Actual source code: ex28.c
1: static char help[] = "Example application of the Bhatnagar-Gross-Krook (BGK) collision operator.\n\
2: This example is a 0D-1V setting for the kinetic equation\n\
3: https://en.wikipedia.org/wiki/Bhatnagar%E2%80%93Gross%E2%80%93Krook_operator\n";
5: #include <petscdmplex.h>
6: #include <petscdmswarm.h>
7: #include <petscts.h>
8: #include <petscdraw.h>
9: #include <petscviewer.h>
11: typedef struct {
12: PetscInt particlesPerCell; /* The number of partices per cell */
13: PetscReal momentTol; /* Tolerance for checking moment conservation */
14: PetscBool monitorhg; /* Flag for using the TS histogram monitor */
15: PetscBool monitorsp; /* Flag for using the TS scatter monitor */
16: PetscBool monitorks; /* Monitor to perform KS test to the maxwellian */
17: PetscBool error; /* Flag for printing the error */
18: PetscInt ostep; /* print the energy at each ostep time steps */
19: PetscDraw draw; /* The draw object for histogram monitoring */
20: PetscDrawHG drawhg; /* The histogram draw context for monitoring */
21: PetscDrawSP drawsp; /* The scatter plot draw context for the monitor */
22: PetscDrawSP drawks; /* Scatterplot draw context for KS test */
23: } AppCtx;
25: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
26: {
27: PetscFunctionBeginUser;
28: options->monitorhg = PETSC_FALSE;
29: options->monitorsp = PETSC_FALSE;
30: options->monitorks = PETSC_FALSE;
31: options->particlesPerCell = 1;
32: options->momentTol = 100.0 * PETSC_MACHINE_EPSILON;
33: options->ostep = 100;
35: PetscOptionsBegin(comm, "", "Collision Options", "DMPLEX");
36: PetscCall(PetscOptionsBool("-monitorhg", "Flag to use the TS histogram monitor", "ex28.c", options->monitorhg, &options->monitorhg, NULL));
37: PetscCall(PetscOptionsBool("-monitorsp", "Flag to use the TS scatter plot monitor", "ex28.c", options->monitorsp, &options->monitorsp, NULL));
38: PetscCall(PetscOptionsBool("-monitorks", "Flag to plot KS test results", "ex28.c", options->monitorks, &options->monitorks, NULL));
39: PetscCall(PetscOptionsInt("-particles_per_cell", "Number of particles per cell", "ex28.c", options->particlesPerCell, &options->particlesPerCell, NULL));
40: PetscCall(PetscOptionsInt("-output_step", "Number of time steps between output", "ex28.c", options->ostep, &options->ostep, NULL));
41: PetscOptionsEnd();
43: PetscFunctionReturn(PETSC_SUCCESS);
44: }
46: /* Create the mesh for velocity space */
47: static PetscErrorCode CreateMesh(MPI_Comm comm, DM *dm, AppCtx *user)
48: {
49: PetscFunctionBeginUser;
50: PetscCall(DMCreate(comm, dm));
51: PetscCall(DMSetType(*dm, DMPLEX));
52: PetscCall(DMSetFromOptions(*dm));
53: PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view"));
54: PetscFunctionReturn(PETSC_SUCCESS);
55: }
57: /* Since we are putting the same number of particles in each cell, this amounts to a uniform distribution of v */
58: static PetscErrorCode SetInitialCoordinates(DM sw)
59: {
60: AppCtx *user;
61: PetscRandom rnd;
62: DM dm;
63: DMPolytopeType ct;
64: PetscBool simplex;
65: PetscReal *centroid, *coords, *xi0, *v0, *J, *invJ, detJ, *vals;
66: PetscInt dim, d, cStart, cEnd, c, Np, p;
68: PetscFunctionBeginUser;
69: PetscCall(PetscRandomCreate(PetscObjectComm((PetscObject)sw), &rnd));
70: PetscCall(PetscRandomSetInterval(rnd, -1.0, 1.0));
71: PetscCall(PetscRandomSetFromOptions(rnd));
73: PetscCall(DMGetApplicationContext(sw, &user));
74: Np = user->particlesPerCell;
75: PetscCall(DMGetDimension(sw, &dim));
76: PetscCall(DMSwarmGetCellDM(sw, &dm));
77: PetscCall(DMGetCoordinatesLocalSetUp(dm));
78: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
79: PetscCall(DMPlexGetCellType(dm, cStart, &ct));
80: simplex = DMPolytopeTypeGetNumVertices(ct) == DMPolytopeTypeGetDim(ct) + 1 ? PETSC_TRUE : PETSC_FALSE;
81: PetscCall(PetscMalloc5(dim, ¢roid, dim, &xi0, dim, &v0, dim * dim, &J, dim * dim, &invJ));
82: for (d = 0; d < dim; ++d) xi0[d] = -1.0;
83: PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
84: PetscCall(DMSwarmGetField(sw, "w_q", NULL, NULL, (void **)&vals));
85: for (c = cStart; c < cEnd; ++c) {
86: if (Np == 1) {
87: PetscCall(DMPlexComputeCellGeometryFVM(dm, c, NULL, centroid, NULL));
88: for (d = 0; d < dim; ++d) {
89: coords[c * dim + d] = centroid[d];
90: if ((coords[c * dim + d] >= -1) && (coords[c * dim + d] <= 1)) {
91: vals[c] = 1.0;
92: } else {
93: vals[c] = 0.;
94: }
95: }
96: } else {
97: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ)); /* affine */
98: for (p = 0; p < Np; ++p) {
99: const PetscInt n = c * Np + p;
100: PetscReal sum = 0.0, refcoords[3];
102: for (d = 0; d < dim; ++d) {
103: PetscCall(PetscRandomGetValueReal(rnd, &refcoords[d]));
104: sum += refcoords[d];
105: }
106: if (simplex && sum > 0.0)
107: for (d = 0; d < dim; ++d) refcoords[d] -= PetscSqrtReal(dim) * sum;
108: vals[n] = 1.0;
109: PetscCall(DMPlexReferenceToCoordinates(dm, c, 1, refcoords, &coords[n * dim]));
110: }
111: }
112: }
113: PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
114: PetscCall(DMSwarmRestoreField(sw, "w_q", NULL, NULL, (void **)&vals));
115: PetscCall(PetscFree5(centroid, xi0, v0, J, invJ));
116: PetscCall(PetscRandomDestroy(&rnd));
117: PetscFunctionReturn(PETSC_SUCCESS);
118: }
120: /* The initial conditions are just the initial particle weights */
121: static PetscErrorCode SetInitialConditions(DM dmSw, Vec u)
122: {
123: DM dm;
124: AppCtx *user;
125: PetscReal *vals;
126: PetscScalar *initialConditions;
127: PetscInt dim, d, cStart, cEnd, c, Np, p, n;
129: PetscFunctionBeginUser;
130: PetscCall(VecGetLocalSize(u, &n));
131: PetscCall(DMGetApplicationContext(dmSw, &user));
132: Np = user->particlesPerCell;
133: PetscCall(DMSwarmGetCellDM(dmSw, &dm));
134: PetscCall(DMGetDimension(dm, &dim));
135: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
136: PetscCheck(n == (cEnd - cStart) * Np, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "TS solution local size %" PetscInt_FMT " != %" PetscInt_FMT " nm particles", n, (cEnd - cStart) * Np);
137: PetscCall(DMSwarmGetField(dmSw, "w_q", NULL, NULL, (void **)&vals));
138: PetscCall(VecGetArray(u, &initialConditions));
139: for (c = cStart; c < cEnd; ++c) {
140: for (p = 0; p < Np; ++p) {
141: const PetscInt n = c * Np + p;
142: for (d = 0; d < dim; d++) initialConditions[n] = vals[n];
143: }
144: }
145: PetscCall(VecRestoreArray(u, &initialConditions));
146: PetscCall(DMSwarmRestoreField(dmSw, "w_q", NULL, NULL, (void **)&vals));
147: PetscFunctionReturn(PETSC_SUCCESS);
148: }
150: static PetscErrorCode CreateParticles(DM dm, DM *sw, AppCtx *user)
151: {
152: PetscInt *cellid;
153: PetscInt dim, cStart, cEnd, c, Np = user->particlesPerCell, p;
155: PetscFunctionBeginUser;
156: PetscCall(DMGetDimension(dm, &dim));
157: PetscCall(DMCreate(PetscObjectComm((PetscObject)dm), sw));
158: PetscCall(DMSetType(*sw, DMSWARM));
159: PetscCall(DMSetDimension(*sw, dim));
160: PetscCall(DMSwarmSetType(*sw, DMSWARM_PIC));
161: PetscCall(DMSwarmSetCellDM(*sw, dm));
162: PetscCall(DMSwarmRegisterPetscDatatypeField(*sw, "kinematics", dim, PETSC_REAL));
163: PetscCall(DMSwarmRegisterPetscDatatypeField(*sw, "w_q", 1, PETSC_SCALAR));
164: PetscCall(DMSwarmFinalizeFieldRegister(*sw));
165: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
166: PetscCall(DMSwarmSetLocalSizes(*sw, (cEnd - cStart) * Np, 0));
167: PetscCall(DMSetFromOptions(*sw));
168: PetscCall(DMSwarmGetField(*sw, DMSwarmPICField_cellid, NULL, NULL, (void **)&cellid));
169: for (c = cStart; c < cEnd; ++c) {
170: for (p = 0; p < Np; ++p) {
171: const PetscInt n = c * Np + p;
172: cellid[n] = c;
173: }
174: }
175: PetscCall(DMSwarmRestoreField(*sw, DMSwarmPICField_cellid, NULL, NULL, (void **)&cellid));
176: PetscCall(PetscObjectSetName((PetscObject)*sw, "Particles"));
177: PetscCall(DMViewFromOptions(*sw, NULL, "-sw_view"));
178: PetscFunctionReturn(PETSC_SUCCESS);
179: }
181: /*
182: f_t = 1/\tau \left( f_eq - f \right)
183: n_t = 1/\tau \left( \int f_eq - \int f \right) = 1/\tau (n - n) = 0
184: v_t = 1/\tau \left( \int v f_eq - \int v f \right) = 1/\tau (v - v) = 0
185: E_t = 1/\tau \left( \int v^2 f_eq - \int v^2 f \right) = 1/\tau (T - T) = 0
187: Let's look at a single cell:
189: \int_C f_t = 1/\tau \left( \int_C f_eq - \int_C f \right)
190: \sum_{x_i \in C} w^i_t = 1/\tau \left( F_eq(C) - \sum_{x_i \in C} w_i \right)
191: */
193: /* This computes the 1D Maxwellian distribution for given mass n, velocity v, and temperature T */
194: static PetscReal ComputePDF(PetscReal m, PetscReal n, PetscReal T, PetscReal v[])
195: {
196: return (n / PetscSqrtReal(2.0 * PETSC_PI * T / m)) * PetscExpReal(-0.5 * m * PetscSqr(v[0]) / T);
197: }
199: /*
200: erf z = \frac{2}{\sqrt\pi} \int^z_0 dt e^{-t^2} and erf \infty = 1
202: We begin with our distribution
204: \sqrt{\frac{m}{2 \pi T}} e^{-m v^2/2T}
206: Let t = \sqrt{m/2T} v, z = \sqrt{m/2T} w, so that we now have
208: \sqrt{\frac{m}{2 \pi T}} \int^w_0 dv e^{-m v^2/2T}
209: = \sqrt{\frac{m}{2 \pi T}} \int^{\sqrt{m/2T} w}_0 \sqrt{2T/m} dt e^{-t^2}
210: = 1/\sqrt{\pi} \int^{\sqrt{m/2T} w}_0 dt e^{-t^2}
211: = 1/2 erf(\sqrt{m/2T} w)
212: */
213: static PetscReal ComputeCDF(PetscReal m, PetscReal n, PetscReal T, PetscReal va, PetscReal vb)
214: {
215: PetscReal alpha = PetscSqrtReal(0.5 * m / T);
216: PetscReal za = alpha * va;
217: PetscReal zb = alpha * vb;
218: PetscReal sum = 0.0;
220: sum += zb >= 0 ? erf(zb) : -erf(-zb);
221: sum -= za >= 0 ? erf(za) : -erf(-za);
222: return 0.5 * n * sum;
223: }
225: static PetscErrorCode CheckDistribution(DM dm, PetscReal m, PetscReal n, PetscReal T, PetscReal v[])
226: {
227: PetscSection coordSection;
228: Vec coordsLocal;
229: PetscReal *xq, *wq;
230: PetscReal vmin, vmax, neq, veq, Teq;
231: PetscInt Nq = 100, q, cStart, cEnd, c;
233: PetscFunctionBeginUser;
234: PetscCall(DMGetBoundingBox(dm, &vmin, &vmax));
235: /* Check analytic over entire line */
236: neq = ComputeCDF(m, n, T, vmin, vmax);
237: PetscCheck(PetscAbsReal(neq - n) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Int f %g != %g mass (%g)", (double)neq, (double)n, (double)(neq - n));
238: /* Check analytic over cells */
239: PetscCall(DMGetCoordinatesLocal(dm, &coordsLocal));
240: PetscCall(DMGetCoordinateSection(dm, &coordSection));
241: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
242: neq = 0.0;
243: for (c = cStart; c < cEnd; ++c) {
244: PetscScalar *vcoords = NULL;
246: PetscCall(DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &vcoords));
247: neq += ComputeCDF(m, n, T, vcoords[0], vcoords[1]);
248: PetscCall(DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &vcoords));
249: }
250: PetscCheck(PetscAbsReal(neq - n) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell Int f %g != %g mass (%g)", (double)neq, (double)n, (double)(neq - n));
251: /* Check quadrature over entire line */
252: PetscCall(PetscMalloc2(Nq, &xq, Nq, &wq));
253: PetscCall(PetscDTGaussQuadrature(100, vmin, vmax, xq, wq));
254: neq = 0.0;
255: for (q = 0; q < Nq; ++q) neq += ComputePDF(m, n, T, &xq[q]) * wq[q];
256: PetscCheck(PetscAbsReal(neq - n) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Int f %g != %g mass (%g)", (double)neq, (double)n, (double)(neq - n));
257: /* Check omemnts with quadrature */
258: veq = 0.0;
259: for (q = 0; q < Nq; ++q) veq += xq[q] * ComputePDF(m, n, T, &xq[q]) * wq[q];
260: veq /= neq;
261: PetscCheck(PetscAbsReal(veq - v[0]) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Int v f %g != %g velocity (%g)", (double)veq, (double)v[0], (double)(veq - v[0]));
262: Teq = 0.0;
263: for (q = 0; q < Nq; ++q) Teq += PetscSqr(xq[q]) * ComputePDF(m, n, T, &xq[q]) * wq[q];
264: Teq = Teq * m / neq - PetscSqr(veq);
265: PetscCheck(PetscAbsReal(Teq - T) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Int v^2 f %g != %g temperature (%g)", (double)Teq, (double)T, (double)(Teq - T));
266: PetscCall(PetscFree2(xq, wq));
267: PetscFunctionReturn(PETSC_SUCCESS);
268: }
270: static PetscErrorCode RHSFunctionParticles(TS ts, PetscReal t, Vec U, Vec R, void *ctx)
271: {
272: const PetscScalar *u;
273: PetscSection coordSection;
274: Vec coordsLocal;
275: PetscScalar *r, *coords;
276: PetscReal n = 0.0, v = 0.0, E = 0.0, T = 0.0, m = 1.0, cn = 0.0, cv = 0.0, cE = 0.0, pE = 0.0, eqE = 0.0;
277: PetscInt dim, d, Np, Ncp, p, cStart, cEnd, c;
278: DM dmSw, plex;
280: PetscFunctionBeginUser;
281: PetscCall(VecGetLocalSize(U, &Np));
282: PetscCall(VecGetArrayRead(U, &u));
283: PetscCall(VecGetArray(R, &r));
284: PetscCall(TSGetDM(ts, &dmSw));
285: PetscCall(DMSwarmGetCellDM(dmSw, &plex));
286: PetscCall(DMGetDimension(dmSw, &dim));
287: PetscCall(DMGetCoordinatesLocal(plex, &coordsLocal));
288: PetscCall(DMGetCoordinateSection(plex, &coordSection));
289: PetscCall(DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd));
290: Np /= dim;
291: Ncp = Np / (cEnd - cStart);
292: /* Calculate moments of particle distribution, note that velocity is in the coordinate */
293: PetscCall(DMSwarmGetField(dmSw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
294: for (p = 0; p < Np; ++p) {
295: PetscReal m1 = 0.0, m2 = 0.0;
297: for (d = 0; d < dim; ++d) {
298: m1 += PetscRealPart(coords[p * dim + d]);
299: m2 += PetscSqr(PetscRealPart(coords[p * dim + d]));
300: }
301: n += u[p];
302: v += u[p] * m1;
303: E += u[p] * m2;
304: }
305: v /= n;
306: T = E * m / n - v * v;
307: PetscCall(PetscInfo(ts, "Time %.2f: mass %.4f velocity: %+.4f temperature: %.4f\n", (double)t, (double)n, (double)v, (double)T));
308: PetscCall(CheckDistribution(plex, m, n, T, &v));
309: /*
310: Begin cellwise evaluation of the collision operator. Essentially, penalize the weights of the particles
311: in that cell against the maxwellian for the number of particles expected to be in that cell
312: */
313: for (c = cStart; c < cEnd; ++c) {
314: PetscScalar *vcoords = NULL;
315: PetscReal relaxation = 1.0, neq;
316: PetscInt sp = c * Ncp, q;
318: /* Calculate equilibrium occupation for this velocity cell */
319: PetscCall(DMPlexVecGetClosure(plex, coordSection, coordsLocal, c, NULL, &vcoords));
320: neq = ComputeCDF(m, n, T, vcoords[0], vcoords[1]);
321: PetscCall(DMPlexVecRestoreClosure(plex, coordSection, coordsLocal, c, NULL, &vcoords));
322: for (q = 0; q < Ncp; ++q) r[sp + q] = (1.0 / relaxation) * (neq - u[sp + q]);
323: }
324: /* Check update */
325: for (p = 0; p < Np; ++p) {
326: PetscReal m1 = 0.0, m2 = 0.0;
327: PetscScalar *vcoords = NULL;
329: for (d = 0; d < dim; ++d) {
330: m1 += PetscRealPart(coords[p * dim + d]);
331: m2 += PetscSqr(PetscRealPart(coords[p * dim + d]));
332: }
333: cn += r[p];
334: cv += r[p] * m1;
335: cE += r[p] * m2;
336: pE += u[p] * m2;
337: PetscCall(DMPlexVecGetClosure(plex, coordSection, coordsLocal, p, NULL, &vcoords));
338: eqE += ComputeCDF(m, n, T, vcoords[0], vcoords[1]) * m2;
339: PetscCall(DMPlexVecRestoreClosure(plex, coordSection, coordsLocal, p, NULL, &vcoords));
340: }
341: PetscCall(PetscInfo(ts, "Time %.2f: mass update %.8f velocity update: %+.8f energy update: %.8f (%.8f, %.8f)\n", (double)t, (double)cn, (double)cv, (double)cE, (double)pE, (double)eqE));
342: PetscCall(DMSwarmRestoreField(dmSw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
343: PetscCall(VecRestoreArrayRead(U, &u));
344: PetscCall(VecRestoreArray(R, &r));
345: PetscFunctionReturn(PETSC_SUCCESS);
346: }
348: static PetscErrorCode HGMonitor(TS ts, PetscInt step, PetscReal t, Vec U, void *ctx)
349: {
350: AppCtx *user = (AppCtx *)ctx;
351: const PetscScalar *u;
352: DM sw, dm;
353: PetscInt dim, Np, p;
355: PetscFunctionBeginUser;
356: if (step < 0) PetscFunctionReturn(PETSC_SUCCESS);
357: if (((user->ostep > 0) && (!(step % user->ostep)))) {
358: PetscDrawAxis axis;
360: PetscCall(TSGetDM(ts, &sw));
361: PetscCall(DMSwarmGetCellDM(sw, &dm));
362: PetscCall(DMGetDimension(dm, &dim));
363: PetscCall(PetscDrawHGReset(user->drawhg));
364: PetscCall(PetscDrawHGGetAxis(user->drawhg, &axis));
365: PetscCall(PetscDrawAxisSetLabels(axis, "Particles", "V", "f(V)"));
366: PetscCall(PetscDrawAxisSetLimits(axis, -3, 3, 0, 100));
367: PetscCall(PetscDrawHGSetLimits(user->drawhg, -3.0, 3.0, 0, 10));
368: PetscCall(VecGetLocalSize(U, &Np));
369: Np /= dim;
370: PetscCall(VecGetArrayRead(U, &u));
371: /* get points from solution vector */
372: for (p = 0; p < Np; ++p) PetscCall(PetscDrawHGAddValue(user->drawhg, u[p]));
373: PetscCall(PetscDrawHGDraw(user->drawhg));
374: PetscCall(VecRestoreArrayRead(U, &u));
375: }
376: PetscFunctionReturn(PETSC_SUCCESS);
377: }
379: static PetscErrorCode SPMonitor(TS ts, PetscInt step, PetscReal t, Vec U, void *ctx)
380: {
381: AppCtx *user = (AppCtx *)ctx;
382: const PetscScalar *u;
383: PetscReal *v, *coords;
384: PetscInt Np, p;
385: DM dmSw;
387: PetscFunctionBeginUser;
389: if (step < 0) PetscFunctionReturn(PETSC_SUCCESS);
390: if (((user->ostep > 0) && (!(step % user->ostep)))) {
391: PetscDrawAxis axis;
393: PetscCall(TSGetDM(ts, &dmSw));
394: PetscCall(PetscDrawSPReset(user->drawsp));
395: PetscCall(PetscDrawSPGetAxis(user->drawsp, &axis));
396: PetscCall(PetscDrawAxisSetLabels(axis, "Particles", "V", "w"));
397: PetscCall(VecGetLocalSize(U, &Np));
398: PetscCall(VecGetArrayRead(U, &u));
399: /* get points from solution vector */
400: PetscCall(PetscMalloc1(Np, &v));
401: for (p = 0; p < Np; ++p) v[p] = PetscRealPart(u[p]);
402: PetscCall(DMSwarmGetField(dmSw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
403: for (p = 0; p < Np - 1; ++p) PetscCall(PetscDrawSPAddPoint(user->drawsp, &coords[p], &v[p]));
404: PetscCall(PetscDrawSPDraw(user->drawsp, PETSC_TRUE));
405: PetscCall(VecRestoreArrayRead(U, &u));
406: PetscCall(DMSwarmRestoreField(dmSw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
407: PetscCall(PetscFree(v));
408: }
409: PetscFunctionReturn(PETSC_SUCCESS);
410: }
412: static PetscErrorCode KSConv(TS ts, PetscInt step, PetscReal t, Vec U, void *ctx)
413: {
414: AppCtx *user = (AppCtx *)ctx;
415: const PetscScalar *u;
416: PetscScalar sup;
417: PetscReal *v, *coords, T = 0., vel = 0., step_cast, w_sum;
418: PetscInt dim, Np, p, cStart, cEnd;
419: DM sw, plex;
421: PetscFunctionBeginUser;
422: if (step < 0) PetscFunctionReturn(PETSC_SUCCESS);
423: if (((user->ostep > 0) && (!(step % user->ostep)))) {
424: PetscDrawAxis axis;
425: PetscCall(PetscDrawSPGetAxis(user->drawks, &axis));
426: PetscCall(PetscDrawAxisSetLabels(axis, "Particles", "t", "D_n"));
427: PetscCall(PetscDrawSPSetLimits(user->drawks, 0., 100, 0., 3.5));
428: PetscCall(TSGetDM(ts, &sw));
429: PetscCall(VecGetLocalSize(U, &Np));
430: PetscCall(VecGetArrayRead(U, &u));
431: /* get points from solution vector */
432: PetscCall(PetscMalloc1(Np, &v));
433: PetscCall(DMSwarmGetCellDM(sw, &plex));
434: PetscCall(DMGetDimension(sw, &dim));
435: PetscCall(DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd));
436: for (p = 0; p < Np; ++p) v[p] = PetscRealPart(u[p]);
437: PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
438: w_sum = 0.;
439: for (p = 0; p < Np; ++p) {
440: w_sum += u[p];
441: T += u[p] * coords[p] * coords[p];
442: vel += u[p] * coords[p];
443: }
444: vel /= w_sum;
445: T = T / w_sum - vel * vel;
446: sup = 0.0;
447: for (p = 0; p < Np; ++p) {
448: PetscReal tmp = 0.;
449: tmp = PetscAbs(u[p] - ComputePDF(1.0, w_sum, T, &coords[p * dim]));
450: if (tmp > sup) sup = tmp;
451: }
452: step_cast = (PetscReal)step;
453: PetscCall(PetscDrawSPAddPoint(user->drawks, &step_cast, &sup));
454: PetscCall(PetscDrawSPDraw(user->drawks, PETSC_TRUE));
455: PetscCall(VecRestoreArrayRead(U, &u));
456: PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
457: PetscCall(PetscFree(v));
458: }
459: PetscFunctionReturn(PETSC_SUCCESS);
460: }
462: static PetscErrorCode InitializeSolve(TS ts, Vec u)
463: {
464: DM dm;
465: AppCtx *user;
467: PetscFunctionBeginUser;
468: PetscCall(TSGetDM(ts, &dm));
469: PetscCall(DMGetApplicationContext(dm, &user));
470: PetscCall(SetInitialCoordinates(dm));
471: PetscCall(SetInitialConditions(dm, u));
472: PetscFunctionReturn(PETSC_SUCCESS);
473: }
474: /*
475: A single particle is generated for each velocity space cell using the dmswarmpicfield_coor and is used to evaluate collisions in that cell.
476: 0 weight ghost particles are initialized outside of a small velocity domain to ensure the tails of the amxwellian are resolved.
477: */
478: int main(int argc, char **argv)
479: {
480: TS ts; /* nonlinear solver */
481: DM dm, sw; /* Velocity space mesh and Particle Swarm */
482: Vec u, w; /* swarm vector */
483: MPI_Comm comm;
484: AppCtx user;
486: PetscFunctionBeginUser;
487: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
488: comm = PETSC_COMM_WORLD;
489: PetscCall(ProcessOptions(comm, &user));
490: PetscCall(CreateMesh(comm, &dm, &user));
491: PetscCall(CreateParticles(dm, &sw, &user));
492: PetscCall(DMSetApplicationContext(sw, &user));
493: PetscCall(TSCreate(comm, &ts));
494: PetscCall(TSSetDM(ts, sw));
495: PetscCall(TSSetMaxTime(ts, 10.0));
496: PetscCall(TSSetTimeStep(ts, 0.01));
497: PetscCall(TSSetMaxSteps(ts, 100000));
498: PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
499: if (user.monitorhg) {
500: PetscCall(PetscDrawCreate(comm, NULL, "monitor", 0, 0, 400, 300, &user.draw));
501: PetscCall(PetscDrawSetFromOptions(user.draw));
502: PetscCall(PetscDrawHGCreate(user.draw, 20, &user.drawhg));
503: PetscCall(PetscDrawHGSetColor(user.drawhg, 3));
504: PetscCall(TSMonitorSet(ts, HGMonitor, &user, NULL));
505: } else if (user.monitorsp) {
506: PetscCall(PetscDrawCreate(comm, NULL, "monitor", 0, 0, 400, 300, &user.draw));
507: PetscCall(PetscDrawSetFromOptions(user.draw));
508: PetscCall(PetscDrawSPCreate(user.draw, 1, &user.drawsp));
509: PetscCall(TSMonitorSet(ts, SPMonitor, &user, NULL));
510: } else if (user.monitorks) {
511: PetscCall(PetscDrawCreate(comm, NULL, "monitor", 0, 0, 400, 300, &user.draw));
512: PetscCall(PetscDrawSetFromOptions(user.draw));
513: PetscCall(PetscDrawSPCreate(user.draw, 1, &user.drawks));
514: PetscCall(TSMonitorSet(ts, KSConv, &user, NULL));
515: }
516: PetscCall(TSSetRHSFunction(ts, NULL, RHSFunctionParticles, &user));
517: PetscCall(TSSetFromOptions(ts));
518: PetscCall(TSSetComputeInitialCondition(ts, InitializeSolve));
519: PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "w_q", &w));
520: PetscCall(VecDuplicate(w, &u));
521: PetscCall(VecCopy(w, u));
522: PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "w_q", &w));
523: PetscCall(TSComputeInitialCondition(ts, u));
524: PetscCall(TSSolve(ts, u));
525: if (user.monitorhg) {
526: PetscCall(PetscDrawSave(user.draw));
527: PetscCall(PetscDrawHGDestroy(&user.drawhg));
528: PetscCall(PetscDrawDestroy(&user.draw));
529: }
530: if (user.monitorsp) {
531: PetscCall(PetscDrawSave(user.draw));
532: PetscCall(PetscDrawSPDestroy(&user.drawsp));
533: PetscCall(PetscDrawDestroy(&user.draw));
534: }
535: if (user.monitorks) {
536: PetscCall(PetscDrawSave(user.draw));
537: PetscCall(PetscDrawSPDestroy(&user.drawks));
538: PetscCall(PetscDrawDestroy(&user.draw));
539: }
540: PetscCall(VecDestroy(&u));
541: PetscCall(TSDestroy(&ts));
542: PetscCall(DMDestroy(&sw));
543: PetscCall(DMDestroy(&dm));
544: PetscCall(PetscFinalize());
545: return 0;
546: }
548: /*TEST
549: build:
550: requires: double !complex
551: test:
552: suffix: 1
553: args: -particles_per_cell 1 -output_step 10 -ts_type euler -dm_plex_dim 1 -dm_plex_box_faces 200 -dm_plex_box_lower -10 -dm_plex_box_upper 10 -dm_view -monitorsp
554: test:
555: suffix: 2
556: args: -particles_per_cell 1 -output_step 50 -ts_type euler -dm_plex_dim 1 -dm_plex_box_faces 200 -dm_plex_box_lower -10 -dm_plex_box_upper 10 -dm_view -monitorks
557: TEST*/