fe[2]));

589:   {
590:     PetscObject  pressure;
591:     MatNullSpace nullspacePres;

593:     PetscCall(DMGetField(dm, 1, NULL, &pressure));
594:     PetscCall(MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nullspacePres));
595:     PetscCall(PetscObjectCompose(pressure, "nullspace", (PetscObject)nullspacePres));
596:     PetscCall(MatNullSpaceDestroy(&nullspacePres));
597:   }

599:   /* Setup particle information */
600:   PetscCall(DMSwarmSetType(sdm, DMSWARM_PIC));
601:   PetscCall(DMSwarmRegisterPetscDatatypeField(sdm, "mass", 1, PETSC_REAL));
602:   PetscCall(DMSwarmFinalizeFieldRegister(sdm));
603:   PetscCall(DMSwarmGetCellDMActive(sdm, &celldm));
604:   PetscCall(DMSwarmCellDMGetCellID(celldm, &cellid));
605:   switch (user->partLayout) {
606:   case PART_LAYOUT_CELL:
607:     PetscCall(DMSwarmSetLocalSizes(sdm, (cEnd - cStart) * user->Npc, 0));
608:     PetscCall(DMSetFromOptions(sdm));
609:     PetscCall(DMSwarmGetField(sdm, cellid, NULL, NULL, (void **)&swarm_cellid));
610:     for (c = cStart; c < cEnd; ++c) {
611:       for (p = 0; p < user->Npc; ++p) {
612:         const PetscInt n = c * user->Npc + p;

614:         swarm_cellid[n] = c;
615:       }
616:     }
617:     PetscCall(DMSwarmRestoreField(sdm, cellid, NULL, NULL, (void **)&swarm_cellid));
618:     PetscCall(DMSwarmSetPointCoordinatesRandom(sdm, user->Npc));
619:     break;
620:   case PART_LAYOUT_BOX:
621:     Np = 1;
622:     for (d = 0; d < dim; ++d) {
623:       n[d]  = user->Npb;
624:       dx[d] = (user->partUpper[d] - user->partLower[d]) / PetscMax(1, n[d] - 1);
625:       Np *= n[d];
626:     }
627:     PetscCall(DMSwarmSetLocalSizes(sdm, Np, 0));
628:     PetscCall(DMSetFromOptions(sdm));
629:     PetscCall(DMSwarmGetField(sdm, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
630:     switch (dim) {
631:     case 2:
632:       x[0] = user->partLower[0];
633:       for (i = 0; i < n[0]; ++i, x[0] += dx[0]) {
634:         x[1] = user->partLower[1];
635:         for (j = 0; j < n[1]; ++j, x[1] += dx[1]) {
636:           const PetscInt p = j * n[0] + i;
637:           for (d = 0; d < dim; ++d) coords[p * dim + d] = x[d];
638:         }
639:       }
640:       break;
641:     case 3:
642:       x[0] = user->partLower[0];
643:       for (i = 0; i < n[0]; ++i, x[0] += dx[0]) {
644:         x[1] = user->partLower[1];
645:         for (j = 0; j < n[1]; ++j, x[1] += dx[1]) {
646:           x[2] = user->partLower[2];
647:           for (k = 0; k < n[2]; ++k, x[2] += dx[2]) {
648:             const PetscInt p = (k * n[1] + j) * n[0] + i;
649:             for (d = 0; d < dim; ++d) coords[p * dim + d] = x[d];
650:           }
651:         }
652:       }
653:       break;
654:     default:
655:       SETERRQ(comm, PETSC_ERR_SUP, "Do not support particle layout in dimension %" PetscInt_FMT, dim);
656:     }
657:     PetscCall(DMSwarmRestoreField(sdm, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
658:     PetscCall(DMSwarmGetField(sdm, cellid, NULL, NULL, (void **)&swarm_cellid));
659:     for (p = 0; p < Np; ++p) swarm_cellid[p] = 0;
660:     PetscCall(DMSwarmRestoreField(sdm, cellid, NULL, NULL, (void **)&swarm_cellid));
661:     PetscCall(DMSwarmMigrate(sdm, PETSC_TRUE));
662:     break;
663:   default:
664:     SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Invalid particle layout type %s", partLayoutTypes[PetscMin(user->partLayout, NUM_PART_LAYOUT_TYPES)]);
665:   }
666:   PetscCall(PetscObjectSetName((PetscObject)sdm, "Particles"));
667:   PetscCall(DMViewFromOptions(sdm, NULL, "-dm_view"));
668:   PetscFunctionReturn(PETSC_SUCCESS);
669: }

671: static PetscErrorCode CreatePressureNullSpace(DM dm, PetscInt ofield, PetscInt nfield, MatNullSpace *nullSpace)
672: {
673:   Vec vec;
674:   PetscErrorCode (*funcs[3])(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *) = {zero, zero, zero};

676:   PetscFunctionBeginUser;
677:   PetscCheck(ofield == 1, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Nullspace must be for pressure field at index 1, not %" PetscInt_FMT, ofield);
678:   funcs[nfield] = constant;
679:   PetscCall(DMCreateGlobalVector(dm, &vec));
680:   PetscCall(DMProjectFunction(dm, 0.0, funcs, NULL, INSERT_ALL_VALUES, vec));
681:   PetscCall(VecNormalize(vec, NULL));
682:   PetscCall(PetscObjectSetName((PetscObject)vec, "Pressure Null Space"));
683:   PetscCall(VecViewFromOptions(vec, NULL, "-pressure_nullspace_view"));
684:   PetscCall(MatNullSpaceCreate(PetscObjectComm((PetscObject)dm), PETSC_FALSE, 1, &vec, nullSpace));
685:   PetscCall(VecDestroy(&vec));
686:   PetscFunctionReturn(PETSC_SUCCESS);
687: }

689: static PetscErrorCode RemoveDiscretePressureNullspace_Private(TS ts, Vec u)
690: {
691:   DM           dm;
692:   MatNullSpace nullsp;

694:   PetscFunctionBeginUser;
695:   PetscCall(TSGetDM(ts, &dm));
696:   PetscCall(CreatePressureNullSpace(dm, 1, 1, &nullsp));
697:   PetscCall(MatNullSpaceRemove(nullsp, u));
698:   PetscCall(MatNullSpaceDestroy(&nullsp));
699:   PetscFunctionReturn(PETSC_SUCCESS);
700: }

702: /* Make the discrete pressure discretely divergence free */
703: static PetscErrorCode RemoveDiscretePressureNullspace(TS ts)
704: {
705:   Vec u;

707:   PetscFunctionBeginUser;
708:   PetscCall(TSGetSolution(ts, &u));
709:   PetscCall(RemoveDiscretePressureNullspace_Private(ts, u));
710:   PetscFunctionReturn(PETSC_SUCCESS);
711: }

713: static PetscErrorCode SetInitialConditions(TS ts, Vec u)
714: {
715:   DM        dm;
716:   PetscReal t;

718:   PetscFunctionBeginUser;
719:   PetscCall(TSGetDM(ts, &dm));
720:   PetscCall(TSGetTime(ts, &t));
721:   PetscCall(DMComputeExactSolution(dm, t, u, NULL));
722:   PetscCall(RemoveDiscretePressureNullspace_Private(ts, u));
723:   PetscFunctionReturn(PETSC_SUCCESS);
724: }

726: static PetscErrorCode MonitorError(TS ts, PetscInt step, PetscReal crtime, Vec u, void *ctx)
727: {
728:   PetscErrorCode (*exactFuncs[3])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
729:   void     *ctxs[3];
730:   DM        dm;
731:   PetscDS   ds;
732:   Vec       v;
733:   PetscReal ferrors[3];
734:   PetscInt  tl, l, f;

736:   PetscFunctionBeginUser;
737:   PetscCall(TSGetDM(ts, &dm));
738:   PetscCall(DMGetDS(dm, &ds));

740:   for (f = 0; f < 3; ++f) PetscCall(PetscDSGetExactSolution(ds, f, &exactFuncs[f], &ctxs[f]));
741:   PetscCall(DMComputeL2FieldDiff(dm, crtime, exactFuncs, ctxs, u, ferrors));
742:   PetscCall(PetscObjectGetTabLevel((PetscObject)ts, &tl));
743:   for (l = 0; l < tl; ++l) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\t"));
744:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Timestep: %04d time = %-8.4g \t L_2 Error: [%2.3g, %2.3g, %2.3g]\n", (int)step, (double)crtime, (double)ferrors[0], (double)ferrors[1], (double)ferrors[2]));

746:   PetscCall(DMGetGlobalVector(dm, &u));
747:   PetscCall(PetscObjectSetName((PetscObject)u, "Numerical Solution"));
748:   PetscCall(VecViewFromOptions(u, NULL, "-sol_vec_view"));
749:   PetscCall(DMRestoreGlobalVector(dm, &u));

751:   PetscCall(DMGetGlobalVector(dm, &v));
752:   PetscCall(DMProjectFunction(dm, 0.0, exactFuncs, ctxs, INSERT_ALL_VALUES, v));
753:   PetscCall(PetscObjectSetName((PetscObject)v, "Exact Solution"));
754:   PetscCall(VecViewFromOptions(v, NULL, "-exact_vec_view"));
755:   PetscCall(DMRestoreGlobalVector(dm, &v));
756:   PetscFunctionReturn(PETSC_SUCCESS);
757: }

759: /* Note that adv->x0 will not be correct after migration */
760: static PetscErrorCode ComputeParticleError(TS ts, Vec u, Vec e)
761: {
762:   AdvCtx            *adv;
763:   DM                 sdm;
764:   Parameter         *param;
765:   const PetscScalar *xp0, *xp;
766:   PetscScalar       *ep;
767:   PetscReal          time;
768:   PetscInt           dim, Np, p;
769:   MPI_Comm           comm;

771:   PetscFunctionBeginUser;
772:   PetscCall(TSGetTime(ts, &time));
773:   PetscCall(TSGetApplicationContext(ts, &adv));
774:   PetscCall(PetscBagGetData(adv->ctx->bag, (void **)&param));
775:   PetscCall(PetscObjectGetComm((PetscObject)ts, &comm));
776:   PetscCall(TSGetDM(ts, &sdm));
777:   PetscCall(DMGetDimension(sdm, &dim));
778:   PetscCall(DMSwarmGetLocalSize(sdm, &Np));
779:   PetscCall(VecGetArrayRead(adv->x0, &xp0));
780:   PetscCall(VecGetArrayRead(u, &xp));
781:   PetscCall(VecGetArrayWrite(e, &ep));
782:   for (p = 0; p < Np; ++p) {
783:     PetscScalar x[3];
784:     PetscReal   x0[3];
785:     PetscInt    d;

787:     for (d = 0; d < dim; ++d) x0[d] = PetscRealPart(xp0[p * dim + d]);
788:     PetscCall(adv->exact(dim, time, x0, 1, x, param));
789:     for (d = 0; d < dim; ++d) ep[p * dim + d] += x[d] - xp[p * dim + d];
790:   }
791:   PetscCall(VecRestoreArrayRead(adv->x0, &xp0));
792:   PetscCall(VecRestoreArrayRead(u, &xp));
793:   PetscCall(VecRestoreArrayWrite(e, &ep));
794:   PetscFunctionReturn(PETSC_SUCCESS);
795: }

797: static PetscErrorCode MonitorParticleError(TS ts, PetscInt step, PetscReal time, Vec u, void *ctx)
798: {
799:   AdvCtx            *adv = (AdvCtx *)ctx;
800:   DM                 sdm;
801:   Parameter         *param;
802:   const PetscScalar *xp0, *xp;
803:   PetscReal          error = 0.0;
804:   PetscInt           dim, tl, l, Np, p;
805:   MPI_Comm           comm;

807:   PetscFunctionBeginUser;
808:   PetscCall(PetscBagGetData(adv->ctx->bag, (void **)&param));
809:   PetscCall(PetscObjectGetComm((PetscObject)ts, &comm));
810:   PetscCall(TSGetDM(ts, &sdm));
811:   PetscCall(DMGetDimension(sdm, &dim));
812:   PetscCall(DMSwarmGetLocalSize(sdm, &Np));
813:   PetscCall(VecGetArrayRead(adv->x0, &xp0));
814:   PetscCall(VecGetArrayRead(u, &xp));
815:   for (p = 0; p < Np; ++p) {
816:     PetscScalar x[3];
817:     PetscReal   x0[3];
818:     PetscReal   perror = 0.0;
819:     PetscInt    d;

821:     for (d = 0; d < dim; ++d) x0[d] = PetscRealPart(xp0[p * dim + d]);
822:     PetscCall(adv->exact(dim, time, x0, 1, x, param));
823:     for (d = 0; d < dim; ++d) perror += PetscSqr(PetscRealPart(x[d] - xp[p * dim + d]));
824:     error += perror;
825:   }
826:   PetscCall(VecRestoreArrayRead(adv->x0, &xp0));
827:   PetscCall(VecRestoreArrayRead(u, &xp));
828:   PetscCall(PetscObjectGetTabLevel((PetscObject)ts, &tl));
829:   for (l = 0; l < tl; ++l) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\t"));
830:   PetscCall(PetscPrintf(comm, "Timestep: %04d time = %-8.4g \t L_2 Particle Error: [%2.3g]\n", (int)step, (double)time, (double)error));
831:   PetscFunctionReturn(PETSC_SUCCESS);
832: }

834: static PetscErrorCode AdvectParticles(TS ts)
835: {
836:   TS        sts;
837:   DM        sdm;
838:   Vec       coordinates;
839:   AdvCtx   *adv;
840:   PetscReal time;
841:   PetscBool lreset, reset;
842:   PetscInt  dim, n, N, newn, newN;

844:   PetscFunctionBeginUser;
845:   PetscCall(PetscObjectQuery((PetscObject)ts, "_SwarmTS", (PetscObject *)&sts));
846:   PetscCall(TSGetDM(sts, &sdm));
847:   PetscCall(TSGetRHSFunction(sts, NULL, NULL, (void **)&adv));
848:   PetscCall(DMGetDimension(sdm, &dim));
849:   PetscCall(DMSwarmGetSize(sdm, &N));
850:   PetscCall(DMSwarmGetLocalSize(sdm, &n));
851:   PetscCall(DMSwarmCreateGlobalVectorFromField(sdm, DMSwarmPICField_coor, &coordinates));
852:   PetscCall(TSGetTime(ts, &time));
853:   PetscCall(TSSetMaxTime(sts, time));
854:   adv->tf = time;
855:   PetscCall(TSSolve(sts, coordinates));
856:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sdm, DMSwarmPICField_coor, &coordinates));
857:   PetscCall(VecCopy(adv->uf, adv->ui));
858:   adv->ti = adv->tf;

860:   PetscCall(DMSwarmMigrate(sdm, PETSC_TRUE));
861:   PetscCall(DMSwarmGetSize(sdm, &newN));
862:   PetscCall(DMSwarmGetLocalSize(sdm, &newn));
863:   lreset = (n != newn || N != newN) ? PETSC_TRUE : PETSC_FALSE;
864:   PetscCallMPI(MPIU_Allreduce(&lreset, &reset, 1, MPIU_BOOL, MPI_LOR, PetscObjectComm((PetscObject)sts)));
865:   if (reset) {
866:     PetscCall(TSReset(sts));
867:     PetscCall(DMSwarmVectorDefineField(sdm, DMSwarmPICField_coor));
868:   }
869:   PetscCall(DMViewFromOptions(sdm, NULL, "-dm_view"));
870:   PetscFunctionReturn(PETSC_SUCCESS);
871: }

873: int main(int argc, char **argv)
874: {
875:   DM        dm, sdm;
876:   TS        ts, sts;
877:   Vec       u, xtmp;
878:   AppCtx    user;
879:   AdvCtx    adv;
880:   PetscReal t;
881:   PetscInt  dim;

883:   PetscFunctionBeginUser;
884:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
885:   PetscCall(ProcessOptions(PETSC_COMM_WORLD, &user));
886:   PetscCall(PetscBagCreate(PETSC_COMM_WORLD, sizeof(Parameter), &user.bag));
887:   PetscCall(SetupParameters(&user));
888:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
889:   PetscCall(CreateMesh(PETSC_COMM_WORLD, &user, &dm));
890:   PetscCall(TSSetDM(ts, dm));
891:   PetscCall(DMSetApplicationContext(dm, &user));
892:   /* Discretize chemical species */
893:   PetscCall(DMCreate(PETSC_COMM_WORLD, &sdm));
894:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)sdm, "part_"));
895:   PetscCall(DMSetType(sdm, DMSWARM));
896:   PetscCall(DMGetDimension(dm, &dim));
897:   PetscCall(DMSetDimension(sdm, dim));
898:   PetscCall(DMSwarmSetCellDM(sdm, dm));
899:   /* Setup problem */
900:   PetscCall(SetupDiscretization(dm, sdm, &user));
901:   PetscCall(DMPlexCreateClosureIndex(dm, NULL));

903:   PetscCall(DMCreateGlobalVector(dm, &u));
904:   PetscCall(DMSetNullSpaceConstructor(dm, 1, CreatePressureNullSpace));

906:   PetscCall(DMTSSetBoundaryLocal(dm, DMPlexTSComputeBoundary, &user));
907:   PetscCall(DMTSSetIFunctionLocal(dm, DMPlexTSComputeIFunctionFEM, &user));
908:   PetscCall(DMTSSetIJacobianLocal(dm, DMPlexTSComputeIJacobianFEM, &user));
909:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
910:   PetscCall(TSSetPreStep(ts, RemoveDiscretePressureNullspace));
911:   PetscCall(TSMonitorSet(ts, MonitorError, &user, NULL));
912:   PetscCall(TSSetFromOptions(ts));

914:   PetscCall(TSSetComputeInitialCondition(ts, SetInitialConditions)); /* Must come after SetFromOptions() */
915:   PetscCall(SetInitialConditions(ts, u));
916:   PetscCall(TSGetTime(ts, &t));
917:   PetscCall(DMSetOutputSequenceNumber(dm, 0, t));
918:   PetscCall(DMTSCheckFromOptions(ts, u));

920:   /* Setup particle position integrator */
921:   PetscCall(TSCreate(PETSC_COMM_WORLD, &sts));
922:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)sts, "part_"));
923:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)sts, (PetscObject)ts, 1));
924:   PetscCall(TSSetDM(sts, sdm));
925:   PetscCall(TSSetProblemType(sts, TS_NONLINEAR));
926:   PetscCall(TSSetExactFinalTime(sts, TS_EXACTFINALTIME_MATCHSTEP));
927:   PetscCall(TSMonitorSet(sts, MonitorParticleError, &adv, NULL));
928:   PetscCall(TSSetFromOptions(sts));
929:   PetscCall(TSSetApplicationContext(sts, &adv));
930:   PetscCall(TSSetComputeExactError(sts, ComputeParticleError));
931:   PetscCall(TSSetComputeInitialCondition(sts, SetInitialParticleConditions));
932:   adv.ti = t;
933:   adv.uf = u;
934:   PetscCall(VecDuplicate(adv.uf, &adv.ui));
935:   PetscCall(VecCopy(u, adv.ui));
936:   PetscCall(TSSetRHSFunction(sts, NULL, FreeStreaming, &adv));
937:   PetscCall(TSSetPostStep(ts, AdvectParticles));
938:   PetscCall(PetscObjectCompose((PetscObject)ts, "_SwarmTS", (PetscObject)sts));
939:   PetscCall(DMSwarmVectorDefineField(sdm, DMSwarmPICField_coor));
940:   PetscCall(DMCreateGlobalVector(sdm, &adv.x0));
941:   PetscCall(DMSwarmCreateGlobalVectorFromField(sdm, DMSwarmPICField_coor, &xtmp));
942:   PetscCall(VecCopy(xtmp, adv.x0));
943:   PetscCall(DMSwarmDestroyGlobalVectorFromField(sdm, DMSwarmPICField_coor, &xtmp));
944:   switch (user.solType) {
945:   case SOL_TRIG_TRIG:
946:     adv.exact = trig_trig_x;
947:     break;
948:   default:
949:     SETERRQ(PetscObjectComm((PetscObject)sdm), PETSC_ERR_ARG_WRONG, "Unsupported solution type: %s (%d)", solTypes[PetscMin(user.solType, NUM_SOL_TYPES)], user.solType);
950:   }
951:   adv.ctx = &user;

953:   PetscCall(TSSolve(ts, u));
954:   PetscCall(DMTSCheckFromOptions(ts, u));
955:   PetscCall(PetscObjectSetName((PetscObject)u, "Numerical Solution"));

957:   PetscCall(VecDestroy(&u));
958:   PetscCall(VecDestroy(&adv.x0));
959:   PetscCall(VecDestroy(&adv.ui));
960:   PetscCall(DMDestroy(&dm));
961:   PetscCall(DMDestroy(&sdm));
962:   PetscCall(TSDestroy(&ts));
963:   PetscCall(TSDestroy(&sts));
964:   PetscCall(PetscBagDestroy(&user.bag));
965:   PetscCall(PetscFinalize());
966:   return 0;
967: }

969: /*TEST

971:   # Swarm does not work with complex
972:   test:
973:     suffix: 2d_tri_p2_p1_p1_tconvp
974:     requires: triangle !single !complex
975:     args: -dm_plex_separate_marker -sol_type trig_trig -dm_refine 2 \
976:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 -temp_petscspace_degree 1 \
977:       -dmts_check .001 -ts_max_steps 4 -ts_dt 0.1 -ts_monitor_cancel \
978:       -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
979:       -pc_type fieldsplit -pc_fieldsplit_0_fields 0,2 -pc_fieldsplit_1_fields 1 -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
980:         -fieldsplit_0_pc_type lu \
981:         -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi \
982:       -omega 0.5 -part_layout_type box -part_lower 0.25,0.25 -part_upper 0.75,0.75 -Npb 5 \
983:       -part_ts_max_steps 2 -part_ts_dt 0.05 -part_ts_convergence_estimate -convest_num_refine 1 -part_ts_monitor_cancel
984:   test:
985:     suffix: 2d_tri_p2_p1_p1_exit
986:     requires: triangle !single !complex
987:     args: -dm_plex_separate_marker -sol_type trig_trig -dm_refine 1 \
988:       -vel_petscspace_degree 2 -pres_petscspace_degree 1 -temp_petscspace_degree 1 \
989:       -dmts_check .001 -ts_max_steps 10 -ts_dt 0.1 \
990:       -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
991:       -pc_type fieldsplit -pc_fieldsplit_0_fields 0,2 -pc_fieldsplit_1_fields 1 -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
992:         -fieldsplit_0_pc_type lu \
993:         -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi \
994:       -omega 0.5 -part_layout_type box -part_lower 0.25,0.25 -part_upper 0.75,0.75 -Npb 5 \
995:       -part_ts_max_steps 20 -part_ts_dt 0.05

997: TEST*/