xref: /petsc/src/ts/tutorials/ex77.c (revision 4e278199b78715991f5c71ebbd945c1489263e6c)
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";
5 
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
9 
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*}
15 
16 where $\nu$ is the kinematic viscosity and $\alpha$ is thermal diffusivity.
17 
18 For visualization, use
19 
20   -dm_view hdf5:$PWD/sol.h5 -sol_vec_view hdf5:$PWD/sol.h5::append -exact_vec_view hdf5:$PWD/sol.h5::append
21 
22 The particles can be visualized using
23 
24   -part_dm_view draw -part_dm_view_swarm_radius 0.03
25 
26 F*/
27 
28 #include <petscdmplex.h>
29 #include <petscdmswarm.h>
30 #include <petscts.h>
31 #include <petscds.h>
32 #include <petscbag.h>
33 
34 typedef enum {SOL_TRIG_TRIG, NUM_SOL_TYPES} SolType;
35 const char *solTypes[NUM_SOL_TYPES+1] = {"trig_trig",  "unknown"};
36 
37 typedef enum {PART_LAYOUT_CELL, PART_LAYOUT_BOX, NUM_PART_LAYOUT_TYPES} PartLayoutType;
38 const char *partLayoutTypes[NUM_PART_LAYOUT_TYPES+1] = {"cell", "box",  "unknown"};
39 
40 typedef struct {
41   PetscReal nu;    /* Kinematic viscosity */
42   PetscReal alpha; /* Thermal diffusivity */
43   PetscReal T_in;  /* Inlet temperature*/
44   PetscReal omega; /* Rotation speed in MMS benchmark */
45 } Parameter;
46 
47 typedef struct {
48   /* Problem definition */
49   PetscBag       bag;          /* Holds problem parameters */
50   SolType        solType;      /* MMS solution type */
51   PartLayoutType partLayout;   /* Type of particle distribution */
52   PetscInt       Npc;          /* The initial number of particles per cell */
53   PetscReal      partLower[3]; /* Lower left corner of particle box */
54   PetscReal      partUpper[3]; /* Upper right corner of particle box */
55   PetscInt       Npb;          /* The initial number of particles per box dimension */
56 } AppCtx;
57 
58 typedef struct {
59   PetscReal ti; /* The time for ui, at the beginning of the advection solve */
60   PetscReal tf; /* The time for uf, at the end of the advection solve */
61   Vec       ui; /* The PDE solution field at ti */
62   Vec       uf; /* The PDE solution field at tf */
63   Vec       x0; /* The initial particle positions at t = 0 */
64   PetscErrorCode (*exact)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *);
65   AppCtx   *ctx; /* Context for exact solution */
66 } AdvCtx;
67 
68 static PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
69 {
70   PetscInt d;
71   for (d = 0; d < Nc; ++d) u[d] = 0.0;
72   return 0;
73 }
74 
75 static PetscErrorCode constant(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] = 1.0;
79   return 0;
80 }
81 
82 /*
83   CASE: trigonometric-trigonometric
84   In 2D we use exact solution:
85 
86     x = r0 cos(w t + theta0)  r0     = sqrt(x0^2 + y0^2)
87     y = r0 sin(w t + theta0)  theta0 = arctan(y0/x0)
88     u = -w r0 sin(theta0) = -w y
89     v =  w r0 cos(theta0) =  w x
90     p = x + y - 1
91     T = t + x + y
92     f = <1, 1>
93     Q = 1 + w (x - y)/r
94 
95   so that
96 
97     \nabla \cdot u = 0 + 0 = 0
98 
99   f = du/dt + u \cdot \nabla u - \nu \Delta u + \nabla p
100     = <0, 0> + u_i d_i u_j - \nu 0 + <1, 1>
101     = <1, 1> + w^2 <-y, x> . <<0, 1>, <-1, 0>>
102     = <1, 1> + w^2 <-x, -y>
103     = <1, 1> - w^2 <x, y>
104 
105   Q = dT/dt + u \cdot \nabla T - \alpha \Delta T
106     = 1 + <u, v> . <1, 1> - \alpha 0
107     = 1 + u + v
108 */
109 static PetscErrorCode trig_trig_x(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *x, void *ctx)
110 {
111   const PetscReal x0     = X[0];
112   const PetscReal y0     = X[1];
113   const PetscReal R0     = PetscSqrtReal(x0*x0 + y0*y0);
114   const PetscReal theta0 = PetscAtan2Real(y0, x0);
115   Parameter      *p      = (Parameter *) ctx;
116 
117   x[0] = R0*PetscCosReal(p->omega*time + theta0);
118   x[1] = R0*PetscSinReal(p->omega*time + theta0);
119   return 0;
120 }
121 static PetscErrorCode trig_trig_u(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *u, void *ctx)
122 {
123   Parameter *p = (Parameter *) ctx;
124 
125   u[0] = -p->omega*X[1];
126   u[1] =  p->omega*X[0];
127   return 0;
128 }
129 static PetscErrorCode trig_trig_u_t(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *u, void *ctx)
130 {
131   u[0] = 0.0;
132   u[1] = 0.0;
133   return 0;
134 }
135 
136 static PetscErrorCode trig_trig_p(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *p, void *ctx)
137 {
138   p[0] = X[0] + X[1] - 1.0;
139   return 0;
140 }
141 
142 static PetscErrorCode trig_trig_T(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *T, void *ctx)
143 {
144   T[0] = time + X[0] + X[1];
145   return 0;
146 }
147 static PetscErrorCode trig_trig_T_t(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *T, void *ctx)
148 {
149   T[0] = 1.0;
150   return 0;
151 }
152 
153 static void f0_trig_trig_v(PetscInt dim, PetscInt Nf, PetscInt NfAux,
154                            const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
155                            const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
156                            PetscReal t, const PetscReal X[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
157 {
158   const PetscReal omega = PetscRealPart(constants[3]);
159   PetscInt        Nc    = dim;
160   PetscInt        c, d;
161 
162   for (d = 0; d < dim; ++d) f0[d] = u_t[uOff[0]+d];
163 
164   for (c = 0; c < Nc; ++c) {
165     for (d = 0; d < dim; ++d) f0[c] += u[d]*u_x[c*dim+d];
166   }
167   f0[0] -= 1.0 - omega*omega*X[0];
168   f0[1] -= 1.0 - omega*omega*X[1];
169 }
170 
171 static void f0_trig_trig_w(PetscInt dim, PetscInt Nf, PetscInt NfAux,
172                            const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
173                            const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
174                            PetscReal t, const PetscReal X[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
175 {
176   const PetscReal omega = PetscRealPart(constants[3]);
177   PetscInt        d;
178 
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] += u_t[uOff[2]] - (1.0 + omega*(X[0] - X[1]));
181 }
182 
183 static void f0_q(PetscInt dim, PetscInt Nf, PetscInt NfAux,
184                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
185                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
186                  PetscReal t, const PetscReal X[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
187 {
188   PetscInt d;
189   for (d = 0, f0[0] = 0.0; d < dim; ++d) f0[0] += u_x[d*dim+d];
190 }
191 
192 /*f1_v = \nu[grad(u) + grad(u)^T] - pI */
193 static void f1_v(PetscInt dim, PetscInt Nf, PetscInt NfAux,
194                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
195                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
196                  PetscReal t, const PetscReal X[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
197 {
198   const PetscReal nu = PetscRealPart(constants[0]);
199   const PetscInt    Nc = dim;
200   PetscInt        c, d;
201 
202   for (c = 0; c < Nc; ++c) {
203     for (d = 0; d < dim; ++d) {
204       f1[c*dim+d] = nu*(u_x[c*dim+d] + u_x[d*dim+c]);
205     }
206     f1[c*dim+c] -= u[uOff[1]];
207   }
208 }
209 
210 static void f1_w(PetscInt dim, PetscInt Nf, PetscInt NfAux,
211                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
212                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
213                  PetscReal t, const PetscReal X[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
214 {
215   const PetscReal alpha = PetscRealPart(constants[1]);
216   PetscInt d;
217   for (d = 0; d < dim; ++d) f1[d] = alpha*u_x[uOff_x[2]+d];
218 }
219 
220 /*Jacobians*/
221 static void g1_qu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
222                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
223                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
224                  PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
225 {
226   PetscInt d;
227   for (d = 0; d < dim; ++d) g1[d*dim+d] = 1.0;
228 }
229 
230 static void g0_vu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
231                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
232                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
233                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
234 {
235   PetscInt c, d;
236   const PetscInt  Nc = dim;
237 
238   for (d = 0; d < dim; ++d) g0[d*dim+d] = u_tShift;
239 
240   for (c = 0; c < Nc; ++c) {
241     for (d = 0; d < dim; ++d) {
242       g0[c*Nc+d] += u_x[c*Nc+d];
243     }
244   }
245 }
246 
247 static void g1_vu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
248                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
249                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
250                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
251 {
252   PetscInt NcI = dim;
253   PetscInt NcJ = dim;
254   PetscInt c, d, e;
255 
256   for (c = 0; c < NcI; ++c) {
257     for (d = 0; d < NcJ; ++d) {
258       for (e = 0; e < dim; ++e) {
259         if (c == d) {
260           g1[(c*NcJ+d)*dim+e] += u[e];
261         }
262       }
263     }
264   }
265 }
266 
267 static void g2_vp(PetscInt dim, PetscInt Nf, PetscInt NfAux,
268                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
269                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
270                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[])
271 {
272   PetscInt d;
273   for (d = 0; d < dim; ++d) g2[d*dim+d] = -1.0;
274 }
275 
276 static void g3_vu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
277                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
278                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
279                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
280 {
281    const PetscReal nu = PetscRealPart(constants[0]);
282    const PetscInt  Nc = dim;
283    PetscInt        c, d;
284 
285   for (c = 0; c < Nc; ++c) {
286     for (d = 0; d < dim; ++d) {
287       g3[((c*Nc+c)*dim+d)*dim+d] += nu; // gradU
288       g3[((c*Nc+d)*dim+d)*dim+c] += nu; // gradU transpose
289     }
290   }
291 }
292 
293 static void g0_wT(PetscInt dim, PetscInt Nf, PetscInt NfAux,
294                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
295                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
296                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
297 {
298   PetscInt d;
299   for (d = 0; d < dim; ++d) g0[d] = u_tShift;
300 }
301 
302 static void g0_wu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
303                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
304                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
305                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
306 {
307   PetscInt d;
308   for (d = 0; d < dim; ++d) g0[d] = u_x[uOff_x[2]+d];
309 }
310 
311 static void g1_wT(PetscInt dim, PetscInt Nf, PetscInt NfAux,
312                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
313                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
314                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
315 {
316   PetscInt d;
317   for (d = 0; d < dim; ++d) g1[d] = u[uOff[0]+d];
318 }
319 
320 static void g3_wT(PetscInt dim, PetscInt Nf, PetscInt NfAux,
321                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
322                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
323                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
324 {
325   const PetscReal alpha = PetscRealPart(constants[1]);
326   PetscInt               d;
327 
328   for (d = 0; d < dim; ++d) g3[d*dim+d] = alpha;
329 }
330 
331 static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
332 {
333   PetscInt       sol, pl, n;
334   PetscErrorCode ierr;
335 
336   PetscFunctionBeginUser;
337   options->solType    = SOL_TRIG_TRIG;
338   options->partLayout = PART_LAYOUT_CELL;
339   options->Npc        = 1;
340   options->Npb        = 1;
341 
342   options->partLower[0] = options->partLower[1] = options->partLower[2] = 0.;
343   options->partUpper[0] = options->partUpper[1] = options->partUpper[2] = 1.;
344   ierr = PetscOptionsBegin(comm, "", "Low Mach flow Problem Options", "DMPLEX");CHKERRQ(ierr);
345   sol  = options->solType;
346   ierr = PetscOptionsEList("-sol_type", "The solution type", "ex77.c", solTypes, NUM_SOL_TYPES, solTypes[options->solType], &sol, NULL);CHKERRQ(ierr);
347   options->solType = (SolType) sol;
348   pl   = options->partLayout;
349   ierr = PetscOptionsEList("-part_layout_type", "The particle layout type", "ex77.c", partLayoutTypes, NUM_PART_LAYOUT_TYPES, partLayoutTypes[options->partLayout], &pl, NULL);CHKERRQ(ierr);
350   options->partLayout = (PartLayoutType) pl;
351   ierr = PetscOptionsInt("-Npc", "The initial number of particles per cell", "ex77.c", options->Npc, &options->Npc, NULL);CHKERRQ(ierr);
352   n    = 3;
353   ierr = PetscOptionsRealArray("-part_lower", "The lower left corner of the particle box", "ex77.c", options->partLower, &n, NULL);CHKERRQ(ierr);
354   n    = 3;
355   ierr = PetscOptionsRealArray("-part_upper", "The upper right corner of the particle box", "ex77.c", options->partUpper, &n, NULL);CHKERRQ(ierr);
356   ierr = PetscOptionsInt("-Npb", "The initial number of particles per box dimension", "ex77.c", options->Npb, &options->Npb, NULL);CHKERRQ(ierr);
357   ierr = PetscOptionsEnd();
358   PetscFunctionReturn(0);
359 }
360 
361 static PetscErrorCode SetupParameters(AppCtx *user)
362 {
363   PetscBag       bag;
364   Parameter     *p;
365   PetscErrorCode ierr;
366 
367   PetscFunctionBeginUser;
368   /* setup PETSc parameter bag */
369   ierr = PetscBagGetData(user->bag, (void **) &p);CHKERRQ(ierr);
370   ierr = PetscBagSetName(user->bag, "par", "Low Mach flow parameters");CHKERRQ(ierr);
371   bag  = user->bag;
372   ierr = PetscBagRegisterReal(bag, &p->nu,    1.0, "nu",    "Kinematic viscosity");CHKERRQ(ierr);
373   ierr = PetscBagRegisterReal(bag, &p->alpha, 1.0, "alpha", "Thermal diffusivity");CHKERRQ(ierr);
374   ierr = PetscBagRegisterReal(bag, &p->T_in,  1.0, "T_in",  "Inlet temperature");CHKERRQ(ierr);
375   ierr = PetscBagRegisterReal(bag, &p->omega, 1.0, "omega", "Rotation speed in MMS benchmark");CHKERRQ(ierr);
376   PetscFunctionReturn(0);
377 }
378 
379 static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
380 {
381   PetscErrorCode ierr;
382 
383   PetscFunctionBeginUser;
384   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
385   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
386   ierr = DMSetFromOptions(*dm);CHKERRQ(ierr);
387   ierr = DMViewFromOptions(*dm, NULL, "-dm_view");CHKERRQ(ierr);
388   PetscFunctionReturn(0);
389 }
390 
391 static PetscErrorCode SetupProblem(DM dm, AppCtx *user)
392 {
393   PetscErrorCode (*exactFuncs[3])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
394   PetscErrorCode (*exactFuncs_t[3])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
395   PetscDS          prob;
396   DMLabel          label;
397   Parameter       *ctx;
398   PetscInt         id;
399   PetscErrorCode   ierr;
400 
401   PetscFunctionBeginUser;
402   ierr = DMGetLabel(dm, "marker", &label);CHKERRQ(ierr);
403   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
404   switch(user->solType){
405   case SOL_TRIG_TRIG:
406     ierr = PetscDSSetResidual(prob, 0, f0_trig_trig_v, f1_v);CHKERRQ(ierr);
407     ierr = PetscDSSetResidual(prob, 2, f0_trig_trig_w, f1_w);CHKERRQ(ierr);
408 
409     exactFuncs[0]   = trig_trig_u;
410     exactFuncs[1]   = trig_trig_p;
411     exactFuncs[2]   = trig_trig_T;
412     exactFuncs_t[0] = trig_trig_u_t;
413     exactFuncs_t[1] = NULL;
414     exactFuncs_t[2] = trig_trig_T_t;
415     break;
416    default: SETERRQ2(PetscObjectComm((PetscObject) prob), PETSC_ERR_ARG_WRONG, "Unsupported solution type: %s (%D)", solTypes[PetscMin(user->solType, NUM_SOL_TYPES)], user->solType);
417   }
418 
419   ierr = PetscDSSetResidual(prob, 1, f0_q, NULL);CHKERRQ(ierr);
420 
421   ierr = PetscDSSetJacobian(prob, 0, 0, g0_vu, g1_vu,  NULL,  g3_vu);CHKERRQ(ierr);
422   ierr = PetscDSSetJacobian(prob, 0, 1, NULL, NULL,  g2_vp, NULL);CHKERRQ(ierr);
423   ierr = PetscDSSetJacobian(prob, 1, 0, NULL, g1_qu, NULL,  NULL);CHKERRQ(ierr);
424   ierr = PetscDSSetJacobian(prob, 2, 0, g0_wu, NULL, NULL,  NULL);CHKERRQ(ierr);
425   ierr = PetscDSSetJacobian(prob, 2, 2, g0_wT, g1_wT, NULL,  g3_wT);CHKERRQ(ierr);
426   /* Setup constants */
427   {
428     Parameter  *param;
429     PetscScalar constants[4];
430 
431     ierr = PetscBagGetData(user->bag, (void **) &param);CHKERRQ(ierr);
432 
433     constants[0] = param->nu;
434     constants[1] = param->alpha;
435     constants[2] = param->T_in;
436     constants[3] = param->omega;
437     ierr = PetscDSSetConstants(prob, 4, constants);CHKERRQ(ierr);
438   }
439   /* Setup Boundary Conditions */
440   ierr = PetscBagGetData(user->bag, (void **) &ctx);CHKERRQ(ierr);
441   id   = 3;
442   ierr = 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);CHKERRQ(ierr);
443   id   = 1;
444   ierr = 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);CHKERRQ(ierr);
445   id   = 2;
446   ierr = 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);CHKERRQ(ierr);
447   id   = 4;
448   ierr = 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);CHKERRQ(ierr);
449   id   = 3;
450   ierr = 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);CHKERRQ(ierr);
451   id   = 1;
452   ierr = 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);CHKERRQ(ierr);
453   id   = 2;
454   ierr = 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);CHKERRQ(ierr);
455   id   = 4;
456   ierr = 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);CHKERRQ(ierr);
457 
458   /*setup exact solution.*/
459   ierr = PetscDSSetExactSolution(prob, 0, exactFuncs[0], ctx);CHKERRQ(ierr);
460   ierr = PetscDSSetExactSolution(prob, 1, exactFuncs[1], ctx);CHKERRQ(ierr);
461   ierr = PetscDSSetExactSolution(prob, 2, exactFuncs[2], ctx);CHKERRQ(ierr);
462   ierr = PetscDSSetExactSolutionTimeDerivative(prob, 0, exactFuncs_t[0], ctx);CHKERRQ(ierr);
463   ierr = PetscDSSetExactSolutionTimeDerivative(prob, 1, exactFuncs_t[1], ctx);CHKERRQ(ierr);
464   ierr = PetscDSSetExactSolutionTimeDerivative(prob, 2, exactFuncs_t[2], ctx);CHKERRQ(ierr);
465   PetscFunctionReturn(0);
466 }
467 
468 /* x_t = v
469 
470    Note that here we use the velocity field at t_{n+1} to advect the particles from
471    t_n to t_{n+1}. If we use both of these fields, we could use Crank-Nicholson or
472    the method of characteristics.
473 */
474 static PetscErrorCode FreeStreaming(TS ts, PetscReal t, Vec X, Vec F, void *ctx)
475 {
476   AdvCtx             *adv = (AdvCtx *) ctx;
477   Vec                 u   = adv->ui;
478   DM                  sdm, dm, vdm;
479   Vec                 vel, locvel, pvel;
480   IS                  vis;
481   DMInterpolationInfo ictx;
482   const PetscScalar  *coords, *v;
483   PetscScalar        *f;
484   PetscInt            vf[1] = {0};
485   PetscInt            dim, Np;
486   PetscErrorCode      ierr;
487 
488   PetscFunctionBeginUser;
489   ierr = TSGetDM(ts, &sdm);CHKERRQ(ierr);
490   ierr = DMSwarmGetCellDM(sdm, &dm);CHKERRQ(ierr);
491   ierr = DMGetGlobalVector(sdm, &pvel);CHKERRQ(ierr);
492   ierr = DMSwarmGetLocalSize(sdm, &Np);CHKERRQ(ierr);
493   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
494   /* Get local velocity */
495   ierr = DMCreateSubDM(dm, 1, vf, &vis, &vdm);CHKERRQ(ierr);
496   ierr = VecGetSubVector(u, vis, &vel);CHKERRQ(ierr);
497   ierr = DMGetLocalVector(vdm, &locvel);CHKERRQ(ierr);
498   ierr = DMPlexInsertBoundaryValues(vdm, PETSC_TRUE, locvel, adv->ti, NULL, NULL, NULL);CHKERRQ(ierr);
499   ierr = DMGlobalToLocalBegin(vdm, vel, INSERT_VALUES, locvel);CHKERRQ(ierr);
500   ierr = DMGlobalToLocalEnd(vdm, vel, INSERT_VALUES, locvel);CHKERRQ(ierr);
501   ierr = VecRestoreSubVector(u, vis, &vel);CHKERRQ(ierr);
502   ierr = ISDestroy(&vis);CHKERRQ(ierr);
503   /* Interpolate velocity */
504   ierr = DMInterpolationCreate(PETSC_COMM_SELF, &ictx);CHKERRQ(ierr);
505   ierr = DMInterpolationSetDim(ictx, dim);CHKERRQ(ierr);
506   ierr = DMInterpolationSetDof(ictx, dim);CHKERRQ(ierr);
507   ierr = VecGetArrayRead(X, &coords);CHKERRQ(ierr);
508   ierr = DMInterpolationAddPoints(ictx, Np, (PetscReal *) coords);CHKERRQ(ierr);
509   ierr = VecRestoreArrayRead(X, &coords);CHKERRQ(ierr);
510   /* Particles that lie outside the domain should be dropped,
511      whereas particles that move to another partition should trigger a migration */
512   ierr = DMInterpolationSetUp(ictx, vdm, PETSC_FALSE, PETSC_TRUE);CHKERRQ(ierr);
513   ierr = VecSet(pvel, 0.);CHKERRQ(ierr);
514   ierr = DMInterpolationEvaluate(ictx, vdm, locvel, pvel);CHKERRQ(ierr);
515   ierr = DMInterpolationDestroy(&ictx);CHKERRQ(ierr);
516   ierr = DMRestoreLocalVector(vdm, &locvel);CHKERRQ(ierr);
517   ierr = DMDestroy(&vdm);CHKERRQ(ierr);
518 
519   ierr = VecGetArray(F, &f);CHKERRQ(ierr);
520   ierr = VecGetArrayRead(pvel, &v);CHKERRQ(ierr);
521   ierr = PetscArraycpy(f, v, Np*dim);CHKERRQ(ierr);
522   ierr = VecRestoreArrayRead(pvel, &v);CHKERRQ(ierr);
523   ierr = VecRestoreArray(F, &f);CHKERRQ(ierr);
524   ierr = DMRestoreGlobalVector(sdm, &pvel);CHKERRQ(ierr);
525   PetscFunctionReturn(0);
526 }
527 
528 static PetscErrorCode SetInitialParticleConditions(TS ts, Vec u)
529 {
530   AppCtx        *user;
531   void          *ctx;
532   DM             dm;
533   PetscScalar   *coords;
534   PetscReal      x[3], dx[3];
535   PetscInt       n[3];
536   PetscInt       Np, dim, d, i, j, k;
537   PetscErrorCode ierr;
538 
539   PetscFunctionBegin;
540   ierr = TSGetApplicationContext(ts, &ctx);CHKERRQ(ierr);
541   user = ((AdvCtx *) ctx)->ctx;
542   ierr = TSGetDM(ts, &dm);CHKERRQ(ierr);
543   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
544   switch (user->partLayout) {
545     case PART_LAYOUT_CELL:
546       ierr = DMSwarmSetPointCoordinatesRandom(dm, user->Npc);CHKERRQ(ierr);
547       break;
548     case PART_LAYOUT_BOX:
549       Np = 1;
550       for (d = 0; d < dim; ++d) {
551         n[d]  = user->Npb;
552         dx[d] = (user->partUpper[d] - user->partLower[d])/PetscMax(1, n[d] - 1);
553         Np   *= n[d];
554       }
555       ierr = VecGetArray(u, &coords);CHKERRQ(ierr);
556       switch (dim) {
557         case 2:
558           x[0] = user->partLower[0];
559           for (i = 0; i < n[0]; ++i, x[0] += dx[0]) {
560             x[1] = user->partLower[1];
561             for (j = 0; j < n[1]; ++j, x[1] += dx[1]) {
562               const PetscInt p = j*n[0] + i;
563               for (d = 0; d < dim; ++d) coords[p*dim + d] = x[d];
564             }
565           }
566           break;
567         case 3:
568           x[0] = user->partLower[0];
569           for (i = 0; i < n[0]; ++i, x[0] += dx[0]) {
570             x[1] = user->partLower[1];
571             for (j = 0; j < n[1]; ++j, x[1] += dx[1]) {
572               x[2] = user->partLower[2];
573               for (k = 0; k < n[2]; ++k, x[2] += dx[2]) {
574                 const PetscInt p = (k*n[1] + j)*n[0] + i;
575                 for (d = 0; d < dim; ++d) coords[p*dim + d] = x[d];
576               }
577             }
578           }
579           break;
580         default: SETERRQ1(PetscObjectComm((PetscObject) ts), PETSC_ERR_SUP, "Do not support particle layout in dimension %D", dim);
581       }
582       ierr = VecRestoreArray(u, &coords);CHKERRQ(ierr);
583       break;
584     default: SETERRQ1(PetscObjectComm((PetscObject) ts), PETSC_ERR_ARG_WRONG, "Invalid particle layout type %s", partLayoutTypes[PetscMin(user->partLayout, NUM_PART_LAYOUT_TYPES)]);
585   }
586   PetscFunctionReturn(0);
587 }
588 
589 static PetscErrorCode SetupDiscretization(DM dm, DM sdm, AppCtx *user)
590 {
591   DM              cdm = dm;
592   PetscFE         fe[3];
593   Parameter      *param;
594   PetscInt       *cellid, n[3];
595   PetscReal       x[3], dx[3];
596   PetscScalar    *coords;
597   DMPolytopeType  ct;
598   PetscInt        dim, d, cStart, cEnd, c, Np, p, i, j, k;
599   PetscBool       simplex;
600   MPI_Comm        comm;
601   PetscErrorCode  ierr;
602 
603   PetscFunctionBeginUser;
604   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
605   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
606   ierr = DMPlexGetCellType(dm, cStart, &ct);CHKERRQ(ierr);
607   simplex = DMPolytopeTypeGetNumVertices(ct) == DMPolytopeTypeGetDim(ct)+1 ? PETSC_TRUE : PETSC_FALSE;
608   /* Create finite element */
609   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
610   ierr = PetscFECreateDefault(comm, dim, dim, simplex, "vel_", PETSC_DEFAULT, &fe[0]);CHKERRQ(ierr);
611   ierr = PetscObjectSetName((PetscObject) fe[0], "velocity");CHKERRQ(ierr);
612 
613   ierr = PetscFECreateDefault(comm, dim, 1, simplex, "pres_", PETSC_DEFAULT, &fe[1]);CHKERRQ(ierr);
614   ierr = PetscFECopyQuadrature(fe[0], fe[1]);CHKERRQ(ierr);
615   ierr = PetscObjectSetName((PetscObject) fe[1], "pressure");CHKERRQ(ierr);
616 
617   ierr = PetscFECreateDefault(comm, dim, 1, simplex, "temp_", PETSC_DEFAULT, &fe[2]);CHKERRQ(ierr);
618   ierr = PetscFECopyQuadrature(fe[0], fe[2]);CHKERRQ(ierr);
619   ierr = PetscObjectSetName((PetscObject) fe[2], "temperature");CHKERRQ(ierr);
620 
621   /* Set discretization and boundary conditions for each mesh */
622   ierr = DMSetField(dm, 0, NULL, (PetscObject) fe[0]);CHKERRQ(ierr);
623   ierr = DMSetField(dm, 1, NULL, (PetscObject) fe[1]);CHKERRQ(ierr);
624   ierr = DMSetField(dm, 2, NULL, (PetscObject) fe[2]);CHKERRQ(ierr);
625   ierr = DMCreateDS(dm);CHKERRQ(ierr);
626   ierr = SetupProblem(dm, user);CHKERRQ(ierr);
627   ierr = PetscBagGetData(user->bag, (void **) &param);CHKERRQ(ierr);
628   while (cdm) {
629     ierr = DMCopyDisc(dm, cdm);CHKERRQ(ierr);
630     ierr = DMGetCoarseDM(cdm, &cdm);CHKERRQ(ierr);
631   }
632   ierr = PetscFEDestroy(&fe[0]);CHKERRQ(ierr);
633   ierr = PetscFEDestroy(&fe[1]);CHKERRQ(ierr);
634   ierr = PetscFEDestroy(&fe[2]);CHKERRQ(ierr);
635 
636   {
637     PetscObject  pressure;
638     MatNullSpace nullspacePres;
639 
640     ierr = DMGetField(dm, 1, NULL, &pressure);CHKERRQ(ierr);
641     ierr = MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nullspacePres);CHKERRQ(ierr);
642     ierr = PetscObjectCompose(pressure, "nullspace", (PetscObject) nullspacePres);CHKERRQ(ierr);
643     ierr = MatNullSpaceDestroy(&nullspacePres);CHKERRQ(ierr);
644   }
645 
646   /* Setup particle information */
647   ierr = DMSwarmSetType(sdm, DMSWARM_PIC);CHKERRQ(ierr);
648   ierr = DMSwarmRegisterPetscDatatypeField(sdm, "mass", 1, PETSC_REAL);CHKERRQ(ierr);
649   ierr = DMSwarmFinalizeFieldRegister(sdm);CHKERRQ(ierr);
650   switch (user->partLayout) {
651     case PART_LAYOUT_CELL:
652       ierr = DMSwarmSetLocalSizes(sdm, (cEnd - cStart) * user->Npc, 0);CHKERRQ(ierr);
653       ierr = DMSetFromOptions(sdm);CHKERRQ(ierr);
654       ierr = DMSwarmGetField(sdm, DMSwarmPICField_cellid, NULL, NULL, (void **) &cellid);CHKERRQ(ierr);
655       for (c = cStart; c < cEnd; ++c) {
656         for (p = 0; p < user->Npc; ++p) {
657           const PetscInt n = c*user->Npc + p;
658 
659           cellid[n] = c;
660         }
661       }
662       ierr = DMSwarmRestoreField(sdm, DMSwarmPICField_cellid, NULL, NULL, (void **) &cellid);CHKERRQ(ierr);
663       ierr = DMSwarmSetPointCoordinatesRandom(sdm, user->Npc);CHKERRQ(ierr);
664       break;
665     case PART_LAYOUT_BOX:
666       Np = 1;
667       for (d = 0; d < dim; ++d) {
668         n[d]  = user->Npb;
669         dx[d] = (user->partUpper[d] - user->partLower[d])/PetscMax(1, n[d] - 1);
670         Np   *= n[d];
671       }
672       ierr = DMSwarmSetLocalSizes(sdm, Np, 0);CHKERRQ(ierr);
673       ierr = DMSetFromOptions(sdm);CHKERRQ(ierr);
674       ierr = DMSwarmGetField(sdm, DMSwarmPICField_coor, NULL, NULL, (void **) &coords);CHKERRQ(ierr);
675       switch (dim) {
676         case 2:
677           x[0] = user->partLower[0];
678           for (i = 0; i < n[0]; ++i, x[0] += dx[0]) {
679             x[1] = user->partLower[1];
680             for (j = 0; j < n[1]; ++j, x[1] += dx[1]) {
681               const PetscInt p = j*n[0] + i;
682               for (d = 0; d < dim; ++d) coords[p*dim + d] = x[d];
683             }
684           }
685           break;
686         case 3:
687           x[0] = user->partLower[0];
688           for (i = 0; i < n[0]; ++i, x[0] += dx[0]) {
689             x[1] = user->partLower[1];
690             for (j = 0; j < n[1]; ++j, x[1] += dx[1]) {
691               x[2] = user->partLower[2];
692               for (k = 0; k < n[2]; ++k, x[2] += dx[2]) {
693                 const PetscInt p = (k*n[1] + j)*n[0] + i;
694                 for (d = 0; d < dim; ++d) coords[p*dim + d] = x[d];
695               }
696             }
697           }
698           break;
699         default: SETERRQ1(comm, PETSC_ERR_SUP, "Do not support particle layout in dimension %D", dim);
700       }
701       ierr = DMSwarmRestoreField(sdm, DMSwarmPICField_coor, NULL, NULL, (void **) &coords);CHKERRQ(ierr);
702       ierr = DMSwarmGetField(sdm, DMSwarmPICField_cellid, NULL, NULL, (void **) &cellid);CHKERRQ(ierr);
703       for (p = 0; p < Np; ++p) cellid[p] = 0;
704       ierr = DMSwarmRestoreField(sdm, DMSwarmPICField_cellid, NULL, NULL, (void **) &cellid);CHKERRQ(ierr);
705       ierr = DMSwarmMigrate(sdm, PETSC_TRUE);CHKERRQ(ierr);
706       break;
707     default: SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Invalid particle layout type %s", partLayoutTypes[PetscMin(user->partLayout, NUM_PART_LAYOUT_TYPES)]);
708   }
709   ierr = PetscObjectSetName((PetscObject) sdm, "Particles");CHKERRQ(ierr);
710   ierr = DMViewFromOptions(sdm, NULL, "-dm_view");CHKERRQ(ierr);
711   PetscFunctionReturn(0);
712 }
713 
714 static PetscErrorCode CreatePressureNullSpace(DM dm, PetscInt ofield, PetscInt nfield, MatNullSpace *nullSpace)
715 {
716   Vec              vec;
717   PetscErrorCode (*funcs[3])(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *) = {zero, zero, zero};
718   PetscErrorCode   ierr;
719 
720   PetscFunctionBeginUser;
721   if (ofield != 1) SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Nullspace must be for pressure field at index 1, not %D", ofield);
722   funcs[nfield] = constant;
723   ierr = DMCreateGlobalVector(dm, &vec);CHKERRQ(ierr);
724   ierr = DMProjectFunction(dm, 0.0, funcs, NULL, INSERT_ALL_VALUES, vec);CHKERRQ(ierr);
725   ierr = VecNormalize(vec, NULL);CHKERRQ(ierr);
726   ierr = PetscObjectSetName((PetscObject) vec, "Pressure Null Space");CHKERRQ(ierr);
727   ierr = VecViewFromOptions(vec, NULL, "-pressure_nullspace_view");CHKERRQ(ierr);
728   ierr = MatNullSpaceCreate(PetscObjectComm((PetscObject) dm), PETSC_FALSE, 1, &vec, nullSpace);CHKERRQ(ierr);
729   ierr = VecDestroy(&vec);CHKERRQ(ierr);
730   PetscFunctionReturn(0);
731 }
732 
733 static PetscErrorCode RemoveDiscretePressureNullspace_Private(TS ts, Vec u)
734 {
735   DM             dm;
736   MatNullSpace   nullsp;
737   PetscErrorCode ierr;
738 
739   PetscFunctionBegin;
740   ierr = TSGetDM(ts, &dm);CHKERRQ(ierr);
741   ierr = CreatePressureNullSpace(dm, 1, 1, &nullsp);CHKERRQ(ierr);
742   ierr = MatNullSpaceRemove(nullsp, u);CHKERRQ(ierr);
743   ierr = MatNullSpaceDestroy(&nullsp);CHKERRQ(ierr);
744   PetscFunctionReturn(0);
745 }
746 
747 /* Make the discrete pressure discretely divergence free */
748 static PetscErrorCode RemoveDiscretePressureNullspace(TS ts)
749 {
750   Vec            u;
751   PetscErrorCode ierr;
752 
753   PetscFunctionBegin;
754   ierr = TSGetSolution(ts, &u);CHKERRQ(ierr);
755   ierr = RemoveDiscretePressureNullspace_Private(ts, u);CHKERRQ(ierr);
756   PetscFunctionReturn(0);
757 }
758 
759 static PetscErrorCode SetInitialConditions(TS ts, Vec u)
760 {
761   DM             dm;
762   PetscReal      t;
763   PetscErrorCode ierr;
764 
765   PetscFunctionBegin;
766   ierr = TSGetDM(ts, &dm);CHKERRQ(ierr);
767   ierr = TSGetTime(ts, &t);CHKERRQ(ierr);
768   ierr = DMComputeExactSolution(dm, t, u, NULL);CHKERRQ(ierr);
769   ierr = RemoveDiscretePressureNullspace_Private(ts, u);CHKERRQ(ierr);
770   PetscFunctionReturn(0);
771 }
772 
773 static PetscErrorCode MonitorError(TS ts, PetscInt step, PetscReal crtime, Vec u, void *ctx)
774 {
775   PetscErrorCode (*exactFuncs[3])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
776   void            *ctxs[3];
777   DM               dm;
778   PetscDS          ds;
779   Vec              v;
780   PetscReal        ferrors[3];
781   PetscInt         tl, l, f;
782   PetscErrorCode   ierr;
783 
784   PetscFunctionBeginUser;
785   ierr = TSGetDM(ts, &dm);CHKERRQ(ierr);
786   ierr = DMGetDS(dm, &ds);CHKERRQ(ierr);
787 
788   for (f = 0; f < 3; ++f) {ierr = PetscDSGetExactSolution(ds, f, &exactFuncs[f], &ctxs[f]);CHKERRQ(ierr);}
789   ierr = DMComputeL2FieldDiff(dm, crtime, exactFuncs, ctxs, u, ferrors);CHKERRQ(ierr);
790   ierr = PetscObjectGetTabLevel((PetscObject) ts, &tl);CHKERRQ(ierr);
791   for (l = 0; l < tl; ++l) {ierr = PetscPrintf(PETSC_COMM_WORLD, "\t");CHKERRQ(ierr);}
792   ierr = 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]);CHKERRQ(ierr);
793 
794   ierr = DMGetGlobalVector(dm, &u);CHKERRQ(ierr);
795   ierr = PetscObjectSetName((PetscObject) u, "Numerical Solution");CHKERRQ(ierr);
796   ierr = VecViewFromOptions(u, NULL, "-sol_vec_view");CHKERRQ(ierr);
797   ierr = DMRestoreGlobalVector(dm, &u);CHKERRQ(ierr);
798 
799   ierr = DMGetGlobalVector(dm, &v);CHKERRQ(ierr);
800   ierr = DMProjectFunction(dm, 0.0, exactFuncs, ctxs, INSERT_ALL_VALUES, v);CHKERRQ(ierr);
801   ierr = PetscObjectSetName((PetscObject) v, "Exact Solution");CHKERRQ(ierr);
802   ierr = VecViewFromOptions(v, NULL, "-exact_vec_view");CHKERRQ(ierr);
803   ierr = DMRestoreGlobalVector(dm, &v);CHKERRQ(ierr);
804 
805   PetscFunctionReturn(0);
806 }
807 
808 /* Note that adv->x0 will not be correct after migration */
809 static PetscErrorCode ComputeParticleError(TS ts, Vec u, Vec e)
810 {
811   AdvCtx            *adv;
812   DM                 sdm;
813   Parameter         *param;
814   const PetscScalar *xp0, *xp;
815   PetscScalar       *ep;
816   PetscReal          time;
817   PetscInt           dim, Np, p;
818   MPI_Comm           comm;
819   PetscErrorCode     ierr;
820 
821   PetscFunctionBeginUser;
822   ierr = TSGetTime(ts, &time);CHKERRQ(ierr);
823   ierr = TSGetApplicationContext(ts, (void **) &adv);CHKERRQ(ierr);
824   ierr = PetscBagGetData(adv->ctx->bag, (void **) &param);CHKERRQ(ierr);
825   ierr = PetscObjectGetComm((PetscObject) ts, &comm);CHKERRQ(ierr);
826   ierr = TSGetDM(ts, &sdm);CHKERRQ(ierr);
827   ierr = DMGetDimension(sdm, &dim);CHKERRQ(ierr);
828   ierr = DMSwarmGetLocalSize(sdm, &Np);CHKERRQ(ierr);
829   ierr = VecGetArrayRead(adv->x0, &xp0);CHKERRQ(ierr);
830   ierr = VecGetArrayRead(u, &xp);CHKERRQ(ierr);
831   ierr = VecGetArrayWrite(e, &ep);CHKERRQ(ierr);
832   for (p = 0; p < Np; ++p) {
833     PetscScalar x[3];
834     PetscReal   x0[3];
835     PetscInt    d;
836 
837     for (d = 0; d < dim; ++d) x0[d] = PetscRealPart(xp0[p*dim+d]);
838     ierr = adv->exact(dim, time, x0, 1, x, param);CHKERRQ(ierr);
839     for (d = 0; d < dim; ++d) ep[p*dim+d] += x[d] - xp[p*dim+d];
840   }
841   ierr = VecRestoreArrayRead(adv->x0, &xp0);CHKERRQ(ierr);
842   ierr = VecRestoreArrayRead(u, &xp);CHKERRQ(ierr);
843   ierr = VecRestoreArrayWrite(e, &ep);CHKERRQ(ierr);
844   PetscFunctionReturn(0);
845 }
846 
847 static PetscErrorCode MonitorParticleError(TS ts, PetscInt step, PetscReal time, Vec u, void *ctx)
848 {
849   AdvCtx            *adv = (AdvCtx *) ctx;
850   DM                 sdm;
851   Parameter         *param;
852   const PetscScalar *xp0, *xp;
853   PetscReal          error = 0.0;
854   PetscInt           dim, tl, l, Np, p;
855   MPI_Comm           comm;
856   PetscErrorCode     ierr;
857 
858   PetscFunctionBeginUser;
859   ierr = PetscBagGetData(adv->ctx->bag, (void **) &param);CHKERRQ(ierr);
860   ierr = PetscObjectGetComm((PetscObject) ts, &comm);CHKERRQ(ierr);
861   ierr = TSGetDM(ts, &sdm);CHKERRQ(ierr);
862   ierr = DMGetDimension(sdm, &dim);CHKERRQ(ierr);
863   ierr = DMSwarmGetLocalSize(sdm, &Np);CHKERRQ(ierr);
864   ierr = VecGetArrayRead(adv->x0, &xp0);CHKERRQ(ierr);
865   ierr = VecGetArrayRead(u, &xp);CHKERRQ(ierr);
866   for (p = 0; p < Np; ++p) {
867     PetscScalar x[3];
868     PetscReal   x0[3];
869     PetscReal   perror = 0.0;
870     PetscInt    d;
871 
872     for (d = 0; d < dim; ++d) x0[d] = PetscRealPart(xp0[p*dim+d]);
873     ierr = adv->exact(dim, time, x0, 1, x, param);CHKERRQ(ierr);
874     for (d = 0; d < dim; ++d) perror += PetscSqr(PetscRealPart(x[d] - xp[p*dim+d]));
875     error += perror;
876   }
877   ierr = VecRestoreArrayRead(adv->x0, &xp0);CHKERRQ(ierr);
878   ierr = VecRestoreArrayRead(u, &xp);CHKERRQ(ierr);
879   ierr = PetscObjectGetTabLevel((PetscObject) ts, &tl);CHKERRQ(ierr);
880   for (l = 0; l < tl; ++l) {ierr = PetscPrintf(PETSC_COMM_WORLD, "\t");CHKERRQ(ierr);}
881   ierr = PetscPrintf(comm, "Timestep: %04d time = %-8.4g \t L_2 Particle Error: [%2.3g]\n", (int) step, (double) time, (double) error);CHKERRQ(ierr);
882   PetscFunctionReturn(0);
883 }
884 
885 static PetscErrorCode AdvectParticles(TS ts)
886 {
887   TS             sts;
888   DM             sdm;
889   Vec            coordinates;
890   AdvCtx        *adv;
891   PetscReal      time;
892   PetscBool      lreset, reset;
893   PetscInt       dim, n, N, newn, newN;
894   PetscErrorCode ierr;
895 
896   PetscFunctionBeginUser;
897   ierr = PetscObjectQuery((PetscObject) ts, "_SwarmTS",  (PetscObject *) &sts);CHKERRQ(ierr);
898   ierr = TSGetDM(sts, &sdm);CHKERRQ(ierr);
899   ierr = TSGetRHSFunction(sts, NULL, NULL, (void **) &adv);CHKERRQ(ierr);
900   ierr = DMGetDimension(sdm, &dim);CHKERRQ(ierr);
901   ierr = DMSwarmGetSize(sdm, &N);CHKERRQ(ierr);
902   ierr = DMSwarmGetLocalSize(sdm, &n);CHKERRQ(ierr);
903   ierr = DMSwarmCreateGlobalVectorFromField(sdm, DMSwarmPICField_coor, &coordinates);CHKERRQ(ierr);
904   ierr = TSGetTime(ts, &time);CHKERRQ(ierr);
905   ierr = TSSetMaxTime(sts, time);CHKERRQ(ierr);
906   adv->tf = time;
907   ierr = TSSolve(sts, coordinates);CHKERRQ(ierr);
908   ierr = DMSwarmDestroyGlobalVectorFromField(sdm, DMSwarmPICField_coor, &coordinates);CHKERRQ(ierr);
909   ierr = VecCopy(adv->uf, adv->ui);CHKERRQ(ierr);
910   adv->ti = adv->tf;
911 
912   ierr = DMSwarmMigrate(sdm, PETSC_TRUE);CHKERRQ(ierr);
913   ierr = DMSwarmGetSize(sdm, &newN);CHKERRQ(ierr);
914   ierr = DMSwarmGetLocalSize(sdm, &newn);CHKERRQ(ierr);
915   lreset = (n != newn || N != newN) ? PETSC_TRUE : PETSC_FALSE;
916   ierr = MPI_Allreduce(&lreset, &reset, 1, MPIU_BOOL, MPI_LOR, PetscObjectComm((PetscObject) sts));CHKERRMPI(ierr);
917   if (reset) {
918     ierr = TSReset(sts);CHKERRQ(ierr);
919     ierr = DMSwarmVectorDefineField(sdm, DMSwarmPICField_coor);CHKERRQ(ierr);
920   }
921   ierr = DMViewFromOptions(sdm, NULL, "-dm_view");CHKERRQ(ierr);
922   PetscFunctionReturn(0);
923 }
924 
925 int main(int argc, char **argv)
926 {
927   DM              dm, sdm;
928   TS              ts, sts;
929   Vec             u, xtmp;
930   AppCtx          user;
931   AdvCtx          adv;
932   PetscReal       t;
933   PetscInt        dim;
934   PetscErrorCode  ierr;
935 
936   ierr = PetscInitialize(&argc, &argv, NULL,help);if (ierr) return ierr;
937   ierr = ProcessOptions(PETSC_COMM_WORLD, &user);CHKERRQ(ierr);
938   ierr = PetscBagCreate(PETSC_COMM_WORLD, sizeof(Parameter), &user.bag);CHKERRQ(ierr);
939   ierr = SetupParameters(&user);CHKERRQ(ierr);
940   ierr = TSCreate(PETSC_COMM_WORLD, &ts);CHKERRQ(ierr);
941   ierr = CreateMesh(PETSC_COMM_WORLD, &user, &dm);CHKERRQ(ierr);
942   ierr = TSSetDM(ts, dm);CHKERRQ(ierr);
943   ierr = DMSetApplicationContext(dm, &user);CHKERRQ(ierr);
944   /* Discretize chemical species */
945   ierr = DMCreate(PETSC_COMM_WORLD, &sdm);CHKERRQ(ierr);
946   ierr = PetscObjectSetOptionsPrefix((PetscObject) sdm, "part_");CHKERRQ(ierr);
947   ierr = DMSetType(sdm, DMSWARM);CHKERRQ(ierr);
948   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
949   ierr = DMSetDimension(sdm, dim);CHKERRQ(ierr);
950   ierr = DMSwarmSetCellDM(sdm, dm);CHKERRQ(ierr);
951   /* Setup problem */
952   ierr = SetupDiscretization(dm, sdm, &user);CHKERRQ(ierr);
953   ierr = DMPlexCreateClosureIndex(dm, NULL);CHKERRQ(ierr);
954 
955   ierr = DMCreateGlobalVector(dm, &u);CHKERRQ(ierr);
956   ierr = DMSetNullSpaceConstructor(dm, 1, CreatePressureNullSpace);CHKERRQ(ierr);
957 
958   ierr = DMTSSetBoundaryLocal(dm, DMPlexTSComputeBoundary, &user);CHKERRQ(ierr);
959   ierr = DMTSSetIFunctionLocal(dm, DMPlexTSComputeIFunctionFEM, &user);CHKERRQ(ierr);
960   ierr = DMTSSetIJacobianLocal(dm, DMPlexTSComputeIJacobianFEM, &user);CHKERRQ(ierr);
961   ierr = TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr);
962   ierr = TSSetPreStep(ts, RemoveDiscretePressureNullspace);CHKERRQ(ierr);
963   ierr = TSMonitorSet(ts, MonitorError, &user, NULL);CHKERRQ(ierr);CHKERRQ(ierr);
964   ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
965 
966   ierr = TSSetComputeInitialCondition(ts, SetInitialConditions);CHKERRQ(ierr); /* Must come after SetFromOptions() */
967   ierr = SetInitialConditions(ts, u);CHKERRQ(ierr);
968   ierr = TSGetTime(ts, &t);CHKERRQ(ierr);
969   ierr = DMSetOutputSequenceNumber(dm, 0, t);CHKERRQ(ierr);
970   ierr = DMTSCheckFromOptions(ts, u);CHKERRQ(ierr);
971 
972   /* Setup particle position integrator */
973   ierr = TSCreate(PETSC_COMM_WORLD, &sts);CHKERRQ(ierr);
974   ierr = PetscObjectSetOptionsPrefix((PetscObject) sts, "part_");CHKERRQ(ierr);
975   ierr = PetscObjectIncrementTabLevel((PetscObject) sts, (PetscObject) ts, 1);CHKERRQ(ierr);
976   ierr = TSSetDM(sts, sdm);CHKERRQ(ierr);
977   ierr = TSSetProblemType(sts, TS_NONLINEAR);CHKERRQ(ierr);
978   ierr = TSSetExactFinalTime(sts, TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr);
979   ierr = TSMonitorSet(sts, MonitorParticleError, &adv, NULL);CHKERRQ(ierr);CHKERRQ(ierr);
980   ierr = TSSetFromOptions(sts);CHKERRQ(ierr);
981   ierr = TSSetApplicationContext(sts, &adv);CHKERRQ(ierr);
982   ierr = TSSetComputeExactError(sts, ComputeParticleError);CHKERRQ(ierr);
983   ierr = TSSetComputeInitialCondition(sts, SetInitialParticleConditions);CHKERRQ(ierr);
984   adv.ti = t;
985   adv.uf = u;
986   ierr = VecDuplicate(adv.uf, &adv.ui);
987   ierr = VecCopy(u, adv.ui);CHKERRQ(ierr);
988   ierr = TSSetRHSFunction(sts, NULL, FreeStreaming, &adv);CHKERRQ(ierr);
989   ierr = TSSetPostStep(ts, AdvectParticles);CHKERRQ(ierr);
990   ierr = PetscObjectCompose((PetscObject) ts, "_SwarmTS", (PetscObject) sts);CHKERRQ(ierr);
991   ierr = DMSwarmVectorDefineField(sdm, DMSwarmPICField_coor);CHKERRQ(ierr);
992   ierr = DMCreateGlobalVector(sdm, &adv.x0);CHKERRQ(ierr);
993   ierr = DMSwarmCreateGlobalVectorFromField(sdm, DMSwarmPICField_coor, &xtmp);CHKERRQ(ierr);
994   ierr = VecCopy(xtmp, adv.x0);CHKERRQ(ierr);
995   ierr = DMSwarmDestroyGlobalVectorFromField(sdm, DMSwarmPICField_coor, &xtmp);CHKERRQ(ierr);
996   switch(user.solType){
997     case SOL_TRIG_TRIG: adv.exact = trig_trig_x;break;
998     default: SETERRQ2(PetscObjectComm((PetscObject) sdm), PETSC_ERR_ARG_WRONG, "Unsupported solution type: %s (%D)", solTypes[PetscMin(user.solType, NUM_SOL_TYPES)], user.solType);
999   }
1000   adv.ctx = &user;
1001 
1002   ierr = TSSolve(ts, u);CHKERRQ(ierr);
1003   ierr = DMTSCheckFromOptions(ts, u);CHKERRQ(ierr);
1004   ierr = PetscObjectSetName((PetscObject) u, "Numerical Solution");CHKERRQ(ierr);
1005 
1006   ierr = VecDestroy(&u);CHKERRQ(ierr);
1007   ierr = VecDestroy(&adv.x0);CHKERRQ(ierr);
1008   ierr = VecDestroy(&adv.ui);CHKERRQ(ierr);
1009   ierr = DMDestroy(&dm);CHKERRQ(ierr);
1010   ierr = DMDestroy(&sdm);CHKERRQ(ierr);
1011   ierr = TSDestroy(&ts);CHKERRQ(ierr);
1012   ierr = TSDestroy(&sts);CHKERRQ(ierr);
1013   ierr = PetscBagDestroy(&user.bag);CHKERRQ(ierr);
1014   ierr = PetscFinalize();
1015   return ierr;
1016 }
1017 
1018 /*TEST
1019 
1020   # Swarm does not work with complex
1021   test:
1022     suffix: 2d_tri_p2_p1_p1_tconvp
1023     requires: triangle !single !complex
1024     args: -dm_plex_separate_marker -sol_type trig_trig -dm_refine 2 \
1025       -vel_petscspace_degree 2 -pres_petscspace_degree 1 -temp_petscspace_degree 1 \
1026       -dmts_check .001 -ts_max_steps 4 -ts_dt 0.1 -ts_monitor_cancel \
1027       -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
1028       -pc_type fieldsplit -pc_fieldsplit_0_fields 0,2 -pc_fieldsplit_1_fields 1 -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
1029         -fieldsplit_0_pc_type lu \
1030         -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi \
1031       -omega 0.5 -part_layout_type box -part_lower 0.25,0.25 -part_upper 0.75,0.75 -Npb 5 \
1032       -part_ts_max_steps 2 -part_ts_dt 0.05 -part_ts_convergence_estimate -convest_num_refine 1 -part_ts_monitor_cancel
1033   test:
1034     suffix: 2d_tri_p2_p1_p1_exit
1035     requires: triangle !single !complex
1036     args: -dm_plex_separate_marker -sol_type trig_trig -dm_refine 1 \
1037       -vel_petscspace_degree 2 -pres_petscspace_degree 1 -temp_petscspace_degree 1 \
1038       -dmts_check .001 -ts_max_steps 10 -ts_dt 0.1 \
1039       -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
1040       -pc_type fieldsplit -pc_fieldsplit_0_fields 0,2 -pc_fieldsplit_1_fields 1 -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
1041         -fieldsplit_0_pc_type lu \
1042         -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi \
1043       -omega 0.5 -part_layout_type box -part_lower 0.25,0.25 -part_upper 0.75,0.75 -Npb 5 \
1044       -part_ts_max_steps 20 -part_ts_dt 0.05
1045 
1046 TEST*/
1047