Actual source code: ex11.c

petsc-3.5.1 2014-08-06
Report Typos and Errors
  1: static char help[] = "Second Order TVD Finite Volume Example.\n";

We use a second order TVD finite volume method to evolve a system of PDEs. Our simple upwinded residual evaluation loops
over all mesh faces and uses a Riemann solver to produce the flux given the face geometry and cell values,
\begin{equation}
f_i = \mathrm{riemann}(\mathrm{phys}, p_\mathrm{centroid}, \hat n, x^L, x^R)
\end{equation}
and then update the cell values given the cell volume.
\begin{eqnarray}
f^L_i &-=& \frac{f_i}{vol^L} \\
f^R_i &+=& \frac{f_i}{vol^R}
\end{eqnarray}

As an example, we can consider the shallow water wave equation,
\begin{eqnarray}
h_t + \nabla\cdot \left( uh \right) &=& 0 \\
(uh)_t + \nabla\cdot \left( u\otimes uh + \frac{g h^2}{2} I \right) &=& 0
\end{eqnarray}
where $h$ is wave height, $u$ is wave velocity, and $g$ is the acceleration due to gravity.

A representative Riemann solver for the shallow water equations is given in the PhysicsRiemann_SW() function,
\begin{eqnarray}
f^{L,R}_h &=& uh^{L,R} \cdot \hat n \\
f^{L,R}_{uh} &=& \frac{f^{L,R}_h}{h^{L,R}} uh^{L,R} + g (h^{L,R})^2 \hat n \\
c^{L,R} &=& \sqrt{g h^{L,R}} \\
s &=& \max\left( \left|\frac{uh^L \cdot \hat n}{h^L}\right| + c^L, \left|\frac{uh^R \cdot \hat n}{h^R}\right| + c^R \right) \\
f_i &=& \frac{A_\mathrm{face}}{2} \left( f^L_i + f^R_i + s \left( x^L_i - x^R_i \right) \right)
\end{eqnarray}
where $c$ is the local gravity wave speed and $f_i$ is a Rusanov flux.

The more sophisticated residual evaluation in RHSFunctionLocal_LS() uses a least-squares fit to a quadratic polynomial
over a neighborhood of the given element.

The mesh is read in from an ExodusII file, usually generated by Cubit.
 37: #include <petscts.h>
 38: #include <petscfv.h>
 39: #include <petscdmplex.h>
 40: #include <petscsf.h>
 41: #include <petscblaslapack.h>

 43: #define DIM 2                   /* Geometric dimension */
 44: #define ALEN(a) (sizeof(a)/sizeof((a)[0]))

 46: static PetscFunctionList PhysicsList;

 48: /* Represents continuum physical equations. */
 49: typedef struct _n_Physics *Physics;

 51: /* Physical model includes boundary conditions, initial conditions, and functionals of interest. It is
 52:  * discretization-independent, but its members depend on the scenario being solved. */
 53: typedef struct _n_Model *Model;

 55: /* 'User' implements a discretization of a continuous model. */
 56: typedef struct _n_User *User;

 58: typedef PetscErrorCode (*RiemannFunction)(const PetscReal*,const PetscReal*,const PetscScalar*,const PetscScalar*,PetscScalar*,void*);
 59: typedef PetscErrorCode (*SolutionFunction)(Model,PetscReal,const PetscReal*,PetscScalar*,void*);
 60: typedef PetscErrorCode (*FunctionalFunction)(Model,PetscReal,const PetscReal*,const PetscScalar*,PetscReal*,void*);
 61: typedef PetscErrorCode (*SetupFields)(Physics,PetscSection);
 62: static PetscErrorCode ModelSolutionSetDefault(Model,SolutionFunction,void*);
 63: static PetscErrorCode ModelFunctionalRegister(Model,const char*,PetscInt*,FunctionalFunction,void*);
 64: static PetscErrorCode OutputVTK(DM,const char*,PetscViewer*);

 66: struct FieldDescription {
 67:   const char *name;
 68:   PetscInt dof;
 69: };

 71: typedef struct _n_FunctionalLink *FunctionalLink;
 72: struct _n_FunctionalLink {
 73:   char               *name;
 74:   FunctionalFunction func;
 75:   void               *ctx;
 76:   PetscInt           offset;
 77:   FunctionalLink     next;
 78: };

 80: struct _n_Physics {
 81:   RiemannFunction riemann;
 82:   PetscInt        dof;          /* number of degrees of freedom per cell */
 83:   PetscReal       maxspeed;     /* kludge to pick initial time step, need to add monitoring and step control */
 84:   void            *data;
 85:   PetscInt        nfields;
 86:   const struct FieldDescription *field_desc;
 87: };

 89: struct _n_Model {
 90:   MPI_Comm         comm;        /* Does not do collective communicaton, but some error conditions can be collective */
 91:   Physics          physics;
 92:   FunctionalLink   functionalRegistry;
 93:   PetscInt         maxComputed;
 94:   PetscInt         numMonitored;
 95:   FunctionalLink   *functionalMonitored;
 96:   PetscInt         numCall;
 97:   FunctionalLink   *functionalCall;
 98:   SolutionFunction solution;
 99:   void             *solutionctx;
100:   PetscReal        maxspeed;    /* estimate of global maximum speed (for CFL calculation) */
101: };

103: struct _n_User {
104:   PetscInt numSplitFaces;
105:   PetscInt vtkInterval;   /* For monitor */
106:   Model    model;
107: };

109: PETSC_STATIC_INLINE PetscScalar DotDIM(const PetscScalar *x,const PetscScalar *y)
110: {
111:   PetscInt    i;
112:   PetscScalar prod=0.0;

114:   for (i=0; i<DIM; i++) prod += x[i]*y[i];
115:   return prod;
116: }
117: PETSC_STATIC_INLINE PetscReal NormDIM(const PetscScalar *x) { return PetscSqrtReal(PetscAbsScalar(DotDIM(x,x))); }
118: PETSC_STATIC_INLINE void axDIM(const PetscScalar a,PetscScalar *x)
119: {
120:   PetscInt i;
121:   for (i=0; i<DIM; i++) x[i] *= a;
122: }
123: PETSC_STATIC_INLINE void waxDIM(const PetscScalar a,const PetscScalar *x, PetscScalar *w)
124: {
125:   PetscInt i;
126:   for (i=0; i<DIM; i++) w[i] = x[i]*a;
127: }
128: PETSC_STATIC_INLINE void NormalSplitDIM(const PetscReal *n,const PetscScalar *x,PetscScalar *xn,PetscScalar *xt)
129: {                               /* Split x into normal and tangential components */
130:   PetscInt    i;
131:   PetscScalar c;
132:   c = DotDIM(x,n)/DotDIM(n,n);
133:   for (i=0; i<DIM; i++) {
134:     xn[i] = c*n[i];
135:     xt[i] = x[i]-xn[i];
136:   }
137: }

139: PETSC_STATIC_INLINE PetscScalar Dot2(const PetscScalar *x,const PetscScalar *y) { return x[0]*y[0] + x[1]*y[1];}
140: PETSC_STATIC_INLINE PetscReal Norm2(const PetscScalar *x) { return PetscSqrtReal(PetscAbsScalar(Dot2(x,x)));}
141: PETSC_STATIC_INLINE void Normalize2(PetscScalar *x) { PetscReal a = 1./Norm2(x); x[0] *= a; x[1] *= a; }
142: PETSC_STATIC_INLINE void Waxpy2(PetscScalar a,const PetscScalar *x,const PetscScalar *y,PetscScalar *w) { w[0] = a*x[0] + y[0]; w[1] = a*x[1] + y[1]; }
143: PETSC_STATIC_INLINE void Scale2(PetscScalar a,const PetscScalar *x,PetscScalar *y) { y[0] = a*x[0]; y[1] = a*x[1]; }

145: PETSC_STATIC_INLINE void WaxpyD(PetscInt dim, PetscScalar a, const PetscScalar *x, const PetscScalar *y, PetscScalar *w) {PetscInt d; for (d = 0; d < dim; ++d) w[d] = a*x[d] + y[d];}
146: PETSC_STATIC_INLINE PetscScalar DotD(PetscInt dim, const PetscScalar *x, const PetscScalar *y) {PetscScalar sum = 0.0; PetscInt d; for (d = 0; d < dim; ++d) sum += x[d]*y[d]; return sum;}
147: PETSC_STATIC_INLINE PetscReal NormD(PetscInt dim, const PetscScalar *x) {return PetscSqrtReal(PetscAbsScalar(DotD(dim,x,x)));}

149: PETSC_STATIC_INLINE void NormalSplit(const PetscReal *n,const PetscScalar *x,PetscScalar *xn,PetscScalar *xt)
150: {                               /* Split x into normal and tangential components */
151:   Scale2(Dot2(x,n)/Dot2(n,n),n,xn);
152:   Waxpy2(-1,xn,x,xt);
153: }

155: /******************* Advect ********************/
156: typedef enum {ADVECT_SOL_TILTED,ADVECT_SOL_BUMP} AdvectSolType;
157: static const char *const AdvectSolTypes[] = {"TILTED","BUMP","AdvectSolType","ADVECT_SOL_",0};
158: typedef enum {ADVECT_SOL_BUMP_CONE,ADVECT_SOL_BUMP_COS} AdvectSolBumpType;
159: static const char *const AdvectSolBumpTypes[] = {"CONE","COS","AdvectSolBumpType","ADVECT_SOL_BUMP_",0};

161: typedef struct {
162:   PetscReal wind[DIM];
163: } Physics_Advect_Tilted;
164: typedef struct {
165:   PetscReal         center[DIM];
166:   PetscReal         radius;
167:   AdvectSolBumpType type;
168: } Physics_Advect_Bump;

170: typedef struct {
171:   PetscReal     inflowState;
172:   AdvectSolType soltype;
173:   union {
174:     Physics_Advect_Tilted tilted;
175:     Physics_Advect_Bump   bump;
176:   } sol;
177:   struct {
178:     PetscInt Error;
179:   } functional;
180: } Physics_Advect;

182: static const struct FieldDescription PhysicsFields_Advect[] = {{"U",1},{NULL,0}};

186: static PetscErrorCode PhysicsBoundary_Advect_Inflow(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
187: {
188:   Physics        phys    = (Physics)ctx;
189:   Physics_Advect *advect = (Physics_Advect*)phys->data;

192:   xG[0] = advect->inflowState;
193:   return(0);
194: }

198: static PetscErrorCode PhysicsBoundary_Advect_Outflow(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
199: {
201:   xG[0] = xI[0];
202:   return(0);
203: }

207: static PetscErrorCode PhysicsRiemann_Advect(const PetscReal *qp, const PetscReal *n, const PetscScalar *xL, const PetscScalar *xR, PetscScalar *flux, Physics phys)
208: {
209:   Physics_Advect *advect = (Physics_Advect*)phys->data;
210:   PetscReal      wind[DIM],wn;

213:   switch (advect->soltype) {
214:   case ADVECT_SOL_TILTED: {
215:     Physics_Advect_Tilted *tilted = &advect->sol.tilted;
216:     wind[0] = tilted->wind[0];
217:     wind[1] = tilted->wind[1];
218:   } break;
219:   case ADVECT_SOL_BUMP:
220:     wind[0] = -qp[1];
221:     wind[1] = qp[0];
222:     break;
223:   default: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for solution type %s",AdvectSolBumpTypes[advect->soltype]);
224:   }
225:   wn      = Dot2(wind, n);
226:   flux[0] = (wn > 0 ? xL[0] : xR[0]) * wn;
227:   return(0);
228: }

232: static PetscErrorCode PhysicsSolution_Advect(Model mod,PetscReal time,const PetscReal *x,PetscScalar *u,void *ctx)
233: {
234:   Physics        phys    = (Physics)ctx;
235:   Physics_Advect *advect = (Physics_Advect*)phys->data;

238:   switch (advect->soltype) {
239:   case ADVECT_SOL_TILTED: {
240:     PetscReal             x0[DIM];
241:     Physics_Advect_Tilted *tilted = &advect->sol.tilted;
242:     Waxpy2(-time,tilted->wind,x,x0);
243:     if (x0[1] > 0) u[0] = 1.*x[0] + 3.*x[1];
244:     else u[0] = advect->inflowState;
245:   } break;
246:   case ADVECT_SOL_BUMP: {
247:     Physics_Advect_Bump *bump = &advect->sol.bump;
248:     PetscReal           x0[DIM],v[DIM],r,cost,sint;
249:     cost  = PetscCosReal(time);
250:     sint  = PetscSinReal(time);
251:     x0[0] = cost*x[0] + sint*x[1];
252:     x0[1] = -sint*x[0] + cost*x[1];
253:     Waxpy2(-1,bump->center,x0,v);
254:     r = Norm2(v);
255:     switch (bump->type) {
256:     case ADVECT_SOL_BUMP_CONE:
257:       u[0] = PetscMax(1 - r/bump->radius,0);
258:       break;
259:     case ADVECT_SOL_BUMP_COS:
260:       u[0] = 0.5 + 0.5*PetscCosReal(PetscMin(r/bump->radius,1)*PETSC_PI);
261:       break;
262:     }
263:   } break;
264:   default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unknown solution type");
265:   }
266:   return(0);
267: }

271: static PetscErrorCode PhysicsFunctional_Advect(Model mod,PetscReal time,const PetscScalar *x,const PetscScalar *y,PetscReal *f,void *ctx)
272: {
273:   Physics        phys    = (Physics)ctx;
274:   Physics_Advect *advect = (Physics_Advect*)phys->data;
275:   PetscScalar    yexact[1];

279:   PhysicsSolution_Advect(mod,time,x,yexact,phys);
280:   f[advect->functional.Error] = PetscAbsScalar(y[0]-yexact[0]);
281:   return(0);
282: }

286: static PetscErrorCode PhysicsCreate_Advect(DM dm, Model mod,Physics phys)
287: {
288:   Physics_Advect *advect;

292:   phys->field_desc = PhysicsFields_Advect;
293:   phys->riemann = (RiemannFunction) PhysicsRiemann_Advect;
294:   PetscNew(&advect);
295:   phys->data = advect;
296:   PetscOptionsHead("Advect options");
297:   {
298:     PetscInt two = 2,dof = 1;
299:     advect->soltype = ADVECT_SOL_TILTED;
300:     PetscOptionsEnum("-advect_sol_type","solution type","",AdvectSolTypes,(PetscEnum)advect->soltype,(PetscEnum*)&advect->soltype,NULL);
301:     switch (advect->soltype) {
302:     case ADVECT_SOL_TILTED: {
303:       Physics_Advect_Tilted *tilted = &advect->sol.tilted;
304:       two = 2;
305:       tilted->wind[0] = 0.0;
306:       tilted->wind[1] = 1.0;
307:       PetscOptionsRealArray("-advect_tilted_wind","background wind vx,vy","",tilted->wind,&two,NULL);
308:       advect->inflowState = -2.0;
309:       PetscOptionsRealArray("-advect_tilted_inflow","Inflow state","",&advect->inflowState,&dof,NULL);
310:       phys->maxspeed = Norm2(tilted->wind);
311:     } break;
312:     case ADVECT_SOL_BUMP: {
313:       Physics_Advect_Bump *bump = &advect->sol.bump;
314:       two = 2;
315:       bump->center[0] = 2.;
316:       bump->center[1] = 0.;
317:       PetscOptionsRealArray("-advect_bump_center","location of center of bump x,y","",bump->center,&two,NULL);
318:       bump->radius = 0.9;
319:       PetscOptionsReal("-advect_bump_radius","radius of bump","",bump->radius,&bump->radius,NULL);
320:       bump->type = ADVECT_SOL_BUMP_CONE;
321:       PetscOptionsEnum("-advect_bump_type","type of bump","",AdvectSolBumpTypes,(PetscEnum)bump->type,(PetscEnum*)&bump->type,NULL);
322:       phys->maxspeed = 3.;       /* radius of mesh, kludge */
323:     } break;
324:     }
325:   }
326:   PetscOptionsTail();
327:   {
328:     const PetscInt inflowids[] = {100,200,300},outflowids[] = {101};
329:     /* Register "canned" boundary conditions and defaults for where to apply. */
330:     DMPlexAddBoundary(dm, PETSC_TRUE, "inflow",  "Face Sets", 0, (void (*)()) PhysicsBoundary_Advect_Inflow,  ALEN(inflowids),  inflowids,  phys);
331:     DMPlexAddBoundary(dm, PETSC_TRUE, "outflow", "Face Sets", 0, (void (*)()) PhysicsBoundary_Advect_Outflow, ALEN(outflowids), outflowids, phys);
332:     /* Initial/transient solution with default boundary conditions */
333:     ModelSolutionSetDefault(mod,PhysicsSolution_Advect,phys);
334:     /* Register "canned" functionals */
335:     ModelFunctionalRegister(mod,"Error",&advect->functional.Error,PhysicsFunctional_Advect,phys);
336:   }
337:   return(0);
338: }

340: /******************* Shallow Water ********************/
341: typedef struct {
342:   PetscReal gravity;
343:   PetscReal boundaryHeight;
344:   struct {
345:     PetscInt Height;
346:     PetscInt Speed;
347:     PetscInt Energy;
348:   } functional;
349: } Physics_SW;
350: typedef struct {
351:   PetscScalar vals[0];
352:   PetscScalar h;
353:   PetscScalar uh[DIM];
354: } SWNode;

356: static const struct FieldDescription PhysicsFields_SW[] = {{"Height",1},{"Momentum",DIM},{NULL,0}};

360: /*
361:  * h_t + div(uh) = 0
362:  * (uh)_t + div (u\otimes uh + g h^2 / 2 I) = 0
363:  *
364:  * */
365: static PetscErrorCode SWFlux(Physics phys,const PetscReal *n,const SWNode *x,SWNode *f)
366: {
367:   Physics_SW  *sw = (Physics_SW*)phys->data;
368:   PetscScalar uhn,u[DIM];
369:   PetscInt    i;

372:   Scale2(1./x->h,x->uh,u);
373:   uhn  = Dot2(x->uh,n);
374:   f->h = uhn;
375:   for (i=0; i<DIM; i++) f->uh[i] = u[i] * uhn + sw->gravity * PetscSqr(x->h) * n[i];
376:   return(0);
377: }

381: static PetscErrorCode PhysicsBoundary_SW_Wall(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
382: {
384:   xG[0] = xI[0];
385:   xG[1] = -xI[1];
386:   xG[2] = -xI[2];
387:   return(0);
388: }

392: static PetscErrorCode PhysicsRiemann_SW(const PetscReal *qp, const PetscReal *n, const PetscScalar *xL, const PetscScalar *xR, PetscScalar *flux, Physics phys)
393: {
394:   Physics_SW   *sw = (Physics_SW*)phys->data;
395:   PetscReal    cL,cR,speed,nn[DIM];
396:   const SWNode *uL = (const SWNode*)xL,*uR = (const SWNode*)xR;
397:   SWNode       fL,fR;
398:   PetscInt     i;

401:   if (uL->h < 0 || uR->h < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Reconstructed thickness is negative");
402:   nn[0] = n[0];
403:   nn[1] = n[1];
404:   Normalize2(nn);
405:   SWFlux(phys,nn,uL,&fL);
406:   SWFlux(phys,nn,uR,&fR);
407:   cL    = PetscSqrtReal(sw->gravity*PetscRealPart(uL->h));
408:   cR    = PetscSqrtReal(sw->gravity*PetscRealPart(uR->h)); /* gravity wave speed */
409:   speed = PetscMax(PetscAbsScalar(Dot2(uL->uh,nn)/uL->h) + cL,PetscAbsScalar(Dot2(uR->uh,nn)/uR->h) + cR);
410:   for (i=0; i<1+DIM; i++) flux[i] = (0.5*(fL.vals[i] + fR.vals[i]) + 0.5*speed*(xL[i] - xR[i])) * Norm2(n);
411:   return(0);
412: }

416: static PetscErrorCode PhysicsSolution_SW(Model mod,PetscReal time,const PetscReal *x,PetscScalar *u,void *ctx)
417: {
418:   PetscReal dx[2],r,sigma;

421:   if (time != 0.0) SETERRQ1(mod->comm,PETSC_ERR_SUP,"No solution known for time %g",(double)time);
422:   dx[0] = x[0] - 1.5;
423:   dx[1] = x[1] - 1.0;
424:   r     = Norm2(dx);
425:   sigma = 0.5;
426:   u[0]  = 1 + 2*PetscExpScalar(-PetscSqr(r)/(2*PetscSqr(sigma)));
427:   u[1]  = 0.0;
428:   u[2]  = 0.0;
429:   return(0);
430: }

434: static PetscErrorCode PhysicsFunctional_SW(Model mod,PetscReal time,const PetscReal *coord,const PetscScalar *xx,PetscReal *f,void *ctx)
435: {
436:   Physics      phys = (Physics)ctx;
437:   Physics_SW   *sw  = (Physics_SW*)phys->data;
438:   const SWNode *x   = (const SWNode*)xx;
439:   PetscScalar  u[2];
440:   PetscReal    h;

443:   h = PetscRealPart(x->h);
444:   Scale2(1./x->h,x->uh,u);
445:   f[sw->functional.Height] = h;
446:   f[sw->functional.Speed]  = Norm2(u) + PetscSqrtReal(sw->gravity*h);
447:   f[sw->functional.Energy] = 0.5*(Dot2(x->uh,u) + sw->gravity*PetscSqr(h));
448:   return(0);
449: }

453: static PetscErrorCode PhysicsCreate_SW(DM dm, Model mod,Physics phys)
454: {
455:   Physics_SW     *sw;

459:   phys->field_desc = PhysicsFields_SW;
460:   phys->riemann = (RiemannFunction) PhysicsRiemann_SW;
461:   PetscNew(&sw);
462:   phys->data    = sw;
463:   PetscOptionsHead("SW options");
464:   {
465:     sw->gravity = 1.0;
466:     PetscOptionsReal("-sw_gravity","Gravitational constant","",sw->gravity,&sw->gravity,NULL);
467:   }
468:   PetscOptionsTail();
469:   phys->maxspeed = PetscSqrtReal(2.0*sw->gravity); /* Mach 1 for depth of 2 */

471:   {
472:     const PetscInt wallids[] = {100,101,200,300};
473:     DMPlexAddBoundary(dm, PETSC_TRUE, "wall", "Face Sets", 0, (void (*)()) PhysicsBoundary_SW_Wall, ALEN(wallids), wallids, phys);
474:     ModelSolutionSetDefault(mod,PhysicsSolution_SW,phys);
475:     ModelFunctionalRegister(mod,"Height",&sw->functional.Height,PhysicsFunctional_SW,phys);
476:     ModelFunctionalRegister(mod,"Speed",&sw->functional.Speed,PhysicsFunctional_SW,phys);
477:     ModelFunctionalRegister(mod,"Energy",&sw->functional.Energy,PhysicsFunctional_SW,phys);
478:   }
479:   return(0);
480: }

482: /******************* Euler ********************/
483: typedef struct {
484:   PetscScalar vals[0];
485:   PetscScalar r;
486:   PetscScalar ru[DIM];
487:   PetscScalar e;
488: } EulerNode;
489: typedef PetscErrorCode (*EquationOfState)(const PetscReal*, const EulerNode*, PetscScalar*);
490: typedef struct {
491:   PetscInt        npars;
492:   PetscReal       pars[DIM];
493:   EquationOfState pressure;
494:   EquationOfState sound;
495:   struct {
496:     PetscInt Density;
497:     PetscInt Momentum;
498:     PetscInt Energy;
499:     PetscInt Pressure;
500:     PetscInt Speed;
501:   } monitor;
502: } Physics_Euler;

504: static const struct FieldDescription PhysicsFields_Euler[] = {{"Density",1},{"Momentum",DIM},{"Energy",1},{NULL,0}};

508: static PetscErrorCode Pressure_PG(const PetscReal *pars,const EulerNode *x,PetscScalar *p)
509: {
510:   PetscScalar ru2;

513:   ru2  = DotDIM(x->ru,x->ru);
514:   ru2 /= x->r;
515:   /* kinematic dof = params[0] */
516:   (*p)=2.0*(x->e-0.5*ru2)/pars[0];
517:   return(0);
518: }

522: static PetscErrorCode SpeedOfSound_PG(const PetscReal *pars,const EulerNode *x,PetscScalar *c)
523: {
524:   PetscScalar p;

527:   /* TODO remove direct usage of Pressure_PG */
528:   Pressure_PG(pars,x,&p);
529:   /* TODO check the sign of p */
530:   /* pars[1] = heat capacity ratio */
531:   (*c)=PetscSqrtScalar(pars[1]*p/x->r);
532:   return(0);
533: }

537: /*
538:  * x = (rho,rho*(u_1),...,rho*e)^T
539:  * x_t+div(f_1(x))+...+div(f_DIM(x)) = 0
540:  *
541:  * f_i(x) = u_i*x+(0,0,...,p,...,p*u_i)^T
542:  *
543:  * */
544: static PetscErrorCode EulerFlux(Physics phys,const PetscReal *n,const EulerNode *x,EulerNode *f)
545: {
546:   Physics_Euler *eu = (Physics_Euler*)phys->data;
547:   PetscScalar   u,nu,p;
548:   PetscInt      i;

551:   u  = DotDIM(x->ru,x->ru);
552:   u /= (x->r * x->r);
553:   nu = DotDIM(x->ru,n);
554:   /* TODO check the sign of p */
555:   eu->pressure(eu->pars,x,&p);
556:   f->r = nu * x->r;
557:   for (i=0; i<DIM; i++) f->ru[i] = nu * x->ru[i] + n[i]*p;
558:   f->e = nu*(x->e+p);
559:   return(0);
560: }

562: /* PetscReal* => EulerNode* conversion */
565: static PetscErrorCode PhysicsBoundary_Euler_Wall(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
566: {
567:   PetscInt    i;
568:   PetscScalar xn[DIM],xt[DIM];

571:   xG[0] = xI[0];
572:   NormalSplitDIM(n,xI+1,xn,xt);
573:   for (i=0; i<DIM; i++) xG[i+1] = -xn[i]+xt[i];
574:   xG[DIM+1] = xI[DIM+1];
575:   return(0);
576: }

578: /* PetscReal* => EulerNode* conversion */
581: static PetscErrorCode PhysicsRiemann_Euler_Rusanov(const PetscReal *qp, const PetscReal *n, const PetscScalar *xL, const PetscScalar *xR, PetscScalar *flux, Physics phys)
582: {
583:   Physics_Euler   *eu = (Physics_Euler*)phys->data;
584:   PetscScalar     cL,cR,speed;
585:   const EulerNode *uL = (const EulerNode*)xL,*uR = (const EulerNode*)xR;
586:   EulerNode       fL,fR;
587:   PetscInt        i;

590:   if (uL->r < 0 || uR->r < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Reconstructed density is negative");
591:   EulerFlux(phys,n,uL,&fL);
592:   EulerFlux(phys,n,uR,&fR);
593:   eu->sound(eu->pars,uL,&cL);
594:   eu->sound(eu->pars,uR,&cR);
595:   speed = PetscMax(cL,cR)+PetscMax(PetscAbsScalar(DotDIM(uL->ru,n)/NormDIM(n)),PetscAbsScalar(DotDIM(uR->ru,n)/NormDIM(n)));
596:   for (i=0; i<2+DIM; i++) flux[i] = 0.5*(fL.vals[i]+fR.vals[i])+0.5*speed*(xL[i]-xR[i]);
597:   return(0);
598: }

602: static PetscErrorCode PhysicsSolution_Euler(Model mod,PetscReal time,const PetscReal *x,PetscScalar *u,void *ctx)
603: {
604:   PetscInt i;

607:   if (time != 0.0) SETERRQ1(mod->comm,PETSC_ERR_SUP,"No solution known for time %g",(double)time);
608:   u[0]     = 1.0;
609:   u[DIM+1] = 1.0+PetscAbsReal(x[0]);
610:   for (i=1; i<DIM+1; i++) u[i] = 0.0;
611:   return(0);
612: }

616: static PetscErrorCode PhysicsFunctional_Euler(Model mod,PetscReal time,const PetscReal *coord,const PetscScalar *xx,PetscReal *f,void *ctx)
617: {
618:   Physics         phys = (Physics)ctx;
619:   Physics_Euler   *eu  = (Physics_Euler*)phys->data;
620:   const EulerNode *x   = (const EulerNode*)xx;
621:   PetscScalar     p;

624:   f[eu->monitor.Density]  = x->r;
625:   f[eu->monitor.Momentum] = NormDIM(x->ru);
626:   f[eu->monitor.Energy]   = x->e;
627:   f[eu->monitor.Speed]    = NormDIM(x->ru)/x->r;
628:   eu->pressure(eu->pars, x, &p);
629:   f[eu->monitor.Pressure] = p;
630:   return(0);
631: }

635: static PetscErrorCode PhysicsCreate_Euler(DM dm, Model mod,Physics phys)
636: {
637:   Physics_Euler   *eu;
638:   PetscErrorCode  ierr;

641:   phys->field_desc = PhysicsFields_Euler;
642:   phys->riemann = (RiemannFunction) PhysicsRiemann_Euler_Rusanov;
643:   PetscNew(&eu);
644:   phys->data    = eu;
645:   PetscOptionsHead("Euler options");
646:   {
647:     eu->pars[0] = 3.0;
648:     eu->pars[1] = 1.67;
649:     PetscOptionsReal("-eu_f","Degrees of freedom","",eu->pars[0],&eu->pars[0],NULL);
650:     PetscOptionsReal("-eu_gamma","Heat capacity ratio","",eu->pars[1],&eu->pars[1],NULL);
651:   }
652:   PetscOptionsTail();
653:   eu->pressure = Pressure_PG;
654:   eu->sound    = SpeedOfSound_PG;
655:   phys->maxspeed = 1.0;
656:   {
657:     const PetscInt wallids[] = {100,101,200,300};
658:     DMPlexAddBoundary(dm, PETSC_TRUE, "wall", "Face Sets", 0, (void (*)()) PhysicsBoundary_Euler_Wall, ALEN(wallids), wallids, phys);
659:     ModelSolutionSetDefault(mod,PhysicsSolution_Euler,phys);
660:     ModelFunctionalRegister(mod,"Speed",&eu->monitor.Speed,PhysicsFunctional_Euler,phys);
661:     ModelFunctionalRegister(mod,"Energy",&eu->monitor.Energy,PhysicsFunctional_Euler,phys);
662:     ModelFunctionalRegister(mod,"Density",&eu->monitor.Density,PhysicsFunctional_Euler,phys);
663:     ModelFunctionalRegister(mod,"Momentum",&eu->monitor.Momentum,PhysicsFunctional_Euler,phys);
664:     ModelFunctionalRegister(mod,"Pressure",&eu->monitor.Pressure,PhysicsFunctional_Euler,phys);
665:   }
666:   return(0);
667: }

671: PetscErrorCode ConstructCellBoundary(DM dm, User user)
672: {
673:   const char     *name   = "Cell Sets";
674:   const char     *bdname = "split faces";
675:   IS             regionIS, innerIS;
676:   const PetscInt *regions, *cells;
677:   PetscInt       numRegions, innerRegion, numCells, c;
678:   PetscInt       cStart, cEnd, cEndInterior, fStart, fEnd;
679:   PetscBool      hasLabel;

683:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
684:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
685:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);

687:   DMPlexHasLabel(dm, name, &hasLabel);
688:   if (!hasLabel) return(0);
689:   DMPlexGetLabelSize(dm, name, &numRegions);
690:   if (numRegions != 2) return(0);
691:   /* Get the inner id */
692:   DMPlexGetLabelIdIS(dm, name, &regionIS);
693:   ISGetIndices(regionIS, &regions);
694:   innerRegion = regions[0];
695:   ISRestoreIndices(regionIS, &regions);
696:   ISDestroy(&regionIS);
697:   /* Find the faces between cells in different regions, could call DMPlexCreateNeighborCSR() */
698:   DMPlexGetStratumIS(dm, name, innerRegion, &innerIS);
699:   ISGetLocalSize(innerIS, &numCells);
700:   ISGetIndices(innerIS, &cells);
701:   DMPlexCreateLabel(dm, bdname);
702:   for (c = 0; c < numCells; ++c) {
703:     const PetscInt cell = cells[c];
704:     const PetscInt *faces;
705:     PetscInt       numFaces, f;

707:     if ((cell < cStart) || (cell >= cEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Got invalid point %d which is not a cell", cell);
708:     DMPlexGetConeSize(dm, cell, &numFaces);
709:     DMPlexGetCone(dm, cell, &faces);
710:     for (f = 0; f < numFaces; ++f) {
711:       const PetscInt face = faces[f];
712:       const PetscInt *neighbors;
713:       PetscInt       nC, regionA, regionB;

715:       if ((face < fStart) || (face >= fEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Got invalid point %d which is not a face", face);
716:       DMPlexGetSupportSize(dm, face, &nC);
717:       if (nC != 2) continue;
718:       DMPlexGetSupport(dm, face, &neighbors);
719:       if ((neighbors[0] >= cEndInterior) || (neighbors[1] >= cEndInterior)) continue;
720:       if ((neighbors[0] < cStart) || (neighbors[0] >= cEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Got invalid point %d which is not a cell", neighbors[0]);
721:       if ((neighbors[1] < cStart) || (neighbors[1] >= cEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Got invalid point %d which is not a cell", neighbors[1]);
722:       DMPlexGetLabelValue(dm, name, neighbors[0], &regionA);
723:       DMPlexGetLabelValue(dm, name, neighbors[1], &regionB);
724:       if (regionA < 0) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Invalid label %s: Cell %d has no value", name, neighbors[0]);
725:       if (regionB < 0) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Invalid label %s: Cell %d has no value", name, neighbors[1]);
726:       if (regionA != regionB) {
727:         DMPlexSetLabelValue(dm, bdname, faces[f], 1);
728:       }
729:     }
730:   }
731:   ISRestoreIndices(innerIS, &cells);
732:   ISDestroy(&innerIS);
733:   {
734:     DMLabel label;

736:     PetscViewerASCIISynchronizedAllow(PETSC_VIEWER_STDOUT_WORLD, PETSC_TRUE);
737:     DMPlexGetLabel(dm, bdname, &label);
738:     DMLabelView(label, PETSC_VIEWER_STDOUT_WORLD);
739:   }
740:   return(0);
741: }

745: /* Right now, I have just added duplicate faces, which see both cells. We can
746: - Add duplicate vertices and decouple the face cones
747: - Disconnect faces from cells across the rotation gap
748: */
749: PetscErrorCode SplitFaces(DM *dmSplit, const char labelName[], User user)
750: {
751:   DM             dm = *dmSplit, sdm;
752:   PetscSF        sfPoint, gsfPoint;
753:   PetscSection   coordSection, newCoordSection;
754:   Vec            coordinates;
755:   IS             idIS;
756:   const PetscInt *ids;
757:   PetscInt       *newpoints;
758:   PetscInt       dim, depth, maxConeSize, maxSupportSize, numLabels, numGhostCells;
759:   PetscInt       numFS, fs, pStart, pEnd, p, cEnd, cEndInterior, vStart, vEnd, v, fStart, fEnd, newf, d, l;
760:   PetscBool      hasLabel;

764:   DMPlexHasLabel(dm, labelName, &hasLabel);
765:   if (!hasLabel) return(0);
766:   DMCreate(PetscObjectComm((PetscObject)dm), &sdm);
767:   DMSetType(sdm, DMPLEX);
768:   DMPlexGetDimension(dm, &dim);
769:   DMPlexSetDimension(sdm, dim);

771:   DMPlexGetLabelIdIS(dm, labelName, &idIS);
772:   ISGetLocalSize(idIS, &numFS);
773:   ISGetIndices(idIS, &ids);

775:   user->numSplitFaces = 0;
776:   for (fs = 0; fs < numFS; ++fs) {
777:     PetscInt numBdFaces;

779:     DMPlexGetStratumSize(dm, labelName, ids[fs], &numBdFaces);
780:     user->numSplitFaces += numBdFaces;
781:   }
782:   DMPlexGetChart(dm, &pStart, &pEnd);
783:   pEnd += user->numSplitFaces;
784:   DMPlexSetChart(sdm, pStart, pEnd);
785:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
786:   DMPlexSetHybridBounds(sdm, cEndInterior, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_DETERMINE);
787:   DMPlexGetHeightStratum(dm, 0, NULL, &cEnd);
788:   numGhostCells = cEnd - cEndInterior;
789:   /* Set cone and support sizes */
790:   DMPlexGetDepth(dm, &depth);
791:   for (d = 0; d <= depth; ++d) {
792:     DMPlexGetDepthStratum(dm, d, &pStart, &pEnd);
793:     for (p = pStart; p < pEnd; ++p) {
794:       PetscInt newp = p;
795:       PetscInt size;

797:       DMPlexGetConeSize(dm, p, &size);
798:       DMPlexSetConeSize(sdm, newp, size);
799:       DMPlexGetSupportSize(dm, p, &size);
800:       DMPlexSetSupportSize(sdm, newp, size);
801:     }
802:   }
803:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
804:   for (fs = 0, newf = fEnd; fs < numFS; ++fs) {
805:     IS             faceIS;
806:     const PetscInt *faces;
807:     PetscInt       numFaces, f;

809:     DMPlexGetStratumIS(dm, labelName, ids[fs], &faceIS);
810:     ISGetLocalSize(faceIS, &numFaces);
811:     ISGetIndices(faceIS, &faces);
812:     for (f = 0; f < numFaces; ++f, ++newf) {
813:       PetscInt size;

815:       /* Right now I think that both faces should see both cells */
816:       DMPlexGetConeSize(dm, faces[f], &size);
817:       DMPlexSetConeSize(sdm, newf, size);
818:       DMPlexGetSupportSize(dm, faces[f], &size);
819:       DMPlexSetSupportSize(sdm, newf, size);
820:     }
821:     ISRestoreIndices(faceIS, &faces);
822:     ISDestroy(&faceIS);
823:   }
824:   DMSetUp(sdm);
825:   /* Set cones and supports */
826:   DMPlexGetMaxSizes(dm, &maxConeSize, &maxSupportSize);
827:   PetscMalloc(PetscMax(maxConeSize, maxSupportSize) * sizeof(PetscInt), &newpoints);
828:   DMPlexGetChart(dm, &pStart, &pEnd);
829:   for (p = pStart; p < pEnd; ++p) {
830:     const PetscInt *points, *orientations;
831:     PetscInt       size, i, newp = p;

833:     DMPlexGetConeSize(dm, p, &size);
834:     DMPlexGetCone(dm, p, &points);
835:     DMPlexGetConeOrientation(dm, p, &orientations);
836:     for (i = 0; i < size; ++i) newpoints[i] = points[i];
837:     DMPlexSetCone(sdm, newp, newpoints);
838:     DMPlexSetConeOrientation(sdm, newp, orientations);
839:     DMPlexGetSupportSize(dm, p, &size);
840:     DMPlexGetSupport(dm, p, &points);
841:     for (i = 0; i < size; ++i) newpoints[i] = points[i];
842:     DMPlexSetSupport(sdm, newp, newpoints);
843:   }
844:   PetscFree(newpoints);
845:   for (fs = 0, newf = fEnd; fs < numFS; ++fs) {
846:     IS             faceIS;
847:     const PetscInt *faces;
848:     PetscInt       numFaces, f;

850:     DMPlexGetStratumIS(dm, labelName, ids[fs], &faceIS);
851:     ISGetLocalSize(faceIS, &numFaces);
852:     ISGetIndices(faceIS, &faces);
853:     for (f = 0; f < numFaces; ++f, ++newf) {
854:       const PetscInt *points;

856:       DMPlexGetCone(dm, faces[f], &points);
857:       DMPlexSetCone(sdm, newf, points);
858:       DMPlexGetSupport(dm, faces[f], &points);
859:       DMPlexSetSupport(sdm, newf, points);
860:     }
861:     ISRestoreIndices(faceIS, &faces);
862:     ISDestroy(&faceIS);
863:   }
864:   ISRestoreIndices(idIS, &ids);
865:   ISDestroy(&idIS);
866:   DMPlexStratify(sdm);
867:   /* Convert coordinates */
868:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
869:   DMGetCoordinateSection(dm, &coordSection);
870:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &newCoordSection);
871:   PetscSectionSetNumFields(newCoordSection, 1);
872:   PetscSectionSetFieldComponents(newCoordSection, 0, dim);
873:   PetscSectionSetChart(newCoordSection, vStart, vEnd);
874:   for (v = vStart; v < vEnd; ++v) {
875:     PetscSectionSetDof(newCoordSection, v, dim);
876:     PetscSectionSetFieldDof(newCoordSection, v, 0, dim);
877:   }
878:   PetscSectionSetUp(newCoordSection);
879:   DMSetCoordinateSection(sdm, newCoordSection);
880:   PetscSectionDestroy(&newCoordSection); /* relinquish our reference */
881:   DMGetCoordinatesLocal(dm, &coordinates);
882:   DMSetCoordinatesLocal(sdm, coordinates);
883:   /* Convert labels */
884:   DMPlexGetNumLabels(dm, &numLabels);
885:   for (l = 0; l < numLabels; ++l) {
886:     const char *lname;
887:     PetscBool  isDepth;

889:     DMPlexGetLabelName(dm, l, &lname);
890:     PetscStrcmp(lname, "depth", &isDepth);
891:     if (isDepth) continue;
892:     DMPlexCreateLabel(sdm, lname);
893:     DMPlexGetLabelIdIS(dm, lname, &idIS);
894:     ISGetLocalSize(idIS, &numFS);
895:     ISGetIndices(idIS, &ids);
896:     for (fs = 0; fs < numFS; ++fs) {
897:       IS             pointIS;
898:       const PetscInt *points;
899:       PetscInt       numPoints;

901:       DMPlexGetStratumIS(dm, lname, ids[fs], &pointIS);
902:       ISGetLocalSize(pointIS, &numPoints);
903:       ISGetIndices(pointIS, &points);
904:       for (p = 0; p < numPoints; ++p) {
905:         PetscInt newpoint = points[p];

907:         DMPlexSetLabelValue(sdm, lname, newpoint, ids[fs]);
908:       }
909:       ISRestoreIndices(pointIS, &points);
910:       ISDestroy(&pointIS);
911:     }
912:     ISRestoreIndices(idIS, &ids);
913:     ISDestroy(&idIS);
914:   }
915:   /* Convert pointSF */
916:   const PetscSFNode *remotePoints;
917:   PetscSFNode       *gremotePoints;
918:   const PetscInt    *localPoints;
919:   PetscInt          *glocalPoints,*newLocation,*newRemoteLocation;
920:   PetscInt          numRoots, numLeaves;
921:   PetscMPIInt       numProcs;

923:   MPI_Comm_size(PetscObjectComm((PetscObject)dm), &numProcs);
924:   DMGetPointSF(dm, &sfPoint);
925:   DMGetPointSF(sdm, &gsfPoint);
926:   DMPlexGetChart(dm,&pStart,&pEnd);
927:   PetscSFGetGraph(sfPoint, &numRoots, &numLeaves, &localPoints, &remotePoints);
928:   if (numRoots >= 0) {
929:     PetscMalloc2(numRoots,&newLocation,pEnd-pStart,&newRemoteLocation);
930:     for (l=0; l<numRoots; l++) newLocation[l] = l; /* + (l >= cEnd ? numGhostCells : 0); */
931:     PetscSFBcastBegin(sfPoint, MPIU_INT, newLocation, newRemoteLocation);
932:     PetscSFBcastEnd(sfPoint, MPIU_INT, newLocation, newRemoteLocation);
933:     PetscMalloc1(numLeaves,    &glocalPoints);
934:     PetscMalloc1(numLeaves, &gremotePoints);
935:     for (l = 0; l < numLeaves; ++l) {
936:       glocalPoints[l]        = localPoints[l]; /* localPoints[l] >= cEnd ? localPoints[l] + numGhostCells : localPoints[l]; */
937:       gremotePoints[l].rank  = remotePoints[l].rank;
938:       gremotePoints[l].index = newRemoteLocation[localPoints[l]];
939:     }
940:     PetscFree2(newLocation,newRemoteLocation);
941:     PetscSFSetGraph(gsfPoint, numRoots+numGhostCells, numLeaves, glocalPoints, PETSC_OWN_POINTER, gremotePoints, PETSC_OWN_POINTER);
942:   }
943:   DMDestroy(dmSplit);
944:   *dmSplit = sdm;
945:   return(0);
946: }

950: PetscErrorCode CreatePartitionVec(DM dm, DM *dmCell, Vec *partition)
951: {
952:   PetscSF        sfPoint;
953:   PetscSection   coordSection;
954:   Vec            coordinates;
955:   PetscSection   sectionCell;
956:   PetscScalar    *part;
957:   PetscInt       cStart, cEnd, c;
958:   PetscMPIInt    rank;

962:   DMGetCoordinateSection(dm, &coordSection);
963:   DMGetCoordinatesLocal(dm, &coordinates);
964:   DMClone(dm, dmCell);
965:   DMGetPointSF(dm, &sfPoint);
966:   DMSetPointSF(*dmCell, sfPoint);
967:   DMSetCoordinateSection(*dmCell, coordSection);
968:   DMSetCoordinatesLocal(*dmCell, coordinates);
969:   MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);
970:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionCell);
971:   DMPlexGetHeightStratum(*dmCell, 0, &cStart, &cEnd);
972:   PetscSectionSetChart(sectionCell, cStart, cEnd);
973:   for (c = cStart; c < cEnd; ++c) {
974:     PetscSectionSetDof(sectionCell, c, 1);
975:   }
976:   PetscSectionSetUp(sectionCell);
977:   DMSetDefaultSection(*dmCell, sectionCell);
978:   PetscSectionDestroy(&sectionCell);
979:   DMCreateLocalVector(*dmCell, partition);
980:   PetscObjectSetName((PetscObject)*partition, "partition");
981:   VecGetArray(*partition, &part);
982:   for (c = cStart; c < cEnd; ++c) {
983:     PetscScalar *p;

985:     DMPlexPointLocalRef(*dmCell, c, part, &p);
986:     p[0] = rank;
987:   }
988:   VecRestoreArray(*partition, &part);
989:   return(0);
990: }

994: PetscErrorCode CreateMassMatrix(DM dm, Vec *massMatrix, User user)
995: {
996:   DM                dmMass, dmFace, dmCell, dmCoord;
997:   PetscSection      coordSection;
998:   Vec               coordinates, facegeom, cellgeom;
999:   PetscSection      sectionMass;
1000:   PetscScalar       *m;
1001:   const PetscScalar *fgeom, *cgeom, *coords;
1002:   PetscInt          vStart, vEnd, v;
1003:   PetscErrorCode    ierr;

1006:   DMGetCoordinateSection(dm, &coordSection);
1007:   DMGetCoordinatesLocal(dm, &coordinates);
1008:   DMClone(dm, &dmMass);
1009:   DMSetCoordinateSection(dmMass, coordSection);
1010:   DMSetCoordinatesLocal(dmMass, coordinates);
1011:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionMass);
1012:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
1013:   PetscSectionSetChart(sectionMass, vStart, vEnd);
1014:   for (v = vStart; v < vEnd; ++v) {
1015:     PetscInt numFaces;

1017:     DMPlexGetSupportSize(dmMass, v, &numFaces);
1018:     PetscSectionSetDof(sectionMass, v, numFaces*numFaces);
1019:   }
1020:   PetscSectionSetUp(sectionMass);
1021:   DMSetDefaultSection(dmMass, sectionMass);
1022:   PetscSectionDestroy(&sectionMass);
1023:   DMGetLocalVector(dmMass, massMatrix);
1024:   VecGetArray(*massMatrix, &m);
1025:   DMPlexTSGetGeometry(dm, &facegeom, &cellgeom, NULL);
1026:   VecGetDM(facegeom, &dmFace);
1027:   VecGetArrayRead(facegeom, &fgeom);
1028:   VecGetDM(cellgeom, &dmCell);
1029:   VecGetArrayRead(cellgeom, &cgeom);
1030:   DMGetCoordinateDM(dm, &dmCoord);
1031:   VecGetArrayRead(coordinates, &coords);
1032:   for (v = vStart; v < vEnd; ++v) {
1033:     const PetscInt    *faces;
1034:     const FaceGeom    *fgA, *fgB, *cg;
1035:     const PetscScalar *vertex;
1036:     PetscInt          numFaces, sides[2], f, g;

1038:     DMPlexPointLocalRead(dmCoord, v, coords, &vertex);
1039:     DMPlexGetSupportSize(dmMass, v, &numFaces);
1040:     DMPlexGetSupport(dmMass, v, &faces);
1041:     for (f = 0; f < numFaces; ++f) {
1042:       sides[0] = faces[f];
1043:       DMPlexPointLocalRead(dmFace, faces[f], fgeom, &fgA);
1044:       for (g = 0; g < numFaces; ++g) {
1045:         const PetscInt *cells = NULL;;
1046:         PetscReal      area   = 0.0;
1047:         PetscInt       numCells;

1049:         sides[1] = faces[g];
1050:         DMPlexPointLocalRead(dmFace, faces[g], fgeom, &fgB);
1051:         DMPlexGetJoin(dmMass, 2, sides, &numCells, &cells);
1052:         if (numCells != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Invalid join for faces");
1053:         DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cg);
1054:         area += PetscAbsScalar((vertex[0] - cg->centroid[0])*(fgA->centroid[1] - cg->centroid[1]) - (vertex[1] - cg->centroid[1])*(fgA->centroid[0] - cg->centroid[0]));
1055:         area += PetscAbsScalar((vertex[0] - cg->centroid[0])*(fgB->centroid[1] - cg->centroid[1]) - (vertex[1] - cg->centroid[1])*(fgB->centroid[0] - cg->centroid[0]));
1056:         m[f*numFaces+g] = Dot2(fgA->normal, fgB->normal)*area*0.5;
1057:         DMPlexRestoreJoin(dmMass, 2, sides, &numCells, &cells);
1058:       }
1059:     }
1060:   }
1061:   VecRestoreArrayRead(facegeom, &fgeom);
1062:   VecRestoreArrayRead(cellgeom, &cgeom);
1063:   VecRestoreArrayRead(coordinates, &coords);
1064:   VecRestoreArray(*massMatrix, &m);
1065:   DMDestroy(&dmMass);
1066:   return(0);
1067: }

1071: PetscErrorCode SetUpLocalSpace(DM dm, User user)
1072: {
1073:   PetscSection   stateSection;
1074:   Physics        phys;
1075:   PetscInt       dof = user->model->physics->dof, *cind, d, stateSize, cStart, cEnd, cEndInterior, c, i;

1079:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
1080:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
1081:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &stateSection);
1082:   phys = user->model->physics;
1083:   PetscSectionSetNumFields(stateSection,phys->nfields);
1084:   for (i=0; i<phys->nfields; i++) {
1085:     PetscSectionSetFieldName(stateSection,i,phys->field_desc[i].name);
1086:     PetscSectionSetFieldComponents(stateSection,i,phys->field_desc[i].dof);
1087:   }
1088:   PetscSectionSetChart(stateSection, cStart, cEnd);
1089:   for (c = cStart; c < cEnd; ++c) {
1090:     for (i=0; i<phys->nfields; i++) {
1091:       PetscSectionSetFieldDof(stateSection,c,i,phys->field_desc[i].dof);
1092:     }
1093:     PetscSectionSetDof(stateSection, c, dof);
1094:   }
1095:   for (c = cEndInterior; c < cEnd; ++c) {
1096:     PetscSectionSetConstraintDof(stateSection, c, dof);
1097:   }
1098:   PetscSectionSetUp(stateSection);
1099:   PetscMalloc1(dof, &cind);
1100:   for (d = 0; d < dof; ++d) cind[d] = d;
1101: #if 0
1102:   for (c = cStart; c < cEnd; ++c) {
1103:     PetscInt val;

1105:     DMPlexGetLabelValue(dm, "vtk", c, &val);
1106:     if (val < 0) {PetscSectionSetConstraintIndices(stateSection, c, cind);}
1107:   }
1108: #endif
1109:   for (c = cEndInterior; c < cEnd; ++c) {
1110:     PetscSectionSetConstraintIndices(stateSection, c, cind);
1111:   }
1112:   PetscFree(cind);
1113:   PetscSectionGetStorageSize(stateSection, &stateSize);
1114:   DMSetDefaultSection(dm,stateSection);
1115:   PetscSectionDestroy(&stateSection);
1116:   return(0);
1117: }

1119: #if 0
1122: PetscErrorCode SetUpBoundaries(DM dm, User user)
1123: {
1124:   Model          mod = user->model;
1126:   BoundaryLink   b;

1129:   PetscOptionsBegin(PetscObjectComm((PetscObject)dm),NULL,"Boundary condition options","");
1130:   for (b = mod->boundary; b; b=b->next) {
1131:     char      optname[512];
1132:     PetscInt  ids[512],len = 512;
1133:     PetscBool flg;
1134:     PetscSNPrintf(optname,sizeof optname,"-bc_%s",b->name);
1135:     PetscMemzero(ids,sizeof(ids));
1136:     PetscOptionsIntArray(optname,"List of boundary IDs","",ids,&len,&flg);
1137:     if (flg) {
1138:       /* TODO: check all IDs to make sure they exist in the mesh */
1139:       PetscFree(b->ids);
1140:       b->numids = len;
1141:       PetscMalloc1(len,&b->ids);
1142:       PetscMemcpy(b->ids,ids,len*sizeof(PetscInt));
1143:     }
1144:   }
1145:   PetscOptionsEnd();
1146:   return(0);
1147: }
1148: #endif

1152: /* Behavior will be different for multi-physics or when using non-default boundary conditions */
1153: static PetscErrorCode ModelSolutionSetDefault(Model mod,SolutionFunction func,void *ctx)
1154: {
1156:   mod->solution    = func;
1157:   mod->solutionctx = ctx;
1158:   return(0);
1159: }

1163: static PetscErrorCode ModelFunctionalRegister(Model mod,const char *name,PetscInt *offset,FunctionalFunction func,void *ctx)
1164: {
1166:   FunctionalLink link,*ptr;
1167:   PetscInt       lastoffset = -1;

1170:   for (ptr=&mod->functionalRegistry; *ptr; ptr = &(*ptr)->next) lastoffset = (*ptr)->offset;
1171:   PetscNew(&link);
1172:   PetscStrallocpy(name,&link->name);
1173:   link->offset = lastoffset + 1;
1174:   link->func   = func;
1175:   link->ctx    = ctx;
1176:   link->next   = NULL;
1177:   *ptr         = link;
1178:   *offset      = link->offset;
1179:   return(0);
1180: }

1184: static PetscErrorCode ModelFunctionalSetFromOptions(Model mod)
1185: {
1187:   PetscInt       i,j;
1188:   FunctionalLink link;
1189:   char           *names[256];

1192:   mod->numMonitored = ALEN(names);
1193:   PetscOptionsStringArray("-monitor","list of functionals to monitor","",names,&mod->numMonitored,NULL);
1194:   /* Create list of functionals that will be computed somehow */
1195:   PetscMalloc1(mod->numMonitored,&mod->functionalMonitored);
1196:   /* Create index of calls that we will have to make to compute these functionals (over-allocation in general). */
1197:   PetscMalloc1(mod->numMonitored,&mod->functionalCall);
1198:   mod->numCall = 0;
1199:   for (i=0; i<mod->numMonitored; i++) {
1200:     for (link=mod->functionalRegistry; link; link=link->next) {
1201:       PetscBool match;
1202:       PetscStrcasecmp(names[i],link->name,&match);
1203:       if (match) break;
1204:     }
1205:     if (!link) SETERRQ1(mod->comm,PETSC_ERR_USER,"No known functional '%s'",names[i]);
1206:     mod->functionalMonitored[i] = link;
1207:     for (j=0; j<i; j++) {
1208:       if (mod->functionalCall[j]->func == link->func && mod->functionalCall[j]->ctx == link->ctx) goto next_name;
1209:     }
1210:     mod->functionalCall[mod->numCall++] = link; /* Just points to the first link using the result. There may be more results. */
1211: next_name:
1212:     PetscFree(names[i]);
1213:   }

1215:   /* Find out the maximum index of any functional computed by a function we will be calling (even if we are not using it) */
1216:   mod->maxComputed = -1;
1217:   for (link=mod->functionalRegistry; link; link=link->next) {
1218:     for (i=0; i<mod->numCall; i++) {
1219:       FunctionalLink call = mod->functionalCall[i];
1220:       if (link->func == call->func && link->ctx == call->ctx) {
1221:         mod->maxComputed = PetscMax(mod->maxComputed,link->offset);
1222:       }
1223:     }
1224:   }
1225:   return(0);
1226: }

1230: static PetscErrorCode FunctionalLinkDestroy(FunctionalLink *link)
1231: {
1233:   FunctionalLink l,next;

1236:   if (!link) return(0);
1237:   l     = *link;
1238:   *link = NULL;
1239:   for (; l; l=next) {
1240:     next = l->next;
1241:     PetscFree(l->name);
1242:     PetscFree(l);
1243:   }
1244:   return(0);
1245: }

1249: PetscErrorCode SetInitialCondition(DM dm, Vec X, User user)
1250: {
1251:   DM                 dmCell;
1252:   Model              mod = user->model;
1253:   Vec                cellgeom;
1254:   const PetscScalar *cgeom;
1255:   PetscScalar       *x;
1256:   PetscInt           cStart, cEnd, cEndInterior, c;
1257:   PetscErrorCode     ierr;

1260:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
1261:   DMPlexTSGetGeometry(dm, NULL, &cellgeom, NULL);
1262:   VecGetDM(cellgeom, &dmCell);
1263:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
1264:   VecGetArrayRead(cellgeom, &cgeom);
1265:   VecGetArray(X, &x);
1266:   for (c = cStart; c < cEndInterior; ++c) {
1267:     const CellGeom *cg;
1268:     PetscScalar    *xc;

1270:     DMPlexPointLocalRead(dmCell,c,cgeom,&cg);
1271:     DMPlexPointGlobalRef(dm,c,x,&xc);
1272:     if (xc) {(*mod->solution)(mod,0.0,cg->centroid,xc,mod->solutionctx);}
1273:   }
1274:   VecRestoreArrayRead(cellgeom, &cgeom);
1275:   VecRestoreArray(X, &x);
1276:   return(0);
1277: }

1281: static PetscErrorCode OutputVTK(DM dm, const char *filename, PetscViewer *viewer)
1282: {

1286:   PetscViewerCreate(PetscObjectComm((PetscObject)dm), viewer);
1287:   PetscViewerSetType(*viewer, PETSCVIEWERVTK);
1288:   PetscViewerFileSetName(*viewer, filename);
1289:   return(0);
1290: }

1294: static PetscErrorCode MonitorVTK(TS ts,PetscInt stepnum,PetscReal time,Vec X,void *ctx)
1295: {
1296:   User           user = (User)ctx;
1297:   DM             dm;
1298:   Vec            cellgeom;
1299:   PetscViewer    viewer;
1300:   char           filename[PETSC_MAX_PATH_LEN],*ftable = NULL;
1301:   PetscReal      xnorm;
1302:   PetscInt       cEndInterior;

1306:   PetscObjectSetName((PetscObject) X, "solution");
1307:   VecGetDM(X,&dm);
1308:   DMPlexTSGetGeometry(dm, NULL, &cellgeom, NULL);
1309:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
1310:   VecNorm(X,NORM_INFINITY,&xnorm);
1311:   if (stepnum >= 0) {           /* No summary for final time */
1312:     Model             mod = user->model;
1313:     PetscInt          c,cStart,cEnd,fcount,i;
1314:     size_t            ftableused,ftablealloc;
1315:     const PetscScalar *cgeom,*x;
1316:     DM                dmCell;
1317:     PetscReal         *fmin,*fmax,*fintegral,*ftmp;
1318:     fcount = mod->maxComputed+1;
1319:     PetscMalloc4(fcount,&fmin,fcount,&fmax,fcount,&fintegral,fcount,&ftmp);
1320:     for (i=0; i<fcount; i++) {
1321:       fmin[i]      = PETSC_MAX_REAL;
1322:       fmax[i]      = PETSC_MIN_REAL;
1323:       fintegral[i] = 0;
1324:     }
1325:     DMPlexGetHeightStratum(dm,0,&cStart,&cEnd);
1326:     VecGetDM(cellgeom,&dmCell);
1327:     VecGetArrayRead(cellgeom,&cgeom);
1328:     VecGetArrayRead(X,&x);
1329:     for (c = cStart; c < cEndInterior; ++c) {
1330:       const CellGeom    *cg;
1331:       const PetscScalar *cx;
1332:       DMPlexPointLocalRead(dmCell,c,cgeom,&cg);
1333:       DMPlexPointGlobalRead(dm,c,x,&cx);
1334:       if (!cx) continue;        /* not a global cell */
1335:       for (i=0; i<mod->numCall; i++) {
1336:         FunctionalLink flink = mod->functionalCall[i];
1337:         (*flink->func)(mod,time,cg->centroid,cx,ftmp,flink->ctx);
1338:       }
1339:       for (i=0; i<fcount; i++) {
1340:         fmin[i]       = PetscMin(fmin[i],ftmp[i]);
1341:         fmax[i]       = PetscMax(fmax[i],ftmp[i]);
1342:         fintegral[i] += cg->volume * ftmp[i];
1343:       }
1344:     }
1345:     VecRestoreArrayRead(cellgeom,&cgeom);
1346:     VecRestoreArrayRead(X,&x);
1347:     MPI_Allreduce(MPI_IN_PLACE,fmin,fcount,MPIU_REAL,MPI_MIN,PetscObjectComm((PetscObject)ts));
1348:     MPI_Allreduce(MPI_IN_PLACE,fmax,fcount,MPIU_REAL,MPI_MAX,PetscObjectComm((PetscObject)ts));
1349:     MPI_Allreduce(MPI_IN_PLACE,fintegral,fcount,MPIU_REAL,MPI_SUM,PetscObjectComm((PetscObject)ts));

1351:     ftablealloc = fcount * 100;
1352:     ftableused  = 0;
1353:     PetscMalloc1(ftablealloc,&ftable);
1354:     for (i=0; i<mod->numMonitored; i++) {
1355:       size_t         countused;
1356:       char           buffer[256],*p;
1357:       FunctionalLink flink = mod->functionalMonitored[i];
1358:       PetscInt       id    = flink->offset;
1359:       if (i % 3) {
1360:         PetscMemcpy(buffer,"  ",2);
1361:         p    = buffer + 2;
1362:       } else if (i) {
1363:         char newline[] = "\n";
1364:         PetscMemcpy(buffer,newline,sizeof newline-1);
1365:         p    = buffer + sizeof newline - 1;
1366:       } else {
1367:         p = buffer;
1368:       }
1369:       PetscSNPrintfCount(p,sizeof buffer-(p-buffer),"%12s [%10.7g,%10.7g] int %10.7g",&countused,flink->name,(double)fmin[id],(double)fmax[id],(double)fintegral[id]);
1370:       countused += p - buffer;
1371:       if (countused > ftablealloc-ftableused-1) { /* reallocate */
1372:         char *ftablenew;
1373:         ftablealloc = 2*ftablealloc + countused;
1374:         PetscMalloc(ftablealloc,&ftablenew);
1375:         PetscMemcpy(ftablenew,ftable,ftableused);
1376:         PetscFree(ftable);
1377:         ftable = ftablenew;
1378:       }
1379:       PetscMemcpy(ftable+ftableused,buffer,countused);
1380:       ftableused += countused;
1381:       ftable[ftableused] = 0;
1382:     }
1383:     PetscFree4(fmin,fmax,fintegral,ftmp);

1385:     PetscPrintf(PetscObjectComm((PetscObject)ts),"% 3D  time %8.4g  |x| %8.4g  %s\n",stepnum,(double)time,(double)xnorm,ftable ? ftable : "");
1386:     PetscFree(ftable);
1387:   }
1388:   if (user->vtkInterval < 1) return(0);
1389:   if ((stepnum == -1) ^ (stepnum % user->vtkInterval == 0)) {
1390:     if (stepnum == -1) {        /* Final time is not multiple of normal time interval, write it anyway */
1391:       TSGetTimeStepNumber(ts,&stepnum);
1392:     }
1393:     PetscSNPrintf(filename,sizeof filename,"ex11-%03D.vtu",stepnum);
1394:     OutputVTK(dm,filename,&viewer);
1395:     VecView(X,viewer);
1396:     PetscViewerDestroy(&viewer);
1397:   }
1398:   return(0);
1399: }

1403: int main(int argc, char **argv)
1404: {
1405:   MPI_Comm          comm;
1406:   PetscFV           fvm;
1407:   User              user;
1408:   Model             mod;
1409:   Physics           phys;
1410:   DM                dm;
1411:   PetscReal         ftime, cfl, dt, minRadius;
1412:   PetscInt          dim, nsteps;
1413:   TS                ts;
1414:   TSConvergedReason reason;
1415:   Vec               X;
1416:   PetscViewer       viewer;
1417:   PetscMPIInt       rank;
1418:   PetscBool         vtkCellGeom, splitFaces;
1419:   PetscInt          overlap, f;
1420:   char              filename[PETSC_MAX_PATH_LEN] = "sevenside.exo";
1421:   PetscErrorCode    ierr;

1423:   PetscInitialize(&argc, &argv, (char*) 0, help);
1424:   comm = PETSC_COMM_WORLD;
1425:   MPI_Comm_rank(comm, &rank);

1427:   PetscNew(&user);
1428:   PetscNew(&user->model);
1429:   PetscNew(&user->model->physics);
1430:   mod  = user->model;
1431:   phys = mod->physics;
1432:   mod->comm = comm;

1434:   /* Register physical models to be available on the command line */
1435:   PetscFunctionListAdd(&PhysicsList,"advect"          ,PhysicsCreate_Advect);
1436:   PetscFunctionListAdd(&PhysicsList,"sw"              ,PhysicsCreate_SW);
1437:   PetscFunctionListAdd(&PhysicsList,"euler"           ,PhysicsCreate_Euler);


1440:   PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Mesh Options","");
1441:   {
1442:     cfl  = 0.9 * 4; /* default SSPRKS2 with s=5 stages is stable for CFL number s-1 */
1443:     PetscOptionsReal("-ufv_cfl","CFL number per step","",cfl,&cfl,NULL);
1444:     PetscOptionsString("-f","Exodus.II filename to read","",filename,filename,sizeof(filename),NULL);
1445:     splitFaces = PETSC_FALSE;
1446:     PetscOptionsBool("-ufv_split_faces","Split faces between cell sets","",splitFaces,&splitFaces,NULL);
1447:     overlap = 1;
1448:     PetscOptionsInt("-ufv_mesh_overlap","Number of cells to overlap partitions","",overlap,&overlap,NULL);
1449:     user->vtkInterval = 1;
1450:     PetscOptionsInt("-ufv_vtk_interval","VTK output interval (0 to disable)","",user->vtkInterval,&user->vtkInterval,NULL);
1451:     vtkCellGeom = PETSC_FALSE;
1452:     PetscOptionsBool("-ufv_vtk_cellgeom","Write cell geometry (for debugging)","",vtkCellGeom,&vtkCellGeom,NULL);
1453:   }
1454:   PetscOptionsEnd();
1455:   DMPlexCreateExodusFromFile(comm, filename, PETSC_TRUE, &dm);
1456:   DMViewFromOptions(dm, NULL, "-dm_view");
1457:   DMPlexGetDimension(dm, &dim);

1459:   PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Physics Options","");
1460:   {
1461:     PetscErrorCode (*physcreate)(DM,Model,Physics);
1462:     char             physname[256]  = "advect";

1464:     DMPlexCreateLabel(dm, "Face Sets");
1465:     PetscOptionsFList("-physics","Physics module to solve","",PhysicsList,physname,physname,sizeof physname,NULL);
1466:     PetscFunctionListFind(PhysicsList,physname,&physcreate);
1467:     PetscMemzero(phys,sizeof(struct _n_Physics));
1468:     (*physcreate)(dm,mod,phys);
1469:     mod->maxspeed = phys->maxspeed;
1470:     /* Count number of fields and dofs */
1471:     for (phys->nfields=0,phys->dof=0; phys->field_desc[phys->nfields].name; phys->nfields++) phys->dof += phys->field_desc[phys->nfields].dof;

1473:     if (mod->maxspeed <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set maxspeed",physname);
1474:     if (phys->dof <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set dof",physname);
1475:     ModelFunctionalSetFromOptions(mod);
1476:   }
1477:   PetscOptionsEnd();
1478:   {
1479:     DM dmDist;

1481:     DMPlexSetAdjacencyUseCone(dm, PETSC_TRUE);
1482:     DMPlexSetAdjacencyUseClosure(dm, PETSC_FALSE);
1483:     DMPlexDistribute(dm, "chaco", overlap, NULL, &dmDist);
1484:     if (dmDist) {
1485:       DMDestroy(&dm);
1486:       dm   = dmDist;
1487:     }
1488:   }
1489:   DMSetFromOptions(dm);
1490:   {
1491:     DM gdm;

1493:     DMPlexConstructGhostCells(dm, NULL, NULL, &gdm);
1494:     DMDestroy(&dm);
1495:     dm   = gdm;
1496:     DMViewFromOptions(dm, NULL, "-dm_view");
1497:   }
1498:   if (splitFaces) {ConstructCellBoundary(dm, user);}
1499:   SplitFaces(&dm, "split faces", user);

1501:   PetscFVCreate(comm, &fvm);
1502:   PetscFVSetFromOptions(fvm);
1503:   DMSetNumFields(dm, phys->nfields);
1504:   for (f = 0; f < phys->nfields; ++f) {DMSetField(dm, f, (PetscObject) fvm);}
1505:   PetscFVSetNumComponents(fvm, phys->dof);
1506:   PetscFVSetSpatialDimension(fvm, dim);

1508:   /* Set up DM with section describing local vector and configure local vector. */
1509:   SetUpLocalSpace(dm, user);

1511:   TSCreate(comm, &ts);
1512:   TSSetType(ts, TSSSP);
1513:   TSSetDM(ts, dm);
1514:   TSMonitorSet(ts,MonitorVTK,user,NULL);
1515:   DMPlexTSSetRHSFunctionLocal(dm, user->model->physics->riemann, user->model->physics);

1517:   DMCreateGlobalVector(dm, &X);
1518:   PetscObjectSetName((PetscObject) X, "solution");
1519:   SetInitialCondition(dm, X, user);
1520:   if (vtkCellGeom) {
1521:     DM  dmCell;
1522:     Vec cellgeom, partition;

1524:     DMPlexTSGetGeometry(dm, NULL, &cellgeom, NULL);
1525:     OutputVTK(dm, "ex11-cellgeom.vtk", &viewer);
1526:     VecView(cellgeom, viewer);
1527:     PetscViewerDestroy(&viewer);
1528:     CreatePartitionVec(dm, &dmCell, &partition);
1529:     OutputVTK(dmCell, "ex11-partition.vtk", &viewer);
1530:     VecView(partition, viewer);
1531:     PetscViewerDestroy(&viewer);
1532:     VecDestroy(&partition);
1533:     DMDestroy(&dmCell);
1534:   }

1536:   DMPlexTSGetGeometry(dm, NULL, NULL, &minRadius);
1537:   TSSetDuration(ts,1000,2.0);
1538:   dt   = cfl * minRadius / user->model->maxspeed;
1539:   TSSetInitialTimeStep(ts,0.0,dt);
1540:   TSSetFromOptions(ts);
1541:   TSSolve(ts,X);
1542:   TSGetSolveTime(ts,&ftime);
1543:   TSGetTimeStepNumber(ts,&nsteps);
1544:   TSGetConvergedReason(ts,&reason);
1545:   PetscPrintf(PETSC_COMM_WORLD,"%s at time %g after %D steps\n",TSConvergedReasons[reason],(double)ftime,nsteps);
1546:   TSDestroy(&ts);

1548:   PetscFunctionListDestroy(&PhysicsList);
1549:   FunctionalLinkDestroy(&user->model->functionalRegistry);
1550:   PetscFree(user->model->functionalMonitored);
1551:   PetscFree(user->model->functionalCall);
1552:   PetscFree(user->model->physics->data);
1553:   PetscFree(user->model->physics);
1554:   PetscFree(user->model);
1555:   PetscFree(user);
1556:   VecDestroy(&X);
1557:   PetscFVDestroy(&fvm);
1558:   DMDestroy(&dm);
1559:   PetscFinalize();
1560:   return(0);
1561: }