Actual source code: ex46.c

petsc-master 2020-11-30
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  1: static char help[] = "Time dependent Navier-Stokes problem in 2d and 3d with finite elements.\n\
  2: We solve the Navier-Stokes in a rectangular\n\
  3: domain, using a parallel unstructured mesh (DMPLEX) to discretize it.\n\
  4: This example supports discretized auxiliary fields (Re) as well as\n\
  5: multilevel nonlinear solvers.\n\
  6: Contributed by: Julian Andrej <juan@tf.uni-kiel.de>\n\n\n";

  8: #include <petscdmplex.h>
  9: #include <petscsnes.h>
 10: #include <petscts.h>
 11: #include <petscds.h>

 13: /*
 14:   Navier-Stokes equation:

 16:   du/dt + u . grad u - \Delta u - grad p = f
 17:   div u  = 0
 18: */

 20: typedef struct {
 21:   PetscInt          dim;
 22:   PetscBool         simplex;
 23:   PetscInt          mms;
 24:   PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
 25: } AppCtx;

 27: #define REYN 400.0

 29: /* MMS1

 31:   u = t + x^2 + y^2;
 32:   v = t + 2*x^2 - 2*x*y;
 33:   p = x + y - 1;

 35:   f_x = -2*t*(x + y) + 2*x*y^2 - 4*x^2*y - 2*x^3 + 4.0/Re - 1.0
 36:   f_y = -2*t*x       + 2*y^3 - 4*x*y^2 - 2*x^2*y + 4.0/Re - 1.0

 38:   so that

 40:     u_t + u \cdot \nabla u - 1/Re \Delta u + \nabla p + f = <1, 1> + <t (2x + 2y) + 2x^3 + 4x^2y - 2xy^2, t 2x + 2x^2y + 4xy^2 - 2y^3> - 1/Re <4, 4> + <1, 1>
 41:                                                     + <-t (2x + 2y) + 2xy^2 - 4x^2y - 2x^3 + 4/Re - 1, -2xt + 2y^3 - 4xy^2 - 2x^2y + 4/Re - 1> = 0
 42:     \nabla \cdot u                                  = 2x - 2x = 0

 44:   where

 46:     <u, v> . <<u_x, v_x>, <u_y, v_y>> = <u u_x + v u_y, u v_x + v v_y>
 47: */
 48: PetscErrorCode mms1_u_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
 49: {
 50:   u[0] = time + x[0]*x[0] + x[1]*x[1];
 51:   u[1] = time + 2.0*x[0]*x[0] - 2.0*x[0]*x[1];
 52:   return 0;
 53: }

 55: PetscErrorCode mms1_p_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *p, void *ctx)
 56: {
 57:   *p = x[0] + x[1] - 1.0;
 58:   return 0;
 59: }

 61: /* MMS 2*/

 63: static PetscErrorCode mms2_u_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
 64: {
 65:   u[0] = PetscSinReal(time + x[0])*PetscSinReal(time + x[1]);
 66:   u[1] = PetscCosReal(time + x[0])*PetscCosReal(time + x[1]);
 67:   return 0;
 68: }

 70: static PetscErrorCode mms2_p_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *p, void *ctx)
 71: {
 72:   *p = PetscSinReal(time + x[0] - x[1]);
 73:   return 0;
 74: }

 76: static void f0_mms1_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
 77:                       const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
 78:                       const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
 79:                       PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
 80: {
 81:   const PetscReal Re    = REYN;
 82:   const PetscInt  Ncomp = dim;
 83:   PetscInt        c, d;

 85:   for (c = 0; c < Ncomp; ++c) {
 86:     for (d = 0; d < dim; ++d) {
 87:       f0[c] += u[d] * u_x[c*dim+d];
 88:     }
 89:   }
 90:   f0[0] += u_t[0];
 91:   f0[1] += u_t[1];

 93:   f0[0] += -2.0*t*(x[0] + x[1]) + 2.0*x[0]*x[1]*x[1] - 4.0*x[0]*x[0]*x[1] - 2.0*x[0]*x[0]*x[0] + 4.0/Re - 1.0;
 94:   f0[1] += -2.0*t*x[0]          + 2.0*x[1]*x[1]*x[1] - 4.0*x[0]*x[1]*x[1] - 2.0*x[0]*x[0]*x[1] + 4.0/Re - 1.0;
 95: }

 97: static void f0_mms2_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
 98:                       const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
 99:                       const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
100:                       PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
101: {
102:   const PetscReal Re    = REYN;
103:   const PetscInt  Ncomp = dim;
104:   PetscInt        c, d;

106:   for (c = 0; c < Ncomp; ++c) {
107:     for (d = 0; d < dim; ++d) {
108:       f0[c] += u[d] * u_x[c*dim+d];
109:     }
110:   }
111:   f0[0] += u_t[0];
112:   f0[1] += u_t[1];

114:   f0[0] -= ( Re*((1.0L/2.0L)*PetscSinReal(2*t + 2*x[0]) + PetscSinReal(2*t + x[0] + x[1]) + PetscCosReal(t + x[0] - x[1])) + 2.0*PetscSinReal(t + x[0])*PetscSinReal(t + x[1]))/Re;
115:   f0[1] -= (-Re*((1.0L/2.0L)*PetscSinReal(2*t + 2*x[1]) + PetscSinReal(2*t + x[0] + x[1]) + PetscCosReal(t + x[0] - x[1])) + 2.0*PetscCosReal(t + x[0])*PetscCosReal(t + x[1]))/Re;
116: }

118: static void f1_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
119:                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
120:                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
121:                  PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
122: {
123:   const PetscReal Re    = REYN;
124:   const PetscInt  Ncomp = dim;
125:   PetscInt        comp, d;

127:   for (comp = 0; comp < Ncomp; ++comp) {
128:     for (d = 0; d < dim; ++d) {
129:       f1[comp*dim+d] = 1.0/Re * u_x[comp*dim+d];
130:     }
131:     f1[comp*dim+comp] -= u[Ncomp];
132:   }
133: }

135: static void f0_p(PetscInt dim, PetscInt Nf, PetscInt NfAux,
136:                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
137:                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
138:                  PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
139: {
140:   PetscInt d;
141:   for (d = 0, f0[0] = 0.0; d < dim; ++d) f0[0] += u_x[d*dim+d];
142: }

144: static void f1_p(PetscInt dim, PetscInt Nf, PetscInt NfAux,
145:                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
146:                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
147:                  PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
148: {
149:   PetscInt d;
150:   for (d = 0; d < dim; ++d) f1[d] = 0.0;
151: }

153: /*
154:   (psi_i, u_j grad_j u_i) ==> (\psi_i, \phi_j grad_j u_i)
155: */
156: static void g0_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
157:                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
158:                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
159:                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
160: {
161:   PetscInt NcI = dim, NcJ = dim;
162:   PetscInt fc, gc;
163:   PetscInt d;

165:   for (d = 0; d < dim; ++d) {
166:     g0[d*dim+d] = u_tShift;
167:   }

169:   for (fc = 0; fc < NcI; ++fc) {
170:     for (gc = 0; gc < NcJ; ++gc) {
171:       g0[fc*NcJ+gc] += u_x[fc*NcJ+gc];
172:     }
173:   }
174: }

176: /*
177:   (psi_i, u_j grad_j u_i) ==> (\psi_i, \u_j grad_j \phi_i)
178: */
179: static void g1_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
180:                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
181:                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
182:                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
183: {
184:   PetscInt NcI = dim;
185:   PetscInt NcJ = dim;
186:   PetscInt fc, gc, dg;
187:   for (fc = 0; fc < NcI; ++fc) {
188:     for (gc = 0; gc < NcJ; ++gc) {
189:       for (dg = 0; dg < dim; ++dg) {
190:         /* kronecker delta */
191:         if (fc == gc) {
192:           g1[(fc*NcJ+gc)*dim+dg] += u[dg];
193:         }
194:       }
195:     }
196:   }
197: }

199: /* < q, \nabla\cdot u >
200:    NcompI = 1, NcompJ = dim */
201: static void g1_pu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
202:                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
203:                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
204:                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
205: {
206:   PetscInt d;
207:   for (d = 0; d < dim; ++d) g1[d*dim+d] = 1.0; /* \frac{\partial\phi^{u_d}}{\partial x_d} */
208: }

210: /* -< \nabla\cdot v, p >
211:     NcompI = dim, NcompJ = 1 */
212: static void g2_up(PetscInt dim, PetscInt Nf, PetscInt NfAux,
213:                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
214:                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
215:                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[])
216: {
217:   PetscInt d;
218:   for (d = 0; d < dim; ++d) g2[d*dim+d] = -1.0; /* \frac{\partial\psi^{u_d}}{\partial x_d} */
219: }

221: /* < \nabla v, \nabla u + {\nabla u}^T >
222:    This just gives \nabla u, give the perdiagonal for the transpose */
223: static void g3_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
224:                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
225:                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
226:                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
227: {
228:   const PetscReal Re    = REYN;
229:   const PetscInt  Ncomp = dim;
230:   PetscInt        compI, d;

232:   for (compI = 0; compI < Ncomp; ++compI) {
233:     for (d = 0; d < dim; ++d) {
234:       g3[((compI*Ncomp+compI)*dim+d)*dim+d] = 1.0/Re;
235:     }
236:   }
237: }

239: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
240: {

244:   options->dim     = 2;
245:   options->simplex = PETSC_TRUE;
246:   options->mms     = 1;

248:   PetscOptionsBegin(comm, "", "Navier-Stokes Equation Options", "DMPLEX");
249:   PetscOptionsInt("-dim", "The topological mesh dimension", "ex46.c", options->dim, &options->dim, NULL);
250:   PetscOptionsBool("-simplex", "Simplicial (true) or tensor (false) mesh", "ex46.c", options->simplex, &options->simplex, NULL);
251:   PetscOptionsInt("-mms", "The manufactured solution to use", "ex46.c", options->mms, &options->mms, NULL);
252:   PetscOptionsEnd();
253:   return(0);
254: }

256: static PetscErrorCode CreateBCLabel(DM dm, const char name[])
257: {
258:   DM             plex;
259:   DMLabel        label;

263:   DMCreateLabel(dm, name);
264:   DMGetLabel(dm, name, &label);
265:   DMConvert(dm, DMPLEX, &plex);
266:   DMPlexMarkBoundaryFaces(plex, 1, label);
267:   DMDestroy(&plex);
268:   return(0);
269: }

271: static PetscErrorCode CreateMesh(MPI_Comm comm, DM *dm, AppCtx *ctx)
272: {
273:   DM             pdm = NULL;
274:   const PetscInt dim = ctx->dim;
275:   PetscBool      hasLabel;

279:   DMPlexCreateBoxMesh(comm, dim, ctx->simplex, NULL, NULL, NULL, NULL, PETSC_TRUE, dm);
280:   PetscObjectSetName((PetscObject) *dm, "Mesh");
281:   /* If no boundary marker exists, mark the whole boundary */
282:   DMHasLabel(*dm, "marker", &hasLabel);
283:   if (!hasLabel) {CreateBCLabel(*dm, "marker");}
284:   /* Distribute mesh over processes */
285:   DMPlexDistribute(*dm, 0, NULL, &pdm);
286:   if (pdm) {
287:     DMDestroy(dm);
288:     *dm  = pdm;
289:   }
290:   DMSetFromOptions(*dm);
291:   DMViewFromOptions(*dm, NULL, "-dm_view");
292:   return(0);
293: }

295: static PetscErrorCode SetupProblem(DM dm, AppCtx *ctx)
296: {
297:   PetscDS        prob;
298:   const PetscInt id = 1;

302:   DMGetDS(dm, &prob);
303:   switch (ctx->mms) {
304:   case 1:
305:     PetscDSSetResidual(prob, 0, f0_mms1_u, f1_u);break;
306:   case 2:
307:     PetscDSSetResidual(prob, 0, f0_mms2_u, f1_u);break;
308:   }
309:   PetscDSSetResidual(prob, 1, f0_p, f1_p);
310:   PetscDSSetJacobian(prob, 0, 0, g0_uu, g1_uu, NULL,  g3_uu);
311:   PetscDSSetJacobian(prob, 0, 1, NULL, NULL, g2_up, NULL);
312:   PetscDSSetJacobian(prob, 1, 0, NULL, g1_pu, NULL,  NULL);
313:   switch (ctx->dim) {
314:   case 2:
315:     switch (ctx->mms) {
316:     case 1:
317:       ctx->exactFuncs[0] = mms1_u_2d;
318:       ctx->exactFuncs[1] = mms1_p_2d;
319:       break;
320:     case 2:
321:       ctx->exactFuncs[0] = mms2_u_2d;
322:       ctx->exactFuncs[1] = mms2_p_2d;
323:       break;
324:     default:
325:       SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid MMS %D", ctx->mms);
326:     }
327:     break;
328:   default:
329:     SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension %D", ctx->dim);
330:   }
331:   DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", "marker", 0, 0, NULL, (void (*)(void)) ctx->exactFuncs[0], NULL, 1, &id, ctx);
332:   return(0);
333: }

335: static PetscErrorCode SetupDiscretization(DM dm, AppCtx *ctx)
336: {
337:   DM              cdm = dm;
338:   const PetscInt  dim = ctx->dim;
339:   PetscFE         fe[2];
340:   MPI_Comm        comm;
341:   PetscErrorCode  ierr;

344:   /* Create finite element */
345:   PetscObjectGetComm((PetscObject) dm, &comm);
346:   PetscFECreateDefault(comm, dim, dim, ctx->simplex, "vel_", PETSC_DEFAULT, &fe[0]);
347:   PetscObjectSetName((PetscObject) fe[0], "velocity");
348:   PetscFECreateDefault(comm, dim, 1, ctx->simplex, "pres_", PETSC_DEFAULT, &fe[1]);
349:   PetscFECopyQuadrature(fe[0], fe[1]);
350:   PetscObjectSetName((PetscObject) fe[1], "pressure");
351:   /* Set discretization and boundary conditions for each mesh */
352:   DMSetField(dm, 0, NULL, (PetscObject) fe[0]);
353:   DMSetField(dm, 1, NULL, (PetscObject) fe[1]);
354:   DMCreateDS(dm);
355:   SetupProblem(dm, ctx);
356:   while (cdm) {
357:     PetscObject  pressure;
358:     MatNullSpace nsp;
359:     PetscBool    hasLabel;

361:     DMGetField(cdm, 1, NULL, &pressure);
362:     MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nsp);
363:     PetscObjectCompose(pressure, "nullspace", (PetscObject) nsp);
364:     MatNullSpaceDestroy(&nsp);

366:     DMHasLabel(cdm, "marker", &hasLabel);
367:     if (!hasLabel) {CreateBCLabel(cdm, "marker");}
368:     DMCopyDisc(dm, cdm);
369:     DMGetCoarseDM(cdm, &cdm);
370:   }
371:   PetscFEDestroy(&fe[0]);
372:   PetscFEDestroy(&fe[1]);
373:   return(0);
374: }

376: static PetscErrorCode MonitorError(TS ts, PetscInt step, PetscReal crtime, Vec u, void *ctx)
377: {
378:   AppCtx        *user = (AppCtx *) ctx;
379:   DM             dm;
380:   PetscReal      ferrors[2];

384:   TSGetDM(ts, &dm);
385:   DMComputeL2FieldDiff(dm, crtime, user->exactFuncs, NULL, u, ferrors);
386:   PetscPrintf(PETSC_COMM_WORLD, "Timestep: %04d time = %-8.4g \t L_2 Error: [%2.3g, %2.3g]\n", (int) step, (double) crtime, (double) ferrors[0], (double) ferrors[1]);
387:   return(0);
388: }

390: int main(int argc, char **argv)
391: {
392:   AppCtx         ctx;
393:   DM             dm;
394:   TS             ts;
395:   Vec            u, r;

398:   PetscInitialize(&argc, &argv, NULL, help);if (ierr) return ierr;
399:   ProcessOptions(PETSC_COMM_WORLD, &ctx);
400:   CreateMesh(PETSC_COMM_WORLD, &dm, &ctx);
401:   DMSetApplicationContext(dm, &ctx);
402:   PetscMalloc1(2, &ctx.exactFuncs);
403:   SetupDiscretization(dm, &ctx);
404:   DMPlexCreateClosureIndex(dm, NULL);

406:   DMCreateGlobalVector(dm, &u);
407:   VecDuplicate(u, &r);

409:   TSCreate(PETSC_COMM_WORLD, &ts);
410:   TSMonitorSet(ts, MonitorError, &ctx, NULL);
411:   TSSetDM(ts, dm);
412:   DMTSSetBoundaryLocal(dm, DMPlexTSComputeBoundary, &ctx);
413:   DMTSSetIFunctionLocal(dm, DMPlexTSComputeIFunctionFEM, &ctx);
414:   DMTSSetIJacobianLocal(dm, DMPlexTSComputeIJacobianFEM, &ctx);
415:   TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER);
416:   TSSetFromOptions(ts);

418:   DMProjectFunction(dm, 0.0, ctx.exactFuncs, NULL, INSERT_ALL_VALUES, u);
419:   TSSolve(ts, u);
420:   VecViewFromOptions(u, NULL, "-sol_vec_view");

422:   VecDestroy(&u);
423:   VecDestroy(&r);
424:   TSDestroy(&ts);
425:   DMDestroy(&dm);
426:   PetscFree(ctx.exactFuncs);
427:   PetscFinalize();
428:   return ierr;
429: }

431: /*TEST

433:   # Full solves
434:   test:
435:     suffix: 2d_p2p1_r1
436:     requires: !single triangle
437:     filter: sed -e "s~ATOL~RTOL~g" -e "s~ABS~RELATIVE~g"
438:     args: -dm_refine 1 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -ts_type beuler -ts_max_steps 10 -ts_dt 0.1 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1.0e-10 -fieldsplit_pressure_pc_type jacobi -ksp_monitor_short -ksp_converged_reason -snes_monitor_short -snes_converged_reason -ts_monitor
439:   test:
440:     suffix: 2d_p2p1_r2
441:     requires: !single triangle
442:     filter: sed -e "s~ATOL~RTOL~g" -e "s~ABS~RELATIVE~g"
443:     args: -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -ts_type beuler -ts_max_steps 10 -ts_dt 0.1 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1.0e-10 -fieldsplit_pressure_pc_type jacobi -ksp_monitor_short -ksp_converged_reason -snes_monitor_short -snes_converged_reason -ts_monitor
444:   test:
445:     suffix: 2d_q2q1_r1
446:     requires: !single
447:     filter: sed -e "s~ATOL~RTOL~g" -e "s~ABS~RELATIVE~g" -e "s~ 0\]~ 0.0\]~g"
448:     args: -simplex 0 -dm_refine 1 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -ts_type beuler -ts_max_steps 10 -ts_dt 0.1 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1.0e-10 -fieldsplit_pressure_pc_type jacobi -ksp_monitor_short -ksp_converged_reason -snes_monitor_short -snes_converged_reason -ts_monitor
449:   test:
450:     suffix: 2d_q2q1_r2
451:     requires: !single
452:     filter: sed -e "s~ATOL~RTOL~g" -e "s~ABS~RELATIVE~g"
453:     args: -simplex 0 -dm_refine 2 -vel_petscspace_degree 2 -pres_petscspace_degree 1 -ts_type beuler -ts_max_steps 10 -ts_dt 0.1 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full -fieldsplit_velocity_pc_type lu -fieldsplit_pressure_ksp_rtol 1.0e-10 -fieldsplit_pressure_pc_type jacobi -ksp_monitor_short -ksp_converged_reason -snes_monitor_short -snes_converged_reason -ts_monitor

455: TEST*/