Actual source code: ex11.c

petsc-3.6.3 2015-12-03
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  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 <petscdmplex.h>
 38: #include <petscds.h>
 39: #include <petscts.h>
 40: #include <petscsf.h> /* For SplitFaces() */

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

 45: static PetscFunctionList PhysicsList;

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

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

 54: /* 'User' implements a discretization of a continuous model. */
 55: typedef struct _n_User *User;
 56: typedef PetscErrorCode (*SolutionFunction)(Model,PetscReal,const PetscReal*,PetscScalar*,void*);
 57: typedef PetscErrorCode (*FunctionalFunction)(Model,PetscReal,const PetscReal*,const PetscScalar*,PetscReal*,void*);
 58: typedef PetscErrorCode (*SetupFields)(Physics,PetscSection);
 59: static PetscErrorCode ModelSolutionSetDefault(Model,SolutionFunction,void*);
 60: static PetscErrorCode ModelFunctionalRegister(Model,const char*,PetscInt*,FunctionalFunction,void*);
 61: static PetscErrorCode OutputVTK(DM,const char*,PetscViewer*);

 63: struct FieldDescription {
 64:   const char *name;
 65:   PetscInt dof;
 66: };

 68: typedef struct _n_FunctionalLink *FunctionalLink;
 69: struct _n_FunctionalLink {
 70:   char               *name;
 71:   FunctionalFunction func;
 72:   void               *ctx;
 73:   PetscInt           offset;
 74:   FunctionalLink     next;
 75: };

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

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

100: struct _n_User {
101:   PetscInt numSplitFaces;
102:   PetscInt vtkInterval;   /* For monitor */
103:   Model    model;
104: };

106: PETSC_STATIC_INLINE PetscScalar DotDIM(const PetscScalar *x,const PetscScalar *y)
107: {
108:   PetscInt    i;
109:   PetscScalar prod=0.0;

111:   for (i=0; i<DIM; i++) prod += x[i]*y[i];
112:   return prod;
113: }
114: PETSC_STATIC_INLINE PetscReal NormDIM(const PetscScalar *x) { return PetscSqrtReal(PetscAbsScalar(DotDIM(x,x))); }
115: PETSC_STATIC_INLINE void axDIM(const PetscScalar a,PetscScalar *x)
116: {
117:   PetscInt i;
118:   for (i=0; i<DIM; i++) x[i] *= a;
119: }
120: PETSC_STATIC_INLINE void waxDIM(const PetscScalar a,const PetscScalar *x, PetscScalar *w)
121: {
122:   PetscInt i;
123:   for (i=0; i<DIM; i++) w[i] = x[i]*a;
124: }
125: PETSC_STATIC_INLINE void NormalSplitDIM(const PetscReal *n,const PetscScalar *x,PetscScalar *xn,PetscScalar *xt)
126: {                               /* Split x into normal and tangential components */
127:   PetscInt    i;
128:   PetscScalar c;
129:   c = DotDIM(x,n)/DotDIM(n,n);
130:   for (i=0; i<DIM; i++) {
131:     xn[i] = c*n[i];
132:     xt[i] = x[i]-xn[i];
133:   }
134: }

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

142: 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];}
143: 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;}
144: PETSC_STATIC_INLINE PetscReal NormD(PetscInt dim, const PetscScalar *x) {return PetscSqrtReal(PetscAbsScalar(DotD(dim,x,x)));}

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

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

158: typedef struct {
159:   PetscReal wind[DIM];
160: } Physics_Advect_Tilted;
161: typedef struct {
162:   PetscReal         center[DIM];
163:   PetscReal         radius;
164:   AdvectSolBumpType type;
165: } Physics_Advect_Bump;

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

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

183: static PetscErrorCode PhysicsBoundary_Advect_Inflow(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
184: {
185:   Physics        phys    = (Physics)ctx;
186:   Physics_Advect *advect = (Physics_Advect*)phys->data;

189:   xG[0] = advect->inflowState;
190:   return(0);
191: }

195: static PetscErrorCode PhysicsBoundary_Advect_Outflow(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
196: {
198:   xG[0] = xI[0];
199:   return(0);
200: }

204: static void PhysicsRiemann_Advect(PetscInt dim, PetscInt Nf, const PetscReal *qp, const PetscReal *n, const PetscScalar *xL, const PetscScalar *xR, PetscScalar *flux, Physics phys)
205: {
206:   Physics_Advect *advect = (Physics_Advect*)phys->data;
207:   PetscReal      wind[DIM],wn;

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

227: static PetscErrorCode PhysicsSolution_Advect(Model mod,PetscReal time,const PetscReal *x,PetscScalar *u,void *ctx)
228: {
229:   Physics        phys    = (Physics)ctx;
230:   Physics_Advect *advect = (Physics_Advect*)phys->data;

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

266: static PetscErrorCode PhysicsFunctional_Advect(Model mod,PetscReal time,const PetscScalar *x,const PetscScalar *y,PetscReal *f,void *ctx)
267: {
268:   Physics        phys    = (Physics)ctx;
269:   Physics_Advect *advect = (Physics_Advect*)phys->data;
270:   PetscScalar    yexact[1];

274:   PhysicsSolution_Advect(mod,time,x,yexact,phys);
275:   f[advect->functional.Error] = PetscAbsScalar(y[0]-yexact[0]);
276:   return(0);
277: }

281: static PetscErrorCode PhysicsCreate_Advect(DM dm, Model mod,Physics phys,PetscOptions *PetscOptionsObject)
282: {
283:   Physics_Advect *advect;

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

335: /******************* Shallow Water ********************/
336: typedef struct {
337:   PetscReal gravity;
338:   PetscReal boundaryHeight;
339:   struct {
340:     PetscInt Height;
341:     PetscInt Speed;
342:     PetscInt Energy;
343:   } functional;
344: } Physics_SW;
345: typedef struct {
346:   PetscScalar vals[0];
347:   PetscScalar h;
348:   PetscScalar uh[DIM];
349: } SWNode;

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

355: /*
356:  * h_t + div(uh) = 0
357:  * (uh)_t + div (u\otimes uh + g h^2 / 2 I) = 0
358:  *
359:  * */
360: static PetscErrorCode SWFlux(Physics phys,const PetscReal *n,const SWNode *x,SWNode *f)
361: {
362:   Physics_SW  *sw = (Physics_SW*)phys->data;
363:   PetscScalar uhn,u[DIM];
364:   PetscInt    i;

367:   Scale2(1./x->h,x->uh,u);
368:   uhn  = Dot2(x->uh,n);
369:   f->h = uhn;
370:   for (i=0; i<DIM; i++) f->uh[i] = u[i] * uhn + sw->gravity * PetscSqr(x->h) * n[i];
371:   return(0);
372: }

376: static PetscErrorCode PhysicsBoundary_SW_Wall(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
377: {
379:   xG[0] = xI[0];
380:   xG[1] = -xI[1];
381:   xG[2] = -xI[2];
382:   return(0);
383: }

387: static void PhysicsRiemann_SW(PetscInt dim, PetscInt Nf, const PetscReal *qp, const PetscReal *n, const PetscScalar *xL, const PetscScalar *xR, PetscScalar *flux, Physics phys)
388: {
389:   Physics_SW   *sw = (Physics_SW*)phys->data;
390:   PetscReal    cL,cR,speed,nn[DIM];
391:   const SWNode *uL = (const SWNode*)xL,*uR = (const SWNode*)xR;
392:   SWNode       fL,fR;
393:   PetscInt     i;

395:   if (uL->h < 0 || uR->h < 0) {for (i=0; i<1+dim; i++) flux[i] = NAN; return;} /* SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Reconstructed thickness is negative"); */
396:   nn[0] = n[0];
397:   nn[1] = n[1];
398:   Normalize2(nn);
399:   SWFlux(phys,nn,uL,&fL);
400:   SWFlux(phys,nn,uR,&fR);
401:   cL    = PetscSqrtReal(sw->gravity*PetscRealPart(uL->h));
402:   cR    = PetscSqrtReal(sw->gravity*PetscRealPart(uR->h)); /* gravity wave speed */
403:   speed = PetscMax(PetscAbsScalar(Dot2(uL->uh,nn)/uL->h) + cL,PetscAbsScalar(Dot2(uR->uh,nn)/uR->h) + cR);
404:   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);
405: }

409: static PetscErrorCode PhysicsSolution_SW(Model mod,PetscReal time,const PetscReal *x,PetscScalar *u,void *ctx)
410: {
411:   PetscReal dx[2],r,sigma;

414:   if (time != 0.0) SETERRQ1(mod->comm,PETSC_ERR_SUP,"No solution known for time %g",(double)time);
415:   dx[0] = x[0] - 1.5;
416:   dx[1] = x[1] - 1.0;
417:   r     = Norm2(dx);
418:   sigma = 0.5;
419:   u[0]  = 1 + 2*PetscExpScalar(-PetscSqr(r)/(2*PetscSqr(sigma)));
420:   u[1]  = 0.0;
421:   u[2]  = 0.0;
422:   return(0);
423: }

427: static PetscErrorCode PhysicsFunctional_SW(Model mod,PetscReal time,const PetscReal *coord,const PetscScalar *xx,PetscReal *f,void *ctx)
428: {
429:   Physics      phys = (Physics)ctx;
430:   Physics_SW   *sw  = (Physics_SW*)phys->data;
431:   const SWNode *x   = (const SWNode*)xx;
432:   PetscScalar  u[2];
433:   PetscReal    h;

436:   h = PetscRealPart(x->h);
437:   Scale2(1./x->h,x->uh,u);
438:   f[sw->functional.Height] = h;
439:   f[sw->functional.Speed]  = Norm2(u) + PetscSqrtReal(sw->gravity*h);
440:   f[sw->functional.Energy] = 0.5*(Dot2(x->uh,u) + sw->gravity*PetscSqr(h));
441:   return(0);
442: }

446: static PetscErrorCode PhysicsCreate_SW(DM dm, Model mod,Physics phys,PetscOptions *PetscOptionsObject)
447: {
448:   Physics_SW     *sw;

452:   phys->field_desc = PhysicsFields_SW;
453:   phys->riemann = (PetscRiemannFunc) PhysicsRiemann_SW;
454:   PetscNew(&sw);
455:   phys->data    = sw;
456:   PetscOptionsHead(PetscOptionsObject,"SW options");
457:   {
458:     sw->gravity = 1.0;
459:     PetscOptionsReal("-sw_gravity","Gravitational constant","",sw->gravity,&sw->gravity,NULL);
460:   }
461:   PetscOptionsTail();
462:   phys->maxspeed = PetscSqrtReal(2.0*sw->gravity); /* Mach 1 for depth of 2 */

464:   {
465:     const PetscInt wallids[] = {100,101,200,300};
466:     DMPlexAddBoundary(dm, PETSC_TRUE, "wall", "Face Sets", 0, 0, NULL, (void (*)()) PhysicsBoundary_SW_Wall, ALEN(wallids), wallids, phys);
467:     ModelSolutionSetDefault(mod,PhysicsSolution_SW,phys);
468:     ModelFunctionalRegister(mod,"Height",&sw->functional.Height,PhysicsFunctional_SW,phys);
469:     ModelFunctionalRegister(mod,"Speed",&sw->functional.Speed,PhysicsFunctional_SW,phys);
470:     ModelFunctionalRegister(mod,"Energy",&sw->functional.Energy,PhysicsFunctional_SW,phys);
471:   }
472:   return(0);
473: }

475: /******************* Euler ********************/
476: typedef struct {
477:   PetscScalar vals[0];
478:   PetscScalar r;
479:   PetscScalar ru[DIM];
480:   PetscScalar e;
481: } EulerNode;
482: typedef PetscErrorCode (*EquationOfState)(const PetscReal*, const EulerNode*, PetscScalar*);
483: typedef struct {
484:   PetscInt        npars;
485:   PetscReal       pars[DIM];
486:   EquationOfState pressure;
487:   EquationOfState sound;
488:   struct {
489:     PetscInt Density;
490:     PetscInt Momentum;
491:     PetscInt Energy;
492:     PetscInt Pressure;
493:     PetscInt Speed;
494:   } monitor;
495: } Physics_Euler;

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

501: static PetscErrorCode Pressure_PG(const PetscReal *pars,const EulerNode *x,PetscScalar *p)
502: {
503:   PetscScalar ru2;

506:   ru2  = DotDIM(x->ru,x->ru);
507:   ru2 /= x->r;
508:   /* kinematic dof = params[0] */
509:   (*p)=2.0*(x->e-0.5*ru2)/pars[0];
510:   return(0);
511: }

515: static PetscErrorCode SpeedOfSound_PG(const PetscReal *pars,const EulerNode *x,PetscScalar *c)
516: {
517:   PetscScalar p;

520:   /* TODO remove direct usage of Pressure_PG */
521:   Pressure_PG(pars,x,&p);
522:   /* TODO check the sign of p */
523:   /* pars[1] = heat capacity ratio */
524:   (*c)=PetscSqrtScalar(pars[1]*p/x->r);
525:   return(0);
526: }

530: /*
531:  * x = (rho,rho*(u_1),...,rho*e)^T
532:  * x_t+div(f_1(x))+...+div(f_DIM(x)) = 0
533:  *
534:  * f_i(x) = u_i*x+(0,0,...,p,...,p*u_i)^T
535:  *
536:  * */
537: static PetscErrorCode EulerFlux(Physics phys,const PetscReal *n,const EulerNode *x,EulerNode *f)
538: {
539:   Physics_Euler *eu = (Physics_Euler*)phys->data;
540:   PetscScalar   u,nu,p;
541:   PetscInt      i;

544:   u  = DotDIM(x->ru,x->ru);
545:   u /= (x->r * x->r);
546:   nu = DotDIM(x->ru,n);
547:   /* TODO check the sign of p */
548:   eu->pressure(eu->pars,x,&p);
549:   f->r = nu * x->r;
550:   for (i=0; i<DIM; i++) f->ru[i] = nu * x->ru[i] + n[i]*p;
551:   f->e = nu*(x->e+p);
552:   return(0);
553: }

555: /* PetscReal* => EulerNode* conversion */
558: static PetscErrorCode PhysicsBoundary_Euler_Wall(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
559: {
560:   PetscInt    i;
561:   PetscScalar xn[DIM],xt[DIM];

564:   xG[0] = xI[0];
565:   NormalSplitDIM(n,xI+1,xn,xt);
566:   for (i=0; i<DIM; i++) xG[i+1] = -xn[i]+xt[i];
567:   xG[DIM+1] = xI[DIM+1];
568:   return(0);
569: }

571: /* PetscReal* => EulerNode* conversion */
574: static void PhysicsRiemann_Euler_Rusanov(PetscInt dim, PetscInt Nf, const PetscReal *qp, const PetscReal *n, const PetscScalar *xL, const PetscScalar *xR, PetscScalar *flux, Physics phys)
575: {
576:   Physics_Euler   *eu = (Physics_Euler*)phys->data;
577:   PetscScalar     cL,cR,speed;
578:   const EulerNode *uL = (const EulerNode*)xL,*uR = (const EulerNode*)xR;
579:   EulerNode       fL,fR;
580:   PetscInt        i;

582:   if (uL->r < 0 || uR->r < 0) {for (i=0; i<2+dim; i++) flux[i] = NAN; return;} /* SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Reconstructed density is negative"); */
583:   EulerFlux(phys,n,uL,&fL);
584:   EulerFlux(phys,n,uR,&fR);
585:   eu->sound(eu->pars,uL,&cL);
586:   eu->sound(eu->pars,uR,&cR);
587:   speed = PetscMax(cL,cR)+PetscMax(PetscAbsScalar(DotDIM(uL->ru,n)/NormDIM(n)),PetscAbsScalar(DotDIM(uR->ru,n)/NormDIM(n)));
588:   for (i=0; i<2+dim; i++) flux[i] = 0.5*(fL.vals[i]+fR.vals[i])+0.5*speed*(xL[i]-xR[i]);
589: }

593: static PetscErrorCode PhysicsSolution_Euler(Model mod,PetscReal time,const PetscReal *x,PetscScalar *u,void *ctx)
594: {
595:   PetscInt i;

598:   if (time != 0.0) SETERRQ1(mod->comm,PETSC_ERR_SUP,"No solution known for time %g",(double)time);
599:   u[0]     = 1.0;
600:   u[DIM+1] = 1.0+PetscAbsReal(x[0]);
601:   for (i=1; i<DIM+1; i++) u[i] = 0.0;
602:   return(0);
603: }

607: static PetscErrorCode PhysicsFunctional_Euler(Model mod,PetscReal time,const PetscReal *coord,const PetscScalar *xx,PetscReal *f,void *ctx)
608: {
609:   Physics         phys = (Physics)ctx;
610:   Physics_Euler   *eu  = (Physics_Euler*)phys->data;
611:   const EulerNode *x   = (const EulerNode*)xx;
612:   PetscScalar     p;

615:   f[eu->monitor.Density]  = x->r;
616:   f[eu->monitor.Momentum] = NormDIM(x->ru);
617:   f[eu->monitor.Energy]   = x->e;
618:   f[eu->monitor.Speed]    = NormDIM(x->ru)/x->r;
619:   eu->pressure(eu->pars, x, &p);
620:   f[eu->monitor.Pressure] = p;
621:   return(0);
622: }

626: static PetscErrorCode PhysicsCreate_Euler(DM dm, Model mod,Physics phys,PetscOptions *PetscOptionsObject)
627: {
628:   Physics_Euler   *eu;
629:   PetscErrorCode  ierr;

632:   phys->field_desc = PhysicsFields_Euler;
633:   phys->riemann = (PetscRiemannFunc) PhysicsRiemann_Euler_Rusanov;
634:   PetscNew(&eu);
635:   phys->data    = eu;
636:   PetscOptionsHead(PetscOptionsObject,"Euler options");
637:   {
638:     eu->pars[0] = 3.0;
639:     eu->pars[1] = 1.67;
640:     PetscOptionsReal("-eu_f","Degrees of freedom","",eu->pars[0],&eu->pars[0],NULL);
641:     PetscOptionsReal("-eu_gamma","Heat capacity ratio","",eu->pars[1],&eu->pars[1],NULL);
642:   }
643:   PetscOptionsTail();
644:   eu->pressure = Pressure_PG;
645:   eu->sound    = SpeedOfSound_PG;
646:   phys->maxspeed = 1.0;
647:   {
648:     const PetscInt wallids[] = {100,101,200,300};
649:     DMPlexAddBoundary(dm, PETSC_TRUE, "wall", "Face Sets", 0, 0, NULL, (void (*)()) PhysicsBoundary_Euler_Wall, ALEN(wallids), wallids, phys);
650:     ModelSolutionSetDefault(mod,PhysicsSolution_Euler,phys);
651:     ModelFunctionalRegister(mod,"Speed",&eu->monitor.Speed,PhysicsFunctional_Euler,phys);
652:     ModelFunctionalRegister(mod,"Energy",&eu->monitor.Energy,PhysicsFunctional_Euler,phys);
653:     ModelFunctionalRegister(mod,"Density",&eu->monitor.Density,PhysicsFunctional_Euler,phys);
654:     ModelFunctionalRegister(mod,"Momentum",&eu->monitor.Momentum,PhysicsFunctional_Euler,phys);
655:     ModelFunctionalRegister(mod,"Pressure",&eu->monitor.Pressure,PhysicsFunctional_Euler,phys);
656:   }
657:   return(0);
658: }

662: PetscErrorCode ConstructCellBoundary(DM dm, User user)
663: {
664:   const char     *name   = "Cell Sets";
665:   const char     *bdname = "split faces";
666:   IS             regionIS, innerIS;
667:   const PetscInt *regions, *cells;
668:   PetscInt       numRegions, innerRegion, numCells, c;
669:   PetscInt       cStart, cEnd, cEndInterior, fStart, fEnd;
670:   PetscBool      hasLabel;

674:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
675:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
676:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);

678:   DMPlexHasLabel(dm, name, &hasLabel);
679:   if (!hasLabel) return(0);
680:   DMPlexGetLabelSize(dm, name, &numRegions);
681:   if (numRegions != 2) return(0);
682:   /* Get the inner id */
683:   DMPlexGetLabelIdIS(dm, name, &regionIS);
684:   ISGetIndices(regionIS, &regions);
685:   innerRegion = regions[0];
686:   ISRestoreIndices(regionIS, &regions);
687:   ISDestroy(&regionIS);
688:   /* Find the faces between cells in different regions, could call DMPlexCreateNeighborCSR() */
689:   DMPlexGetStratumIS(dm, name, innerRegion, &innerIS);
690:   ISGetLocalSize(innerIS, &numCells);
691:   ISGetIndices(innerIS, &cells);
692:   DMPlexCreateLabel(dm, bdname);
693:   for (c = 0; c < numCells; ++c) {
694:     const PetscInt cell = cells[c];
695:     const PetscInt *faces;
696:     PetscInt       numFaces, f;

698:     if ((cell < cStart) || (cell >= cEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Got invalid point %d which is not a cell", cell);
699:     DMPlexGetConeSize(dm, cell, &numFaces);
700:     DMPlexGetCone(dm, cell, &faces);
701:     for (f = 0; f < numFaces; ++f) {
702:       const PetscInt face = faces[f];
703:       const PetscInt *neighbors;
704:       PetscInt       nC, regionA, regionB;

706:       if ((face < fStart) || (face >= fEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Got invalid point %d which is not a face", face);
707:       DMPlexGetSupportSize(dm, face, &nC);
708:       if (nC != 2) continue;
709:       DMPlexGetSupport(dm, face, &neighbors);
710:       if ((neighbors[0] >= cEndInterior) || (neighbors[1] >= cEndInterior)) continue;
711:       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]);
712:       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]);
713:       DMPlexGetLabelValue(dm, name, neighbors[0], &regionA);
714:       DMPlexGetLabelValue(dm, name, neighbors[1], &regionB);
715:       if (regionA < 0) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Invalid label %s: Cell %d has no value", name, neighbors[0]);
716:       if (regionB < 0) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Invalid label %s: Cell %d has no value", name, neighbors[1]);
717:       if (regionA != regionB) {
718:         DMPlexSetLabelValue(dm, bdname, faces[f], 1);
719:       }
720:     }
721:   }
722:   ISRestoreIndices(innerIS, &cells);
723:   ISDestroy(&innerIS);
724:   {
725:     DMLabel label;

727:     PetscViewerASCIISynchronizedAllow(PETSC_VIEWER_STDOUT_WORLD, PETSC_TRUE);
728:     DMPlexGetLabel(dm, bdname, &label);
729:     DMLabelView(label, PETSC_VIEWER_STDOUT_WORLD);
730:   }
731:   return(0);
732: }

736: /* Right now, I have just added duplicate faces, which see both cells. We can
737: - Add duplicate vertices and decouple the face cones
738: - Disconnect faces from cells across the rotation gap
739: */
740: PetscErrorCode SplitFaces(DM *dmSplit, const char labelName[], User user)
741: {
742:   DM             dm = *dmSplit, sdm;
743:   PetscSF        sfPoint, gsfPoint;
744:   PetscSection   coordSection, newCoordSection;
745:   Vec            coordinates;
746:   IS             idIS;
747:   const PetscInt *ids;
748:   PetscInt       *newpoints;
749:   PetscInt       dim, depth, maxConeSize, maxSupportSize, numLabels, numGhostCells;
750:   PetscInt       numFS, fs, pStart, pEnd, p, cEnd, cEndInterior, vStart, vEnd, v, fStart, fEnd, newf, d, l;
751:   PetscBool      hasLabel;

755:   DMPlexHasLabel(dm, labelName, &hasLabel);
756:   if (!hasLabel) return(0);
757:   DMCreate(PetscObjectComm((PetscObject)dm), &sdm);
758:   DMSetType(sdm, DMPLEX);
759:   DMGetDimension(dm, &dim);
760:   DMSetDimension(sdm, dim);

762:   DMPlexGetLabelIdIS(dm, labelName, &idIS);
763:   ISGetLocalSize(idIS, &numFS);
764:   ISGetIndices(idIS, &ids);

766:   user->numSplitFaces = 0;
767:   for (fs = 0; fs < numFS; ++fs) {
768:     PetscInt numBdFaces;

770:     DMPlexGetStratumSize(dm, labelName, ids[fs], &numBdFaces);
771:     user->numSplitFaces += numBdFaces;
772:   }
773:   DMPlexGetChart(dm, &pStart, &pEnd);
774:   pEnd += user->numSplitFaces;
775:   DMPlexSetChart(sdm, pStart, pEnd);
776:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
777:   DMPlexSetHybridBounds(sdm, cEndInterior, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_DETERMINE);
778:   DMPlexGetHeightStratum(dm, 0, NULL, &cEnd);
779:   numGhostCells = cEnd - cEndInterior;
780:   /* Set cone and support sizes */
781:   DMPlexGetDepth(dm, &depth);
782:   for (d = 0; d <= depth; ++d) {
783:     DMPlexGetDepthStratum(dm, d, &pStart, &pEnd);
784:     for (p = pStart; p < pEnd; ++p) {
785:       PetscInt newp = p;
786:       PetscInt size;

788:       DMPlexGetConeSize(dm, p, &size);
789:       DMPlexSetConeSize(sdm, newp, size);
790:       DMPlexGetSupportSize(dm, p, &size);
791:       DMPlexSetSupportSize(sdm, newp, size);
792:     }
793:   }
794:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
795:   for (fs = 0, newf = fEnd; fs < numFS; ++fs) {
796:     IS             faceIS;
797:     const PetscInt *faces;
798:     PetscInt       numFaces, f;

800:     DMPlexGetStratumIS(dm, labelName, ids[fs], &faceIS);
801:     ISGetLocalSize(faceIS, &numFaces);
802:     ISGetIndices(faceIS, &faces);
803:     for (f = 0; f < numFaces; ++f, ++newf) {
804:       PetscInt size;

806:       /* Right now I think that both faces should see both cells */
807:       DMPlexGetConeSize(dm, faces[f], &size);
808:       DMPlexSetConeSize(sdm, newf, size);
809:       DMPlexGetSupportSize(dm, faces[f], &size);
810:       DMPlexSetSupportSize(sdm, newf, size);
811:     }
812:     ISRestoreIndices(faceIS, &faces);
813:     ISDestroy(&faceIS);
814:   }
815:   DMSetUp(sdm);
816:   /* Set cones and supports */
817:   DMPlexGetMaxSizes(dm, &maxConeSize, &maxSupportSize);
818:   PetscMalloc(PetscMax(maxConeSize, maxSupportSize) * sizeof(PetscInt), &newpoints);
819:   DMPlexGetChart(dm, &pStart, &pEnd);
820:   for (p = pStart; p < pEnd; ++p) {
821:     const PetscInt *points, *orientations;
822:     PetscInt       size, i, newp = p;

824:     DMPlexGetConeSize(dm, p, &size);
825:     DMPlexGetCone(dm, p, &points);
826:     DMPlexGetConeOrientation(dm, p, &orientations);
827:     for (i = 0; i < size; ++i) newpoints[i] = points[i];
828:     DMPlexSetCone(sdm, newp, newpoints);
829:     DMPlexSetConeOrientation(sdm, newp, orientations);
830:     DMPlexGetSupportSize(dm, p, &size);
831:     DMPlexGetSupport(dm, p, &points);
832:     for (i = 0; i < size; ++i) newpoints[i] = points[i];
833:     DMPlexSetSupport(sdm, newp, newpoints);
834:   }
835:   PetscFree(newpoints);
836:   for (fs = 0, newf = fEnd; fs < numFS; ++fs) {
837:     IS             faceIS;
838:     const PetscInt *faces;
839:     PetscInt       numFaces, f;

841:     DMPlexGetStratumIS(dm, labelName, ids[fs], &faceIS);
842:     ISGetLocalSize(faceIS, &numFaces);
843:     ISGetIndices(faceIS, &faces);
844:     for (f = 0; f < numFaces; ++f, ++newf) {
845:       const PetscInt *points;

847:       DMPlexGetCone(dm, faces[f], &points);
848:       DMPlexSetCone(sdm, newf, points);
849:       DMPlexGetSupport(dm, faces[f], &points);
850:       DMPlexSetSupport(sdm, newf, points);
851:     }
852:     ISRestoreIndices(faceIS, &faces);
853:     ISDestroy(&faceIS);
854:   }
855:   ISRestoreIndices(idIS, &ids);
856:   ISDestroy(&idIS);
857:   DMPlexStratify(sdm);
858:   /* Convert coordinates */
859:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
860:   DMGetCoordinateSection(dm, &coordSection);
861:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &newCoordSection);
862:   PetscSectionSetNumFields(newCoordSection, 1);
863:   PetscSectionSetFieldComponents(newCoordSection, 0, dim);
864:   PetscSectionSetChart(newCoordSection, vStart, vEnd);
865:   for (v = vStart; v < vEnd; ++v) {
866:     PetscSectionSetDof(newCoordSection, v, dim);
867:     PetscSectionSetFieldDof(newCoordSection, v, 0, dim);
868:   }
869:   PetscSectionSetUp(newCoordSection);
870:   DMSetCoordinateSection(sdm, PETSC_DETERMINE, newCoordSection);
871:   PetscSectionDestroy(&newCoordSection); /* relinquish our reference */
872:   DMGetCoordinatesLocal(dm, &coordinates);
873:   DMSetCoordinatesLocal(sdm, coordinates);
874:   /* Convert labels */
875:   DMPlexGetNumLabels(dm, &numLabels);
876:   for (l = 0; l < numLabels; ++l) {
877:     const char *lname;
878:     PetscBool  isDepth;

880:     DMPlexGetLabelName(dm, l, &lname);
881:     PetscStrcmp(lname, "depth", &isDepth);
882:     if (isDepth) continue;
883:     DMPlexCreateLabel(sdm, lname);
884:     DMPlexGetLabelIdIS(dm, lname, &idIS);
885:     ISGetLocalSize(idIS, &numFS);
886:     ISGetIndices(idIS, &ids);
887:     for (fs = 0; fs < numFS; ++fs) {
888:       IS             pointIS;
889:       const PetscInt *points;
890:       PetscInt       numPoints;

892:       DMPlexGetStratumIS(dm, lname, ids[fs], &pointIS);
893:       ISGetLocalSize(pointIS, &numPoints);
894:       ISGetIndices(pointIS, &points);
895:       for (p = 0; p < numPoints; ++p) {
896:         PetscInt newpoint = points[p];

898:         DMPlexSetLabelValue(sdm, lname, newpoint, ids[fs]);
899:       }
900:       ISRestoreIndices(pointIS, &points);
901:       ISDestroy(&pointIS);
902:     }
903:     ISRestoreIndices(idIS, &ids);
904:     ISDestroy(&idIS);
905:   }
906:   /* Convert pointSF */
907:   const PetscSFNode *remotePoints;
908:   PetscSFNode       *gremotePoints;
909:   const PetscInt    *localPoints;
910:   PetscInt          *glocalPoints,*newLocation,*newRemoteLocation;
911:   PetscInt          numRoots, numLeaves;
912:   PetscMPIInt       numProcs;

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

941: PetscErrorCode CreatePartitionVec(DM dm, DM *dmCell, Vec *partition)
942: {
943:   PetscSF        sfPoint;
944:   PetscSection   coordSection;
945:   Vec            coordinates;
946:   PetscSection   sectionCell;
947:   PetscScalar    *part;
948:   PetscInt       cStart, cEnd, c;
949:   PetscMPIInt    rank;

953:   DMGetCoordinateSection(dm, &coordSection);
954:   DMGetCoordinatesLocal(dm, &coordinates);
955:   DMClone(dm, dmCell);
956:   DMGetPointSF(dm, &sfPoint);
957:   DMSetPointSF(*dmCell, sfPoint);
958:   DMSetCoordinateSection(*dmCell, PETSC_DETERMINE, coordSection);
959:   DMSetCoordinatesLocal(*dmCell, coordinates);
960:   MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);
961:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionCell);
962:   DMPlexGetHeightStratum(*dmCell, 0, &cStart, &cEnd);
963:   PetscSectionSetChart(sectionCell, cStart, cEnd);
964:   for (c = cStart; c < cEnd; ++c) {
965:     PetscSectionSetDof(sectionCell, c, 1);
966:   }
967:   PetscSectionSetUp(sectionCell);
968:   DMSetDefaultSection(*dmCell, sectionCell);
969:   PetscSectionDestroy(&sectionCell);
970:   DMCreateLocalVector(*dmCell, partition);
971:   PetscObjectSetName((PetscObject)*partition, "partition");
972:   VecGetArray(*partition, &part);
973:   for (c = cStart; c < cEnd; ++c) {
974:     PetscScalar *p;

976:     DMPlexPointLocalRef(*dmCell, c, part, &p);
977:     p[0] = rank;
978:   }
979:   VecRestoreArray(*partition, &part);
980:   return(0);
981: }

985: PetscErrorCode CreateMassMatrix(DM dm, Vec *massMatrix, User user)
986: {
987:   DM                dmMass, dmFace, dmCell, dmCoord;
988:   PetscSection      coordSection;
989:   Vec               coordinates, facegeom, cellgeom;
990:   PetscSection      sectionMass;
991:   PetscScalar       *m;
992:   const PetscScalar *fgeom, *cgeom, *coords;
993:   PetscInt          vStart, vEnd, v;
994:   PetscErrorCode    ierr;

997:   DMGetCoordinateSection(dm, &coordSection);
998:   DMGetCoordinatesLocal(dm, &coordinates);
999:   DMClone(dm, &dmMass);
1000:   DMSetCoordinateSection(dmMass, PETSC_DETERMINE, coordSection);
1001:   DMSetCoordinatesLocal(dmMass, coordinates);
1002:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionMass);
1003:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
1004:   PetscSectionSetChart(sectionMass, vStart, vEnd);
1005:   for (v = vStart; v < vEnd; ++v) {
1006:     PetscInt numFaces;

1008:     DMPlexGetSupportSize(dmMass, v, &numFaces);
1009:     PetscSectionSetDof(sectionMass, v, numFaces*numFaces);
1010:   }
1011:   PetscSectionSetUp(sectionMass);
1012:   DMSetDefaultSection(dmMass, sectionMass);
1013:   PetscSectionDestroy(&sectionMass);
1014:   DMGetLocalVector(dmMass, massMatrix);
1015:   VecGetArray(*massMatrix, &m);
1016:   DMPlexTSGetGeometryFVM(dm, &facegeom, &cellgeom, NULL);
1017:   VecGetDM(facegeom, &dmFace);
1018:   VecGetArrayRead(facegeom, &fgeom);
1019:   VecGetDM(cellgeom, &dmCell);
1020:   VecGetArrayRead(cellgeom, &cgeom);
1021:   DMGetCoordinateDM(dm, &dmCoord);
1022:   VecGetArrayRead(coordinates, &coords);
1023:   for (v = vStart; v < vEnd; ++v) {
1024:     const PetscInt        *faces;
1025:     const PetscFVFaceGeom *fgA, *fgB, *cg;
1026:     const PetscScalar     *vertex;
1027:     PetscInt               numFaces, sides[2], f, g;

1029:     DMPlexPointLocalRead(dmCoord, v, coords, &vertex);
1030:     DMPlexGetSupportSize(dmMass, v, &numFaces);
1031:     DMPlexGetSupport(dmMass, v, &faces);
1032:     for (f = 0; f < numFaces; ++f) {
1033:       sides[0] = faces[f];
1034:       DMPlexPointLocalRead(dmFace, faces[f], fgeom, &fgA);
1035:       for (g = 0; g < numFaces; ++g) {
1036:         const PetscInt *cells = NULL;;
1037:         PetscReal      area   = 0.0;
1038:         PetscInt       numCells;

1040:         sides[1] = faces[g];
1041:         DMPlexPointLocalRead(dmFace, faces[g], fgeom, &fgB);
1042:         DMPlexGetJoin(dmMass, 2, sides, &numCells, &cells);
1043:         if (numCells != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Invalid join for faces");
1044:         DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cg);
1045:         area += PetscAbsScalar((vertex[0] - cg->centroid[0])*(fgA->centroid[1] - cg->centroid[1]) - (vertex[1] - cg->centroid[1])*(fgA->centroid[0] - cg->centroid[0]));
1046:         area += PetscAbsScalar((vertex[0] - cg->centroid[0])*(fgB->centroid[1] - cg->centroid[1]) - (vertex[1] - cg->centroid[1])*(fgB->centroid[0] - cg->centroid[0]));
1047:         m[f*numFaces+g] = Dot2(fgA->normal, fgB->normal)*area*0.5;
1048:         DMPlexRestoreJoin(dmMass, 2, sides, &numCells, &cells);
1049:       }
1050:     }
1051:   }
1052:   VecRestoreArrayRead(facegeom, &fgeom);
1053:   VecRestoreArrayRead(cellgeom, &cgeom);
1054:   VecRestoreArrayRead(coordinates, &coords);
1055:   VecRestoreArray(*massMatrix, &m);
1056:   DMDestroy(&dmMass);
1057:   return(0);
1058: }

1062: /* Behavior will be different for multi-physics or when using non-default boundary conditions */
1063: static PetscErrorCode ModelSolutionSetDefault(Model mod,SolutionFunction func,void *ctx)
1064: {
1066:   mod->solution    = func;
1067:   mod->solutionctx = ctx;
1068:   return(0);
1069: }

1073: static PetscErrorCode ModelFunctionalRegister(Model mod,const char *name,PetscInt *offset,FunctionalFunction func,void *ctx)
1074: {
1076:   FunctionalLink link,*ptr;
1077:   PetscInt       lastoffset = -1;

1080:   for (ptr=&mod->functionalRegistry; *ptr; ptr = &(*ptr)->next) lastoffset = (*ptr)->offset;
1081:   PetscNew(&link);
1082:   PetscStrallocpy(name,&link->name);
1083:   link->offset = lastoffset + 1;
1084:   link->func   = func;
1085:   link->ctx    = ctx;
1086:   link->next   = NULL;
1087:   *ptr         = link;
1088:   *offset      = link->offset;
1089:   return(0);
1090: }

1094: static PetscErrorCode ModelFunctionalSetFromOptions(Model mod,PetscOptions *PetscOptionsObject)
1095: {
1097:   PetscInt       i,j;
1098:   FunctionalLink link;
1099:   char           *names[256];

1102:   mod->numMonitored = ALEN(names);
1103:   PetscOptionsStringArray("-monitor","list of functionals to monitor","",names,&mod->numMonitored,NULL);
1104:   /* Create list of functionals that will be computed somehow */
1105:   PetscMalloc1(mod->numMonitored,&mod->functionalMonitored);
1106:   /* Create index of calls that we will have to make to compute these functionals (over-allocation in general). */
1107:   PetscMalloc1(mod->numMonitored,&mod->functionalCall);
1108:   mod->numCall = 0;
1109:   for (i=0; i<mod->numMonitored; i++) {
1110:     for (link=mod->functionalRegistry; link; link=link->next) {
1111:       PetscBool match;
1112:       PetscStrcasecmp(names[i],link->name,&match);
1113:       if (match) break;
1114:     }
1115:     if (!link) SETERRQ1(mod->comm,PETSC_ERR_USER,"No known functional '%s'",names[i]);
1116:     mod->functionalMonitored[i] = link;
1117:     for (j=0; j<i; j++) {
1118:       if (mod->functionalCall[j]->func == link->func && mod->functionalCall[j]->ctx == link->ctx) goto next_name;
1119:     }
1120:     mod->functionalCall[mod->numCall++] = link; /* Just points to the first link using the result. There may be more results. */
1121: next_name:
1122:     PetscFree(names[i]);
1123:   }

1125:   /* Find out the maximum index of any functional computed by a function we will be calling (even if we are not using it) */
1126:   mod->maxComputed = -1;
1127:   for (link=mod->functionalRegistry; link; link=link->next) {
1128:     for (i=0; i<mod->numCall; i++) {
1129:       FunctionalLink call = mod->functionalCall[i];
1130:       if (link->func == call->func && link->ctx == call->ctx) {
1131:         mod->maxComputed = PetscMax(mod->maxComputed,link->offset);
1132:       }
1133:     }
1134:   }
1135:   return(0);
1136: }

1140: static PetscErrorCode FunctionalLinkDestroy(FunctionalLink *link)
1141: {
1143:   FunctionalLink l,next;

1146:   if (!link) return(0);
1147:   l     = *link;
1148:   *link = NULL;
1149:   for (; l; l=next) {
1150:     next = l->next;
1151:     PetscFree(l->name);
1152:     PetscFree(l);
1153:   }
1154:   return(0);
1155: }

1159: PetscErrorCode SetInitialCondition(DM dm, Vec X, User user)
1160: {
1161:   DM                 dmCell;
1162:   Model              mod = user->model;
1163:   Vec                cellgeom;
1164:   const PetscScalar *cgeom;
1165:   PetscScalar       *x;
1166:   PetscInt           cStart, cEnd, cEndInterior, c;
1167:   PetscErrorCode     ierr;

1170:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
1171:   DMPlexTSGetGeometryFVM(dm, NULL, &cellgeom, NULL);
1172:   VecGetDM(cellgeom, &dmCell);
1173:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
1174:   VecGetArrayRead(cellgeom, &cgeom);
1175:   VecGetArray(X, &x);
1176:   for (c = cStart; c < cEndInterior; ++c) {
1177:     const PetscFVCellGeom *cg;
1178:     PetscScalar           *xc;

1180:     DMPlexPointLocalRead(dmCell,c,cgeom,&cg);
1181:     DMPlexPointGlobalRef(dm,c,x,&xc);
1182:     if (xc) {(*mod->solution)(mod,0.0,cg->centroid,xc,mod->solutionctx);}
1183:   }
1184:   VecRestoreArrayRead(cellgeom, &cgeom);
1185:   VecRestoreArray(X, &x);
1186:   return(0);
1187: }

1191: static PetscErrorCode OutputVTK(DM dm, const char *filename, PetscViewer *viewer)
1192: {

1196:   PetscViewerCreate(PetscObjectComm((PetscObject)dm), viewer);
1197:   PetscViewerSetType(*viewer, PETSCVIEWERVTK);
1198:   PetscViewerFileSetName(*viewer, filename);
1199:   return(0);
1200: }

1204: static PetscErrorCode MonitorVTK(TS ts,PetscInt stepnum,PetscReal time,Vec X,void *ctx)
1205: {
1206:   User           user = (User)ctx;
1207:   DM             dm;
1208:   Vec            cellgeom;
1209:   PetscViewer    viewer;
1210:   char           filename[PETSC_MAX_PATH_LEN],*ftable = NULL;
1211:   PetscReal      xnorm;
1212:   PetscInt       cEndInterior;

1216:   PetscObjectSetName((PetscObject) X, "solution");
1217:   VecGetDM(X,&dm);
1218:   DMPlexTSGetGeometryFVM(dm, NULL, &cellgeom, NULL);
1219:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
1220:   VecNorm(X,NORM_INFINITY,&xnorm);
1221:   if (stepnum >= 0) {           /* No summary for final time */
1222:     Model             mod = user->model;
1223:     PetscInt          c,cStart,cEnd,fcount,i;
1224:     size_t            ftableused,ftablealloc;
1225:     const PetscScalar *cgeom,*x;
1226:     DM                dmCell;
1227:     PetscReal         *fmin,*fmax,*fintegral,*ftmp;
1228:     fcount = mod->maxComputed+1;
1229:     PetscMalloc4(fcount,&fmin,fcount,&fmax,fcount,&fintegral,fcount,&ftmp);
1230:     for (i=0; i<fcount; i++) {
1231:       fmin[i]      = PETSC_MAX_REAL;
1232:       fmax[i]      = PETSC_MIN_REAL;
1233:       fintegral[i] = 0;
1234:     }
1235:     DMPlexGetHeightStratum(dm,0,&cStart,&cEnd);
1236:     VecGetDM(cellgeom,&dmCell);
1237:     VecGetArrayRead(cellgeom,&cgeom);
1238:     VecGetArrayRead(X,&x);
1239:     for (c = cStart; c < cEndInterior; ++c) {
1240:       const PetscFVCellGeom *cg;
1241:       const PetscScalar     *cx;
1242:       DMPlexPointLocalRead(dmCell,c,cgeom,&cg);
1243:       DMPlexPointGlobalRead(dm,c,x,&cx);
1244:       if (!cx) continue;        /* not a global cell */
1245:       for (i=0; i<mod->numCall; i++) {
1246:         FunctionalLink flink = mod->functionalCall[i];
1247:         (*flink->func)(mod,time,cg->centroid,cx,ftmp,flink->ctx);
1248:       }
1249:       for (i=0; i<fcount; i++) {
1250:         fmin[i]       = PetscMin(fmin[i],ftmp[i]);
1251:         fmax[i]       = PetscMax(fmax[i],ftmp[i]);
1252:         fintegral[i] += cg->volume * ftmp[i];
1253:       }
1254:     }
1255:     VecRestoreArrayRead(cellgeom,&cgeom);
1256:     VecRestoreArrayRead(X,&x);
1257:     MPI_Allreduce(MPI_IN_PLACE,fmin,fcount,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)ts));
1258:     MPI_Allreduce(MPI_IN_PLACE,fmax,fcount,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
1259:     MPI_Allreduce(MPI_IN_PLACE,fintegral,fcount,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));

1261:     ftablealloc = fcount * 100;
1262:     ftableused  = 0;
1263:     PetscMalloc1(ftablealloc,&ftable);
1264:     for (i=0; i<mod->numMonitored; i++) {
1265:       size_t         countused;
1266:       char           buffer[256],*p;
1267:       FunctionalLink flink = mod->functionalMonitored[i];
1268:       PetscInt       id    = flink->offset;
1269:       if (i % 3) {
1270:         PetscMemcpy(buffer,"  ",2);
1271:         p    = buffer + 2;
1272:       } else if (i) {
1273:         char newline[] = "\n";
1274:         PetscMemcpy(buffer,newline,sizeof newline-1);
1275:         p    = buffer + sizeof newline - 1;
1276:       } else {
1277:         p = buffer;
1278:       }
1279:       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]);
1280:       countused += p - buffer;
1281:       if (countused > ftablealloc-ftableused-1) { /* reallocate */
1282:         char *ftablenew;
1283:         ftablealloc = 2*ftablealloc + countused;
1284:         PetscMalloc(ftablealloc,&ftablenew);
1285:         PetscMemcpy(ftablenew,ftable,ftableused);
1286:         PetscFree(ftable);
1287:         ftable = ftablenew;
1288:       }
1289:       PetscMemcpy(ftable+ftableused,buffer,countused);
1290:       ftableused += countused;
1291:       ftable[ftableused] = 0;
1292:     }
1293:     PetscFree4(fmin,fmax,fintegral,ftmp);

1295:     PetscPrintf(PetscObjectComm((PetscObject)ts),"% 3D  time %8.4g  |x| %8.4g  %s\n",stepnum,(double)time,(double)xnorm,ftable ? ftable : "");
1296:     PetscFree(ftable);
1297:   }
1298:   if (user->vtkInterval < 1) return(0);
1299:   if ((stepnum == -1) ^ (stepnum % user->vtkInterval == 0)) {
1300:     if (stepnum == -1) {        /* Final time is not multiple of normal time interval, write it anyway */
1301:       TSGetTimeStepNumber(ts,&stepnum);
1302:     }
1303:     PetscSNPrintf(filename,sizeof filename,"ex11-%03D.vtu",stepnum);
1304:     OutputVTK(dm,filename,&viewer);
1305:     VecView(X,viewer);
1306:     PetscViewerDestroy(&viewer);
1307:   }
1308:   return(0);
1309: }

1313: int main(int argc, char **argv)
1314: {
1315:   MPI_Comm          comm;
1316:   PetscDS           prob;
1317:   PetscFV           fvm;
1318:   User              user;
1319:   Model             mod;
1320:   Physics           phys;
1321:   DM                dm;
1322:   PetscReal         ftime, cfl, dt, minRadius;
1323:   PetscInt          dim, nsteps;
1324:   TS                ts;
1325:   TSConvergedReason reason;
1326:   Vec               X;
1327:   PetscViewer       viewer;
1328:   PetscBool         vtkCellGeom, splitFaces;
1329:   PetscInt          overlap;
1330:   char              filename[PETSC_MAX_PATH_LEN] = "sevenside.exo";
1331:   PetscErrorCode    ierr;

1333:   PetscInitialize(&argc, &argv, (char*) 0, help);
1334:   comm = PETSC_COMM_WORLD;

1336:   PetscNew(&user);
1337:   PetscNew(&user->model);
1338:   PetscNew(&user->model->physics);
1339:   mod  = user->model;
1340:   phys = mod->physics;
1341:   mod->comm = comm;

1343:   /* Register physical models to be available on the command line */
1344:   PetscFunctionListAdd(&PhysicsList,"advect"          ,PhysicsCreate_Advect);
1345:   PetscFunctionListAdd(&PhysicsList,"sw"              ,PhysicsCreate_SW);
1346:   PetscFunctionListAdd(&PhysicsList,"euler"           ,PhysicsCreate_Euler);


1349:   PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Mesh Options","");
1350:   {
1351:     cfl  = 0.9 * 4; /* default SSPRKS2 with s=5 stages is stable for CFL number s-1 */
1352:     PetscOptionsReal("-ufv_cfl","CFL number per step","",cfl,&cfl,NULL);
1353:     PetscOptionsString("-f","Exodus.II filename to read","",filename,filename,sizeof(filename),NULL);
1354:     splitFaces = PETSC_FALSE;
1355:     PetscOptionsBool("-ufv_split_faces","Split faces between cell sets","",splitFaces,&splitFaces,NULL);
1356:     overlap = 1;
1357:     PetscOptionsInt("-ufv_mesh_overlap","Number of cells to overlap partitions","",overlap,&overlap,NULL);
1358:     user->vtkInterval = 1;
1359:     PetscOptionsInt("-ufv_vtk_interval","VTK output interval (0 to disable)","",user->vtkInterval,&user->vtkInterval,NULL);
1360:     vtkCellGeom = PETSC_FALSE;
1361:     PetscOptionsBool("-ufv_vtk_cellgeom","Write cell geometry (for debugging)","",vtkCellGeom,&vtkCellGeom,NULL);
1362:   }
1363:   PetscOptionsEnd();
1364:   DMPlexCreateFromFile(comm, filename, PETSC_TRUE, &dm);
1365:   DMViewFromOptions(dm, NULL, "-dm_view");
1366:   DMGetDimension(dm, &dim);

1368:   PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Physics Options","");
1369:   {
1370:     PetscErrorCode (*physcreate)(DM,Model,Physics,PetscOptions*);
1371:     char             physname[256]  = "advect";

1373:     DMPlexCreateLabel(dm, "Face Sets");
1374:     PetscOptionsFList("-physics","Physics module to solve","",PhysicsList,physname,physname,sizeof physname,NULL);
1375:     PetscFunctionListFind(PhysicsList,physname,&physcreate);
1376:     PetscMemzero(phys,sizeof(struct _n_Physics));
1377:     (*physcreate)(dm,mod,phys,PetscOptionsObject);
1378:     mod->maxspeed = phys->maxspeed;
1379:     /* Count number of fields and dofs */
1380:     for (phys->nfields=0,phys->dof=0; phys->field_desc[phys->nfields].name; phys->nfields++) phys->dof += phys->field_desc[phys->nfields].dof;

1382:     if (mod->maxspeed <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set maxspeed",physname);
1383:     if (phys->dof <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set dof",physname);
1384:     ModelFunctionalSetFromOptions(mod,PetscOptionsObject);
1385:   }
1386:   PetscOptionsEnd();
1387:   {
1388:     DM dmDist;

1390:     DMPlexSetAdjacencyUseCone(dm, PETSC_TRUE);
1391:     DMPlexSetAdjacencyUseClosure(dm, PETSC_FALSE);
1392:     DMPlexDistribute(dm, overlap, NULL, &dmDist);
1393:     if (dmDist) {
1394:       DMDestroy(&dm);
1395:       dm   = dmDist;
1396:     }
1397:   }
1398:   DMSetFromOptions(dm);
1399:   {
1400:     DM gdm;

1402:     DMPlexConstructGhostCells(dm, NULL, NULL, &gdm);
1403:     DMDestroy(&dm);
1404:     dm   = gdm;
1405:     DMViewFromOptions(dm, NULL, "-dm_view");
1406:   }
1407:   if (splitFaces) {ConstructCellBoundary(dm, user);}
1408:   SplitFaces(&dm, "split faces", user);

1410:   PetscFVCreate(comm, &fvm);
1411:   PetscFVSetFromOptions(fvm);
1412:   PetscFVSetNumComponents(fvm, phys->dof);
1413:   PetscFVSetSpatialDimension(fvm, dim);
1414:   DMGetDS(dm, &prob);
1415:   /* FV is now structured with one field having all physics as components */
1416:   PetscDSAddDiscretization(prob, (PetscObject) fvm);
1417:   PetscDSSetRiemannSolver(prob, 0, user->model->physics->riemann);
1418:   PetscDSSetContext(prob, 0, user->model->physics);

1420:   TSCreate(comm, &ts);
1421:   TSSetType(ts, TSSSP);
1422:   TSSetDM(ts, dm);
1423:   TSMonitorSet(ts,MonitorVTK,user,NULL);
1424:   DMTSSetRHSFunctionLocal(dm, DMPlexTSComputeRHSFunctionFVM, user);

1426:   DMCreateGlobalVector(dm, &X);
1427:   PetscObjectSetName((PetscObject) X, "solution");
1428:   SetInitialCondition(dm, X, user);
1429:   if (vtkCellGeom) {
1430:     DM  dmCell;
1431:     Vec cellgeom, partition;

1433:     DMPlexTSGetGeometryFVM(dm, NULL, &cellgeom, NULL);
1434:     OutputVTK(dm, "ex11-cellgeom.vtk", &viewer);
1435:     VecView(cellgeom, viewer);
1436:     PetscViewerDestroy(&viewer);
1437:     CreatePartitionVec(dm, &dmCell, &partition);
1438:     OutputVTK(dmCell, "ex11-partition.vtk", &viewer);
1439:     VecView(partition, viewer);
1440:     PetscViewerDestroy(&viewer);
1441:     VecDestroy(&partition);
1442:     DMDestroy(&dmCell);
1443:   }

1445:   DMPlexTSGetGeometryFVM(dm, NULL, NULL, &minRadius);
1446:   TSSetDuration(ts,1000,2.0);
1447:   dt   = cfl * minRadius / user->model->maxspeed;
1448:   TSSetInitialTimeStep(ts,0.0,dt);
1449:   TSSetFromOptions(ts);
1450:   TSSolve(ts,X);
1451:   TSGetSolveTime(ts,&ftime);
1452:   TSGetTimeStepNumber(ts,&nsteps);
1453:   TSGetConvergedReason(ts,&reason);
1454:   PetscPrintf(PETSC_COMM_WORLD,"%s at time %g after %D steps\n",TSConvergedReasons[reason],(double)ftime,nsteps);
1455:   TSDestroy(&ts);

1457:   PetscFunctionListDestroy(&PhysicsList);
1458:   FunctionalLinkDestroy(&user->model->functionalRegistry);
1459:   PetscFree(user->model->functionalMonitored);
1460:   PetscFree(user->model->functionalCall);
1461:   PetscFree(user->model->physics->data);
1462:   PetscFree(user->model->physics);
1463:   PetscFree(user->model);
1464:   PetscFree(user);
1465:   VecDestroy(&X);
1466:   PetscFVDestroy(&fvm);
1467:   DMDestroy(&dm);
1468:   PetscFinalize();
1469:   return(0);
1470: }