1: static char help[] = "Second Order TVD Finite Volume Example.\n";

 37:  #include <petscdmplex.h>
 38:  #include <petscdmforest.h>
 39:  #include <petscds.h>
 40:  #include <petscts.h>
 41: #include <petscsf.h> /* For SplitFaces() */

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

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

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

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

 88: struct _n_Model {
 89:   MPI_Comm         comm;        /* Does not do collective communicaton, but some error conditions can be collective */
 90:   Physics          physics;
 91:   FunctionalLink   functionalRegistry;
 92:   PetscInt         maxComputed;
 93:   PetscInt         numMonitored;
 94:   FunctionalLink   *functionalMonitored;
 95:   PetscInt         numCall;
 96:   FunctionalLink   *functionalCall;
 97:   SolutionFunction solution;
 98:   SetUpBCFunction  setupbc;
 99:   void             *solutionctx;
100:   PetscReal        maxspeed;    /* estimate of global maximum speed (for CFL calculation) */
101:   PetscReal        bounds[2*DIM];
102:   DMBoundaryType   bcs[3];
103:   PetscErrorCode   (*errorIndicator)(PetscInt, PetscReal, PetscInt, const PetscScalar[], const PetscScalar[], PetscReal *, void *);
104:   void             *errorCtx;
105: };

107: struct _n_User {
108:   PetscInt numSplitFaces;
109:   PetscInt vtkInterval;   /* For monitor */
110:   char outputBasename[PETSC_MAX_PATH_LEN]; /* Basename for output files */
111:   PetscInt monitorStepOffset;
112:   Model    model;
113: };

115: PETSC_STATIC_INLINE PetscReal DotDIMReal(const PetscReal *x,const PetscReal *y)
116: {
117:   PetscInt  i;
118:   PetscReal prod=0.0;

120:   for (i=0; i<DIM; i++) prod += x[i]*y[i];
121:   return prod;
122: }
123: PETSC_STATIC_INLINE PetscReal NormDIM(const PetscReal *x) { return PetscSqrtReal(PetscAbsReal(DotDIMReal(x,x))); }

125: PETSC_STATIC_INLINE PetscReal Dot2Real(const PetscReal *x,const PetscReal *y) { return x[0]*y[0] + x[1]*y[1];}
126: PETSC_STATIC_INLINE PetscReal Norm2Real(const PetscReal *x) { return PetscSqrtReal(PetscAbsReal(Dot2Real(x,x)));}
127: PETSC_STATIC_INLINE void Normalize2Real(PetscReal *x) { PetscReal a = 1./Norm2Real(x); x[0] *= a; x[1] *= a; }
128: PETSC_STATIC_INLINE void Waxpy2Real(PetscReal a,const PetscReal *x,const PetscReal *y,PetscReal *w) { w[0] = a*x[0] + y[0]; w[1] = a*x[1] + y[1]; }
129: PETSC_STATIC_INLINE void Scale2Real(PetscReal a,const PetscReal *x,PetscReal *y) { y[0] = a*x[0]; y[1] = a*x[1]; }

131: /******************* Advect ********************/
132: typedef enum {ADVECT_SOL_TILTED,ADVECT_SOL_BUMP,ADVECT_SOL_BUMP_CAVITY} AdvectSolType;
133: static const char *const AdvectSolTypes[] = {"TILTED","BUMP","BUMP_CAVITY","AdvectSolType","ADVECT_SOL_",0};
134: typedef enum {ADVECT_SOL_BUMP_CONE,ADVECT_SOL_BUMP_COS} AdvectSolBumpType;
135: static const char *const AdvectSolBumpTypes[] = {"CONE","COS","AdvectSolBumpType","ADVECT_SOL_BUMP_",0};

137: typedef struct {
138:   PetscReal wind[DIM];
139: } Physics_Advect_Tilted;
140: typedef struct {
141:   PetscReal         center[DIM];
142:   PetscReal         radius;
143:   AdvectSolBumpType type;
144: } Physics_Advect_Bump;

146: typedef struct {
147:   PetscReal     inflowState;
148:   AdvectSolType soltype;
149:   union {
150:     Physics_Advect_Tilted tilted;
151:     Physics_Advect_Bump   bump;
152:   } sol;
153:   struct {
154:     PetscInt Solution;
155:     PetscInt Error;
156:   } functional;
157: } Physics_Advect;

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

161: static PetscErrorCode PhysicsBoundary_Advect_Inflow(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
162: {
163:   Physics        phys    = (Physics)ctx;
164:   Physics_Advect *advect = (Physics_Advect*)phys->data;

167:   xG[0] = advect->inflowState;
168:   return(0);
169: }

171: static PetscErrorCode PhysicsBoundary_Advect_Outflow(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
172: {
174:   xG[0] = xI[0];
175:   return(0);
176: }

178: static void PhysicsRiemann_Advect(PetscInt dim, PetscInt Nf, const PetscReal *qp, const PetscReal *n, const PetscScalar *xL, const PetscScalar *xR, PetscInt numConstants, const PetscScalar constants[], PetscScalar *flux, Physics phys)
179: {
180:   Physics_Advect *advect = (Physics_Advect*)phys->data;
181:   PetscReal      wind[DIM],wn;

183:   switch (advect->soltype) {
184:   case ADVECT_SOL_TILTED: {
185:     Physics_Advect_Tilted *tilted = &advect->sol.tilted;
186:     wind[0] = tilted->wind[0];
187:     wind[1] = tilted->wind[1];
188:   } break;
189:   case ADVECT_SOL_BUMP:
190:     wind[0] = -qp[1];
191:     wind[1] = qp[0];
192:     break;
193:   case ADVECT_SOL_BUMP_CAVITY:
194:     {
195:       PetscInt  i;
196:       PetscReal comp2[3] = {0.,0.,0.}, rad2;

198:       rad2 = 0.;
199:       for (i = 0; i < dim; i++) {
200:         comp2[i] = qp[i] * qp[i];
201:         rad2    += comp2[i];
202:       }

204:       wind[0] = -qp[1];
205:       wind[1] = qp[0];
206:       if (rad2 > 1.) {
207:         PetscInt  maxI = 0;
208:         PetscReal maxComp2 = comp2[0];

210:         for (i = 1; i < dim; i++) {
211:           if (comp2[i] > maxComp2) {
212:             maxI     = i;
213:             maxComp2 = comp2[i];
214:           }
215:         }
216:         wind[maxI] = 0.;
217:       }
218:     }
219:     break;
220:   default:
221:   {
222:     PetscInt i;
223:     for (i = 0; i < DIM; ++i) wind[i] = 0.0;
224:   }
225:   /* default: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for solution type %s",AdvectSolBumpTypes[advect->soltype]); */
226:   }
227:   wn      = Dot2Real(wind, n);
228:   flux[0] = (wn > 0 ? xL[0] : xR[0]) * wn;
229: }

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

237:   switch (advect->soltype) {
238:   case ADVECT_SOL_TILTED: {
239:     PetscReal             x0[DIM];
240:     Physics_Advect_Tilted *tilted = &advect->sol.tilted;
241:     Waxpy2Real(-time,tilted->wind,x,x0);
242:     if (x0[1] > 0) u[0] = 1.*x[0] + 3.*x[1];
243:     else u[0] = advect->inflowState;
244:   } break;
245:   case ADVECT_SOL_BUMP_CAVITY:
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:     Waxpy2Real(-1,bump->center,x0,v);
254:     r = Norm2Real(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: }

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

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

283: static PetscErrorCode SetUpBC_Advect(PetscDS prob, Physics phys)
284: {
286:   const PetscInt inflowids[] = {100,200,300},outflowids[] = {101};

289:   /* Register "canned" boundary conditions and defaults for where to apply. */
290:   PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "inflow",  "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_Advect_Inflow,  ALEN(inflowids),  inflowids,  phys);
291:   PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "outflow", "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_Advect_Outflow, ALEN(outflowids), outflowids, phys);
292:   return(0);
293: }

295: static PetscErrorCode PhysicsCreate_Advect(Model mod,Physics phys,PetscOptionItems *PetscOptionsObject)
296: {
297:   Physics_Advect *advect;

301:   phys->field_desc = PhysicsFields_Advect;
302:   phys->riemann    = (PetscRiemannFunc)PhysicsRiemann_Advect;
303:   PetscNew(&advect);
304:   phys->data       = advect;
305:   mod->setupbc = SetUpBC_Advect;

307:   PetscOptionsHead(PetscOptionsObject,"Advect options");
308:   {
309:     PetscInt two = 2,dof = 1;
310:     advect->soltype = ADVECT_SOL_TILTED;
311:     PetscOptionsEnum("-advect_sol_type","solution type","",AdvectSolTypes,(PetscEnum)advect->soltype,(PetscEnum*)&advect->soltype,NULL);
312:     switch (advect->soltype) {
313:     case ADVECT_SOL_TILTED: {
314:       Physics_Advect_Tilted *tilted = &advect->sol.tilted;
315:       two = 2;
316:       tilted->wind[0] = 0.0;
317:       tilted->wind[1] = 1.0;
318:       PetscOptionsRealArray("-advect_tilted_wind","background wind vx,vy","",tilted->wind,&two,NULL);
319:       advect->inflowState = -2.0;
320:       PetscOptionsRealArray("-advect_tilted_inflow","Inflow state","",&advect->inflowState,&dof,NULL);
321:       phys->maxspeed = Norm2Real(tilted->wind);
322:     } break;
323:     case ADVECT_SOL_BUMP_CAVITY:
324:     case ADVECT_SOL_BUMP: {
325:       Physics_Advect_Bump *bump = &advect->sol.bump;
326:       two = 2;
327:       bump->center[0] = 2.;
328:       bump->center[1] = 0.;
329:       PetscOptionsRealArray("-advect_bump_center","location of center of bump x,y","",bump->center,&two,NULL);
330:       bump->radius = 0.9;
331:       PetscOptionsReal("-advect_bump_radius","radius of bump","",bump->radius,&bump->radius,NULL);
332:       bump->type = ADVECT_SOL_BUMP_CONE;
333:       PetscOptionsEnum("-advect_bump_type","type of bump","",AdvectSolBumpTypes,(PetscEnum)bump->type,(PetscEnum*)&bump->type,NULL);
334:       phys->maxspeed = 3.;       /* radius of mesh, kludge */
335:     } break;
336:     }
337:   }
338:   PetscOptionsTail();
339:   /* Initial/transient solution with default boundary conditions */
340:   ModelSolutionSetDefault(mod,PhysicsSolution_Advect,phys);
341:   /* Register "canned" functionals */
342:   ModelFunctionalRegister(mod,"Solution",&advect->functional.Solution,PhysicsFunctional_Advect,phys);
343:   ModelFunctionalRegister(mod,"Error",&advect->functional.Error,PhysicsFunctional_Advect,phys);
344:   mod->bcs[0] = mod->bcs[1] = mod->bcs[2] = DM_BOUNDARY_GHOSTED;
345:   return(0);
346: }

348: /******************* Shallow Water ********************/
349: typedef struct {
350:   PetscReal gravity;
351:   PetscReal boundaryHeight;
352:   struct {
353:     PetscInt Height;
354:     PetscInt Speed;
355:     PetscInt Energy;
356:   } functional;
357: } Physics_SW;
358: typedef struct {
359:   PetscReal h;
360:   PetscReal uh[DIM];
361: } SWNode;
362: typedef union {
363:   SWNode    swnode;
364:   PetscReal vals[DIM+1];
365: } SWNodeUnion;

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

369: /*
370:  * h_t + div(uh) = 0
371:  * (uh)_t + div (u\otimes uh + g h^2 / 2 I) = 0
372:  *
373:  * */
374: static PetscErrorCode SWFlux(Physics phys,const PetscReal *n,const SWNode *x,SWNode *f)
375: {
376:   Physics_SW  *sw = (Physics_SW*)phys->data;
377:   PetscReal   uhn,u[DIM];
378:   PetscInt     i;

381:   Scale2Real(1./x->h,x->uh,u);
382:   uhn  = x->uh[0] * n[0] + x->uh[1] * n[1];
383:   f->h = uhn;
384:   for (i=0; i<DIM; i++) f->uh[i] = u[i] * uhn + sw->gravity * PetscSqr(x->h) * n[i];
385:   return(0);
386: }

388: static PetscErrorCode PhysicsBoundary_SW_Wall(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
389: {
391:   xG[0] = xI[0];
392:   xG[1] = -xI[1];
393:   xG[2] = -xI[2];
394:   return(0);
395: }

397: static void PhysicsRiemann_SW(PetscInt dim, PetscInt Nf, const PetscReal *qp, const PetscReal *n, const PetscScalar *xL, const PetscScalar *xR, PetscInt numConstants, const PetscScalar constants[], PetscScalar *flux, Physics phys)
398: {
399:   Physics_SW   *sw = (Physics_SW*)phys->data;
400:   PetscReal    cL,cR,speed;
401:   PetscReal    nn[DIM];
402: #if !defined(PETSC_USE_COMPLEX)
403:   const SWNode *uL = (const SWNode*)xL,*uR = (const SWNode*)xR;
404: #else
405:   SWNodeUnion  uLreal, uRreal;
406:   const SWNode *uL = &uLreal.swnode;
407:   const SWNode *uR = &uRreal.swnode;
408: #endif
409:   SWNodeUnion  fL,fR;
410:   PetscInt     i;
411:   PetscReal    zero=0.;

413: #if defined(PETSC_USE_COMPLEX)
414:   for (i = 0; i < 1+dim; i++) uLreal.vals[i] = PetscRealPart(xL[i]);
415:   for (i = 0; i < 1+dim; i++) uRreal.vals[i] = PetscRealPart(xR[i]);
416: #endif
417:   if (uL->h < 0 || uR->h < 0) {for (i=0; i<1+dim; i++) flux[i] = zero/zero; return;} /* SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Reconstructed thickness is negative"); */
418:   nn[0] = n[0];
419:   nn[1] = n[1];
420:   Normalize2Real(nn);
421:   SWFlux(phys,nn,uL,&(fL.swnode));
422:   SWFlux(phys,nn,uR,&(fR.swnode));
423:   cL    = PetscSqrtReal(sw->gravity*uL->h);
424:   cR    = PetscSqrtReal(sw->gravity*uR->h); /* gravity wave speed */
425:   speed = PetscMax(PetscAbsReal(Dot2Real(uL->uh,nn)/uL->h) + cL,PetscAbsReal(Dot2Real(uR->uh,nn)/uR->h) + cR);
426:   for (i=0; i<1+dim; i++) flux[i] = (0.5*(fL.vals[i] + fR.vals[i]) + 0.5*speed*(xL[i] - xR[i])) * Norm2Real(n);
427: }

429: static PetscErrorCode PhysicsSolution_SW(Model mod,PetscReal time,const PetscReal *x,PetscScalar *u,void *ctx)
430: {
431:   PetscReal dx[2],r,sigma;

434:   if (time != 0.0) SETERRQ1(mod->comm,PETSC_ERR_SUP,"No solution known for time %g",(double)time);
435:   dx[0] = x[0] - 1.5;
436:   dx[1] = x[1] - 1.0;
437:   r     = Norm2Real(dx);
438:   sigma = 0.5;
439:   u[0]  = 1 + 2*PetscExpReal(-PetscSqr(r)/(2*PetscSqr(sigma)));
440:   u[1]  = 0.0;
441:   u[2]  = 0.0;
442:   return(0);
443: }

445: static PetscErrorCode PhysicsFunctional_SW(Model mod,PetscReal time,const PetscReal *coord,const PetscScalar *xx,PetscReal *f,void *ctx)
446: {
447:   Physics      phys = (Physics)ctx;
448:   Physics_SW   *sw  = (Physics_SW*)phys->data;
449:   const SWNode *x   = (const SWNode*)xx;
450:   PetscReal  u[2];
451:   PetscReal    h;

454:   h = x->h;
455:   Scale2Real(1./x->h,x->uh,u);
456:   f[sw->functional.Height] = h;
457:   f[sw->functional.Speed]  = Norm2Real(u) + PetscSqrtReal(sw->gravity*h);
458:   f[sw->functional.Energy] = 0.5*(Dot2Real(x->uh,u) + sw->gravity*PetscSqr(h));
459:   return(0);
460: }

462: static PetscErrorCode SetUpBC_SW(PetscDS prob,Physics phys)
463: {
465:   const PetscInt wallids[] = {100,101,200,300};
467:   PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "wall", "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_SW_Wall, ALEN(wallids), wallids, phys);
468:   return(0);
469: }

471: static PetscErrorCode PhysicsCreate_SW(Model mod,Physics phys,PetscOptionItems *PetscOptionsObject)
472: {
473:   Physics_SW     *sw;

477:   phys->field_desc = PhysicsFields_SW;
478:   phys->riemann = (PetscRiemannFunc) PhysicsRiemann_SW;
479:   PetscNew(&sw);
480:   phys->data    = sw;
481:   mod->setupbc  = SetUpBC_SW;

483:   PetscOptionsHead(PetscOptionsObject,"SW options");
484:   {
485:     sw->gravity = 1.0;
486:     PetscOptionsReal("-sw_gravity","Gravitational constant","",sw->gravity,&sw->gravity,NULL);
487:   }
488:   PetscOptionsTail();
489:   phys->maxspeed = PetscSqrtReal(2.0*sw->gravity); /* Mach 1 for depth of 2 */

491:   ModelSolutionSetDefault(mod,PhysicsSolution_SW,phys);
492:   ModelFunctionalRegister(mod,"Height",&sw->functional.Height,PhysicsFunctional_SW,phys);
493:   ModelFunctionalRegister(mod,"Speed",&sw->functional.Speed,PhysicsFunctional_SW,phys);
494:   ModelFunctionalRegister(mod,"Energy",&sw->functional.Energy,PhysicsFunctional_SW,phys);

496:   mod->bcs[0] = mod->bcs[1] = mod->bcs[2] = DM_BOUNDARY_GHOSTED;

498:   return(0);
499: }

501: /******************* Euler Density Shock (EULER_IV_SHOCK,EULER_SS_SHOCK) ********************/
502: /* An initial-value and self-similar solutions of the compressible Euler equations */
503: /* Ravi Samtaney and D. I. Pullin */
504: /* Phys. Fluids 8, 2650 (1996); http://dx.doi.org/10.1063/1.869050 */
505: typedef enum {EULER_PAR_GAMMA,EULER_PAR_RHOR,EULER_PAR_AMACH,EULER_PAR_ITANA,EULER_PAR_SIZE} EulerParamIdx;
506: typedef enum {EULER_IV_SHOCK,EULER_SS_SHOCK,EULER_SHOCK_TUBE,EULER_LINEAR_WAVE} EulerType;
507: typedef struct {
508:   PetscReal r;
509:   PetscReal ru[DIM];
510:   PetscReal E;
511: } EulerNode;
512: typedef union {
513:   EulerNode eulernode;
514:   PetscReal vals[DIM+2];
515: } EulerNodeUnion;
516: typedef PetscErrorCode (*EquationOfState)(const PetscReal*, const EulerNode*, PetscReal*);
517: typedef struct {
518:   EulerType       type;
519:   PetscReal       pars[EULER_PAR_SIZE];
520:   EquationOfState sound;
521:   struct {
522:     PetscInt Density;
523:     PetscInt Momentum;
524:     PetscInt Energy;
525:     PetscInt Pressure;
526:     PetscInt Speed;
527:   } monitor;
528: } Physics_Euler;

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

532: /* initial condition */
533: int initLinearWave(EulerNode *ux, const PetscReal gamma, const PetscReal coord[], const PetscReal Lx);
534: static PetscErrorCode PhysicsSolution_Euler(Model mod, PetscReal time, const PetscReal *x, PetscScalar *u, void *ctx)
535: {
536:   PetscInt i;
537:   Physics         phys = (Physics)ctx;
538:   Physics_Euler   *eu  = (Physics_Euler*)phys->data;
539:   EulerNode       *uu  = (EulerNode*)u;
540:   PetscReal        p0,gamma,c;
542:   if (time != 0.0) SETERRQ1(mod->comm,PETSC_ERR_SUP,"No solution known for time %g",(double)time);

544:   for (i=0; i<DIM; i++) uu->ru[i] = 0.0; /* zero out initial velocity */
545:   /* set E and rho */
546:   gamma = eu->pars[EULER_PAR_GAMMA];

548:   if (eu->type==EULER_IV_SHOCK || eu->type==EULER_SS_SHOCK) {
549:     /******************* Euler Density Shock ********************/
550:     /* On initial-value and self-similar solutions of the compressible Euler equations */
551:     /* Ravi Samtaney and D. I. Pullin */
552:     /* Phys. Fluids 8, 2650 (1996); http://dx.doi.org/10.1063/1.869050 */
553:     /* initial conditions 1: left of shock, 0: left of discontinuity 2: right of discontinuity,  */
554:     p0 = 1.;
555:     if (x[0] < 0.0 + x[1]*eu->pars[EULER_PAR_ITANA]) {
556:       if (x[0] < mod->bounds[0]*0.5) { /* left of shock (1) */
557:         PetscReal amach,rho,press,gas1,p1;
558:         amach = eu->pars[EULER_PAR_AMACH];
559:         rho = 1.;
560:         press = p0;
561:         p1 = press*(1.0+2.0*gamma/(gamma+1.0)*(amach*amach-1.0));
562:         gas1 = (gamma-1.0)/(gamma+1.0);
563:         uu->r = rho*(p1/press+gas1)/(gas1*p1/press+1.0);
564:         uu->ru[0]   = ((uu->r - rho)*PetscSqrtReal(gamma*press/rho)*amach);
565:         uu->E = p1/(gamma-1.0) + .5/uu->r*uu->ru[0]*uu->ru[0];
566:       }
567:       else { /* left of discontinuity (0) */
568:         uu->r = 1.; /* rho = 1 */
569:         uu->E = p0/(gamma-1.0);
570:       }
571:     }
572:     else { /* right of discontinuity (2) */
573:       uu->r = eu->pars[EULER_PAR_RHOR];
574:       uu->E = p0/(gamma-1.0);
575:     }
576:   }
577:   else if (eu->type==EULER_SHOCK_TUBE) {
578:     /* For (x<x0) set (rho,u,p)=(8,0,10) and for (x>x0) set (rho,u,p)=(1,0,1). Choose x0 to the midpoint of the domain in the x-direction. */
579:     if (x[0] < 0.0 ) {
580:       uu->r = 8.;
581:       uu->E = 10./(gamma-1.);
582:     }
583:     else {
584:       uu->r = 1.;
585:       uu->E = 1./(gamma-1.);
586:     }
587:   }
588:   else if (eu->type==EULER_LINEAR_WAVE) {
589:     initLinearWave( uu, gamma, x, mod->bounds[1] - mod->bounds[0]);
590:   }
591:   else SETERRQ1(mod->comm,PETSC_ERR_SUP,"Unknown type %d",eu->type);

593:   /* set phys->maxspeed: (mod->maxspeed = phys->maxspeed) in main; */
594:   eu->sound(&gamma,uu,&c);
595:   c = (uu->ru[0]/uu->r) + c;
596:   if (c > phys->maxspeed) phys->maxspeed = c;

598:   return(0);
599: }

601: static PetscErrorCode Pressure_PG(const PetscReal gamma,const EulerNode *x,PetscReal *p)
602: {
603:   PetscReal ru2;

606:   ru2  = DotDIMReal(x->ru,x->ru);
607:   (*p)=(x->E - 0.5*ru2/x->r)*(gamma - 1.0); /* (E - rho V^2/2)(gamma-1) = e rho (gamma-1) */
608:   return(0);
609: }

611: static PetscErrorCode SpeedOfSound_PG(const PetscReal *gamma, const EulerNode *x, PetscReal *c)
612: {
613:   PetscReal p;

616:   Pressure_PG(*gamma,x,&p);
617:   if (p<0.) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"negative pressure time %g -- NEED TO FIX!!!!!!",(double) p);
618:   /* pars[EULER_PAR_GAMMA] = heat capacity ratio */
619:   (*c)=PetscSqrtReal(*gamma * p / x->r);
620:   return(0);
621: }

623: /*
624:  * x = (rho,rho*(u_1),...,rho*e)^T
625:  * x_t+div(f_1(x))+...+div(f_DIM(x)) = 0
626:  *
627:  * f_i(x) = u_i*x+(0,0,...,p,...,p*u_i)^T
628:  *
629:  */
630: static PetscErrorCode EulerFlux(Physics phys,const PetscReal *n,const EulerNode *x,EulerNode *f)
631: {
632:   Physics_Euler *eu = (Physics_Euler*)phys->data;
633:   PetscReal     nu,p;
634:   PetscInt      i;

637:   Pressure_PG(eu->pars[EULER_PAR_GAMMA],x,&p);
638:   nu = DotDIMReal(x->ru,n);
639:   f->r = nu;   /* A rho u */
640:   nu /= x->r;  /* A u */
641:   for (i=0; i<DIM; i++) f->ru[i] = nu * x->ru[i] + n[i]*p;  /* r u^2 + p */
642:   f->E = nu * (x->E + p); /* u(e+p) */
643:   return(0);
644: }

646: /* PetscReal* => EulerNode* conversion */
647: static PetscErrorCode PhysicsBoundary_Euler_Wall(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *a_xI, PetscScalar *a_xG, void *ctx)
648: {
649:   PetscInt    i;
650:   const EulerNode *xI = (const EulerNode*)a_xI;
651:   EulerNode       *xG = (EulerNode*)a_xG;
652:   Physics         phys = (Physics)ctx;
653:   Physics_Euler   *eu  = (Physics_Euler*)phys->data;
655:   xG->r = xI->r;           /* ghost cell density - same */
656:   xG->E = xI->E;           /* ghost cell energy - same */
657:   if (n[1] != 0.) {        /* top and bottom */
658:     xG->ru[0] =  xI->ru[0]; /* copy tang to wall */
659:     xG->ru[1] = -xI->ru[1]; /* reflect perp to t/b wall */
660:   }
661:   else { /* sides */
662:     for (i=0; i<DIM; i++) xG->ru[i] = xI->ru[i]; /* copy */
663:   }
664:   if (eu->type == EULER_LINEAR_WAVE) { /* debug */
665: #if 0
666:     PetscPrintf(PETSC_COMM_WORLD,"%s coord=%g,%g\n",PETSC_FUNCTION_NAME,c[0],c[1]);
667: #endif
668:   }
669:   return(0);
670: }
671: int godunovflux( const PetscScalar *ul, const PetscScalar *ur, PetscScalar *flux, const PetscReal *nn, const int *ndim, const PetscReal *gamma);
672: /* PetscReal* => EulerNode* conversion */
673: static void PhysicsRiemann_Euler_Godunov( PetscInt dim, PetscInt Nf, const PetscReal *qp, const PetscReal *n,
674:                                           const PetscScalar *xL, const PetscScalar *xR, PetscInt numConstants, const PetscScalar constants[], PetscScalar *flux, Physics phys)
675: {
676:   Physics_Euler   *eu = (Physics_Euler*)phys->data;
677:   PetscReal       cL,cR,speed,velL,velR,nn[DIM],s2;
678:   PetscInt        i;
679:   PetscErrorCode  ierr;

682:   for (i=0,s2=0.; i<DIM; i++) {
683:     nn[i] = n[i];
684:     s2 += nn[i]*nn[i];
685:   }
686:   s2 = PetscSqrtReal(s2); /* |n|_2 = sum(n^2)^1/2 */
687:   for (i=0.; i<DIM; i++) nn[i] /= s2;
688:   if (0) { /* Rusanov */
689:     const EulerNode *uL = (const EulerNode*)xL,*uR = (const EulerNode*)xR;
690:     EulerNodeUnion  fL,fR;
691:     EulerFlux(phys,nn,uL,&(fL.eulernode));
692:     EulerFlux(phys,nn,uR,&(fR.eulernode));
693:     eu->sound(&eu->pars[EULER_PAR_GAMMA],uL,&cL);if (ierr) exit(13);
694:     eu->sound(&eu->pars[EULER_PAR_GAMMA],uR,&cR);if (ierr) exit(14);
695:     velL = DotDIMReal(uL->ru,nn)/uL->r;
696:     velR = DotDIMReal(uR->ru,nn)/uR->r;
697:     speed = PetscMax(velR + cR, velL + cL);
698:     for (i=0; i<2+dim; i++) flux[i] = 0.5*((fL.vals[i]+fR.vals[i]) + speed*(xL[i] - xR[i]))*s2;
699:   }
700:   else {
701:     int dim = DIM;
702:     /* int iwave =  */
703:     godunovflux(xL, xR, flux, nn, &dim, &eu->pars[EULER_PAR_GAMMA]);
704:     for (i=0; i<2+dim; i++) flux[i] *= s2;
705:   }
706:   PetscFunctionReturnVoid();
707: }

709: static PetscErrorCode PhysicsFunctional_Euler(Model mod,PetscReal time,const PetscReal *coord,const PetscScalar *xx,PetscReal *f,void *ctx)
710: {
711:   Physics         phys = (Physics)ctx;
712:   Physics_Euler   *eu  = (Physics_Euler*)phys->data;
713:   const EulerNode *x   = (const EulerNode*)xx;
714:   PetscReal       p;

717:   f[eu->monitor.Density]  = x->r;
718:   f[eu->monitor.Momentum] = NormDIM(x->ru);
719:   f[eu->monitor.Energy]   = x->E;
720:   f[eu->monitor.Speed]    = NormDIM(x->ru)/x->r;
721:   Pressure_PG(eu->pars[EULER_PAR_GAMMA], x, &p);
722:   f[eu->monitor.Pressure] = p;
723:   return(0);
724: }

726: static PetscErrorCode SetUpBC_Euler(PetscDS prob,Physics phys)
727: {
728:   PetscErrorCode  ierr;
729:   Physics_Euler   *eu = (Physics_Euler *) phys->data;
730:   if (eu->type == EULER_LINEAR_WAVE) {
731:     const PetscInt wallids[] = {100,101};
732:     PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "wall", "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_Euler_Wall, ALEN(wallids), wallids, phys);
733:   }
734:   else {
735:     const PetscInt wallids[] = {100,101,200,300};
736:     PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "wall", "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_Euler_Wall, ALEN(wallids), wallids, phys);
737:   }
738:   return(0);
739: }

741: static PetscErrorCode PhysicsCreate_Euler(Model mod,Physics phys,PetscOptionItems *PetscOptionsObject)
742: {
743:   Physics_Euler   *eu;
744:   PetscErrorCode  ierr;

747:   phys->field_desc = PhysicsFields_Euler;
748:   phys->riemann = (PetscRiemannFunc) PhysicsRiemann_Euler_Godunov;
749:   PetscNew(&eu);
750:   phys->data    = eu;
751:   mod->setupbc = SetUpBC_Euler;
752:   PetscOptionsHead(PetscOptionsObject,"Euler options");
753:   {
754:     PetscReal alpha;
755:     char type[64] = "linear_wave";
756:     PetscBool  is;
757:     mod->bcs[0] = mod->bcs[1] = mod->bcs[2] = DM_BOUNDARY_GHOSTED;
758:     eu->pars[EULER_PAR_GAMMA] = 1.4;
759:     eu->pars[EULER_PAR_AMACH] = 2.02;
760:     eu->pars[EULER_PAR_RHOR] = 3.0;
761:     eu->pars[EULER_PAR_ITANA] = 0.57735026918963; /* angle of Euler self similar (SS) shock */
762:     PetscOptionsReal("-eu_gamma","Heat capacity ratio","",eu->pars[EULER_PAR_GAMMA],&eu->pars[EULER_PAR_GAMMA],NULL);
763:     PetscOptionsReal("-eu_amach","Shock speed (Mach)","",eu->pars[EULER_PAR_AMACH],&eu->pars[EULER_PAR_AMACH],NULL);
764:     PetscOptionsReal("-eu_rho2","Density right of discontinuity","",eu->pars[EULER_PAR_RHOR],&eu->pars[EULER_PAR_RHOR],NULL);
765:     alpha = 60.;
766:     PetscOptionsReal("-eu_alpha","Angle of discontinuity","",alpha,&alpha,NULL);
767:     if (alpha<=0. || alpha>90.) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Alpha bust be > 0 and <= 90 (%g)",alpha);
768:     eu->pars[EULER_PAR_ITANA] = 1./PetscTanReal( alpha * PETSC_PI / 180.0 );
769:     PetscOptionsString("-eu_type","Type of Euler test","",type,type,sizeof(type),NULL);
770:     PetscStrcmp(type,"linear_wave", &is);
771:     if (is) {
772:       eu->type = EULER_LINEAR_WAVE;
773:       mod->bcs[0] = mod->bcs[1] = mod->bcs[2] = DM_BOUNDARY_PERIODIC;
774:       mod->bcs[1] = DM_BOUNDARY_GHOSTED; /* debug */
775:       PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",PETSC_FUNCTION_NAME,"linear_wave");
776:     }
777:     else {
778:       if (DIM != 2) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"DIM must be 2 unless linear wave test %s",type);
779:       PetscStrcmp(type,"iv_shock", &is);
780:       if (is) {
781:         eu->type = EULER_IV_SHOCK;
782:         PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",PETSC_FUNCTION_NAME,"iv_shock");
783:       }
784:       else {
785:         PetscStrcmp(type,"ss_shock", &is);
786:         if (is) {
787:           eu->type = EULER_SS_SHOCK;
788:           PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",PETSC_FUNCTION_NAME,"ss_shock");
789:         }
790:         else {
791:           PetscStrcmp(type,"shock_tube", &is);
792:           if (is) eu->type = EULER_SHOCK_TUBE;
793:           else SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Unknown Euler type %s",type);
794:           PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",PETSC_FUNCTION_NAME,"shock_tube");
795:         }
796:       }
797:     }
798:   }
799:   PetscOptionsTail();
800:   eu->sound = SpeedOfSound_PG;
801:   phys->maxspeed = 0.; /* will get set in solution */
802:   ModelSolutionSetDefault(mod,PhysicsSolution_Euler,phys);
803:   ModelFunctionalRegister(mod,"Speed",&eu->monitor.Speed,PhysicsFunctional_Euler,phys);
804:   ModelFunctionalRegister(mod,"Energy",&eu->monitor.Energy,PhysicsFunctional_Euler,phys);
805:   ModelFunctionalRegister(mod,"Density",&eu->monitor.Density,PhysicsFunctional_Euler,phys);
806:   ModelFunctionalRegister(mod,"Momentum",&eu->monitor.Momentum,PhysicsFunctional_Euler,phys);
807:   ModelFunctionalRegister(mod,"Pressure",&eu->monitor.Pressure,PhysicsFunctional_Euler,phys);

809:   return(0);
810: }

812: static PetscErrorCode ErrorIndicator_Simple(PetscInt dim, PetscReal volume, PetscInt numComps, const PetscScalar u[], const PetscScalar grad[], PetscReal *error, void *ctx)
813: {
814:   PetscReal      err = 0.;
815:   PetscInt       i, j;

818:   for (i = 0; i < numComps; i++) {
819:     for (j = 0; j < dim; j++) {
820:       err += PetscSqr(PetscRealPart(grad[i * dim + j]));
821:     }
822:   }
823:   *error = volume * err;
824:   return(0);
825: }

827: PetscErrorCode ConstructCellBoundary(DM dm, User user)
828: {
829:   const char     *name   = "Cell Sets";
830:   const char     *bdname = "split faces";
831:   IS             regionIS, innerIS;
832:   const PetscInt *regions, *cells;
833:   PetscInt       numRegions, innerRegion, numCells, c;
834:   PetscInt       cStart, cEnd, cEndInterior, fStart, fEnd;
835:   PetscBool      hasLabel;

839:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
840:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
841:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);

843:   DMHasLabel(dm, name, &hasLabel);
844:   if (!hasLabel) return(0);
845:   DMGetLabelSize(dm, name, &numRegions);
846:   if (numRegions != 2) return(0);
847:   /* Get the inner id */
848:   DMGetLabelIdIS(dm, name, &regionIS);
849:   ISGetIndices(regionIS, &regions);
850:   innerRegion = regions[0];
851:   ISRestoreIndices(regionIS, &regions);
852:   ISDestroy(&regionIS);
853:   /* Find the faces between cells in different regions, could call DMPlexCreateNeighborCSR() */
854:   DMGetStratumIS(dm, name, innerRegion, &innerIS);
855:   ISGetLocalSize(innerIS, &numCells);
856:   ISGetIndices(innerIS, &cells);
857:   DMCreateLabel(dm, bdname);
858:   for (c = 0; c < numCells; ++c) {
859:     const PetscInt cell = cells[c];
860:     const PetscInt *faces;
861:     PetscInt       numFaces, f;

863:     if ((cell < cStart) || (cell >= cEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Got invalid point %d which is not a cell", cell);
864:     DMPlexGetConeSize(dm, cell, &numFaces);
865:     DMPlexGetCone(dm, cell, &faces);
866:     for (f = 0; f < numFaces; ++f) {
867:       const PetscInt face = faces[f];
868:       const PetscInt *neighbors;
869:       PetscInt       nC, regionA, regionB;

871:       if ((face < fStart) || (face >= fEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Got invalid point %d which is not a face", face);
872:       DMPlexGetSupportSize(dm, face, &nC);
873:       if (nC != 2) continue;
874:       DMPlexGetSupport(dm, face, &neighbors);
875:       if ((neighbors[0] >= cEndInterior) || (neighbors[1] >= cEndInterior)) continue;
876:       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]);
877:       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]);
878:       DMGetLabelValue(dm, name, neighbors[0], &regionA);
879:       DMGetLabelValue(dm, name, neighbors[1], &regionB);
880:       if (regionA < 0) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Invalid label %s: Cell %d has no value", name, neighbors[0]);
881:       if (regionB < 0) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Invalid label %s: Cell %d has no value", name, neighbors[1]);
882:       if (regionA != regionB) {
883:         DMSetLabelValue(dm, bdname, faces[f], 1);
884:       }
885:     }
886:   }
887:   ISRestoreIndices(innerIS, &cells);
888:   ISDestroy(&innerIS);
889:   {
890:     DMLabel label;

892:     DMGetLabel(dm, bdname, &label);
893:     DMLabelView(label, PETSC_VIEWER_STDOUT_WORLD);
894:   }
895:   return(0);
896: }

898: /* Right now, I have just added duplicate faces, which see both cells. We can
899: - Add duplicate vertices and decouple the face cones
900: - Disconnect faces from cells across the rotation gap
901: */
902: PetscErrorCode SplitFaces(DM *dmSplit, const char labelName[], User user)
903: {
904:   DM             dm = *dmSplit, sdm;
905:   PetscSF        sfPoint, gsfPoint;
906:   PetscSection   coordSection, newCoordSection;
907:   Vec            coordinates;
908:   IS             idIS;
909:   const PetscInt *ids;
910:   PetscInt       *newpoints;
911:   PetscInt       dim, depth, maxConeSize, maxSupportSize, numLabels, numGhostCells;
912:   PetscInt       numFS, fs, pStart, pEnd, p, cEnd, cEndInterior, vStart, vEnd, v, fStart, fEnd, newf, d, l;
913:   PetscBool      hasLabel;

917:   DMHasLabel(dm, labelName, &hasLabel);
918:   if (!hasLabel) return(0);
919:   DMCreate(PetscObjectComm((PetscObject)dm), &sdm);
920:   DMSetType(sdm, DMPLEX);
921:   DMGetDimension(dm, &dim);
922:   DMSetDimension(sdm, dim);

924:   DMGetLabelIdIS(dm, labelName, &idIS);
925:   ISGetLocalSize(idIS, &numFS);
926:   ISGetIndices(idIS, &ids);

928:   user->numSplitFaces = 0;
929:   for (fs = 0; fs < numFS; ++fs) {
930:     PetscInt numBdFaces;

932:     DMGetStratumSize(dm, labelName, ids[fs], &numBdFaces);
933:     user->numSplitFaces += numBdFaces;
934:   }
935:   DMPlexGetChart(dm, &pStart, &pEnd);
936:   pEnd += user->numSplitFaces;
937:   DMPlexSetChart(sdm, pStart, pEnd);
938:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
939:   DMPlexSetHybridBounds(sdm, cEndInterior, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_DETERMINE);
940:   DMPlexGetHeightStratum(dm, 0, NULL, &cEnd);
941:   numGhostCells = cEnd - cEndInterior;
942:   /* Set cone and support sizes */
943:   DMPlexGetDepth(dm, &depth);
944:   for (d = 0; d <= depth; ++d) {
945:     DMPlexGetDepthStratum(dm, d, &pStart, &pEnd);
946:     for (p = pStart; p < pEnd; ++p) {
947:       PetscInt newp = p;
948:       PetscInt size;

950:       DMPlexGetConeSize(dm, p, &size);
951:       DMPlexSetConeSize(sdm, newp, size);
952:       DMPlexGetSupportSize(dm, p, &size);
953:       DMPlexSetSupportSize(sdm, newp, size);
954:     }
955:   }
956:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
957:   for (fs = 0, newf = fEnd; fs < numFS; ++fs) {
958:     IS             faceIS;
959:     const PetscInt *faces;
960:     PetscInt       numFaces, f;

962:     DMGetStratumIS(dm, labelName, ids[fs], &faceIS);
963:     ISGetLocalSize(faceIS, &numFaces);
964:     ISGetIndices(faceIS, &faces);
965:     for (f = 0; f < numFaces; ++f, ++newf) {
966:       PetscInt size;

968:       /* Right now I think that both faces should see both cells */
969:       DMPlexGetConeSize(dm, faces[f], &size);
970:       DMPlexSetConeSize(sdm, newf, size);
971:       DMPlexGetSupportSize(dm, faces[f], &size);
972:       DMPlexSetSupportSize(sdm, newf, size);
973:     }
974:     ISRestoreIndices(faceIS, &faces);
975:     ISDestroy(&faceIS);
976:   }
977:   DMSetUp(sdm);
978:   /* Set cones and supports */
979:   DMPlexGetMaxSizes(dm, &maxConeSize, &maxSupportSize);
980:   PetscMalloc1(PetscMax(maxConeSize, maxSupportSize), &newpoints);
981:   DMPlexGetChart(dm, &pStart, &pEnd);
982:   for (p = pStart; p < pEnd; ++p) {
983:     const PetscInt *points, *orientations;
984:     PetscInt       size, i, newp = p;

986:     DMPlexGetConeSize(dm, p, &size);
987:     DMPlexGetCone(dm, p, &points);
988:     DMPlexGetConeOrientation(dm, p, &orientations);
989:     for (i = 0; i < size; ++i) newpoints[i] = points[i];
990:     DMPlexSetCone(sdm, newp, newpoints);
991:     DMPlexSetConeOrientation(sdm, newp, orientations);
992:     DMPlexGetSupportSize(dm, p, &size);
993:     DMPlexGetSupport(dm, p, &points);
994:     for (i = 0; i < size; ++i) newpoints[i] = points[i];
995:     DMPlexSetSupport(sdm, newp, newpoints);
996:   }
997:   PetscFree(newpoints);
998:   for (fs = 0, newf = fEnd; fs < numFS; ++fs) {
999:     IS             faceIS;
1000:     const PetscInt *faces;
1001:     PetscInt       numFaces, f;

1003:     DMGetStratumIS(dm, labelName, ids[fs], &faceIS);
1004:     ISGetLocalSize(faceIS, &numFaces);
1005:     ISGetIndices(faceIS, &faces);
1006:     for (f = 0; f < numFaces; ++f, ++newf) {
1007:       const PetscInt *points;

1009:       DMPlexGetCone(dm, faces[f], &points);
1010:       DMPlexSetCone(sdm, newf, points);
1011:       DMPlexGetSupport(dm, faces[f], &points);
1012:       DMPlexSetSupport(sdm, newf, points);
1013:     }
1014:     ISRestoreIndices(faceIS, &faces);
1015:     ISDestroy(&faceIS);
1016:   }
1017:   ISRestoreIndices(idIS, &ids);
1018:   ISDestroy(&idIS);
1019:   DMPlexStratify(sdm);
1020:   /* Convert coordinates */
1021:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
1022:   DMGetCoordinateSection(dm, &coordSection);
1023:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &newCoordSection);
1024:   PetscSectionSetNumFields(newCoordSection, 1);
1025:   PetscSectionSetFieldComponents(newCoordSection, 0, dim);
1026:   PetscSectionSetChart(newCoordSection, vStart, vEnd);
1027:   for (v = vStart; v < vEnd; ++v) {
1028:     PetscSectionSetDof(newCoordSection, v, dim);
1029:     PetscSectionSetFieldDof(newCoordSection, v, 0, dim);
1030:   }
1031:   PetscSectionSetUp(newCoordSection);
1032:   DMSetCoordinateSection(sdm, PETSC_DETERMINE, newCoordSection);
1033:   PetscSectionDestroy(&newCoordSection); /* relinquish our reference */
1034:   DMGetCoordinatesLocal(dm, &coordinates);
1035:   DMSetCoordinatesLocal(sdm, coordinates);
1036:   /* Convert labels */
1037:   DMGetNumLabels(dm, &numLabels);
1038:   for (l = 0; l < numLabels; ++l) {
1039:     const char *lname;
1040:     PetscBool  isDepth;

1042:     DMGetLabelName(dm, l, &lname);
1043:     PetscStrcmp(lname, "depth", &isDepth);
1044:     if (isDepth) continue;
1045:     DMCreateLabel(sdm, lname);
1046:     DMGetLabelIdIS(dm, lname, &idIS);
1047:     ISGetLocalSize(idIS, &numFS);
1048:     ISGetIndices(idIS, &ids);
1049:     for (fs = 0; fs < numFS; ++fs) {
1050:       IS             pointIS;
1051:       const PetscInt *points;
1052:       PetscInt       numPoints;

1054:       DMGetStratumIS(dm, lname, ids[fs], &pointIS);
1055:       ISGetLocalSize(pointIS, &numPoints);
1056:       ISGetIndices(pointIS, &points);
1057:       for (p = 0; p < numPoints; ++p) {
1058:         PetscInt newpoint = points[p];

1060:         DMSetLabelValue(sdm, lname, newpoint, ids[fs]);
1061:       }
1062:       ISRestoreIndices(pointIS, &points);
1063:       ISDestroy(&pointIS);
1064:     }
1065:     ISRestoreIndices(idIS, &ids);
1066:     ISDestroy(&idIS);
1067:   }
1068:   {
1069:     /* Convert pointSF */
1070:     const PetscSFNode *remotePoints;
1071:     PetscSFNode       *gremotePoints;
1072:     const PetscInt    *localPoints;
1073:     PetscInt          *glocalPoints,*newLocation,*newRemoteLocation;
1074:     PetscInt          numRoots, numLeaves;
1075:     PetscMPIInt       size;

1077:     MPI_Comm_size(PetscObjectComm((PetscObject)dm), &size);
1078:     DMGetPointSF(dm, &sfPoint);
1079:     DMGetPointSF(sdm, &gsfPoint);
1080:     DMPlexGetChart(dm,&pStart,&pEnd);
1081:     PetscSFGetGraph(sfPoint, &numRoots, &numLeaves, &localPoints, &remotePoints);
1082:     if (numRoots >= 0) {
1083:       PetscMalloc2(numRoots,&newLocation,pEnd-pStart,&newRemoteLocation);
1084:       for (l=0; l<numRoots; l++) newLocation[l] = l; /* + (l >= cEnd ? numGhostCells : 0); */
1085:       PetscSFBcastBegin(sfPoint, MPIU_INT, newLocation, newRemoteLocation);
1086:       PetscSFBcastEnd(sfPoint, MPIU_INT, newLocation, newRemoteLocation);
1087:       PetscMalloc1(numLeaves,    &glocalPoints);
1088:       PetscMalloc1(numLeaves, &gremotePoints);
1089:       for (l = 0; l < numLeaves; ++l) {
1090:         glocalPoints[l]        = localPoints[l]; /* localPoints[l] >= cEnd ? localPoints[l] + numGhostCells : localPoints[l]; */
1091:         gremotePoints[l].rank  = remotePoints[l].rank;
1092:         gremotePoints[l].index = newRemoteLocation[localPoints[l]];
1093:       }
1094:       PetscFree2(newLocation,newRemoteLocation);
1095:       PetscSFSetGraph(gsfPoint, numRoots+numGhostCells, numLeaves, glocalPoints, PETSC_OWN_POINTER, gremotePoints, PETSC_OWN_POINTER);
1096:     }
1097:     DMDestroy(dmSplit);
1098:     *dmSplit = sdm;
1099:   }
1100:   return(0);
1101: }

1103: PetscErrorCode CreatePartitionVec(DM dm, DM *dmCell, Vec *partition)
1104: {
1105:   PetscSF        sfPoint;
1106:   PetscSection   coordSection;
1107:   Vec            coordinates;
1108:   PetscSection   sectionCell;
1109:   PetscScalar    *part;
1110:   PetscInt       cStart, cEnd, c;
1111:   PetscMPIInt    rank;

1115:   DMGetCoordinateSection(dm, &coordSection);
1116:   DMGetCoordinatesLocal(dm, &coordinates);
1117:   DMClone(dm, dmCell);
1118:   DMGetPointSF(dm, &sfPoint);
1119:   DMSetPointSF(*dmCell, sfPoint);
1120:   DMSetCoordinateSection(*dmCell, PETSC_DETERMINE, coordSection);
1121:   DMSetCoordinatesLocal(*dmCell, coordinates);
1122:   MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);
1123:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionCell);
1124:   DMPlexGetHeightStratum(*dmCell, 0, &cStart, &cEnd);
1125:   PetscSectionSetChart(sectionCell, cStart, cEnd);
1126:   for (c = cStart; c < cEnd; ++c) {
1127:     PetscSectionSetDof(sectionCell, c, 1);
1128:   }
1129:   PetscSectionSetUp(sectionCell);
1130:   DMSetDefaultSection(*dmCell, sectionCell);
1131:   PetscSectionDestroy(&sectionCell);
1132:   DMCreateLocalVector(*dmCell, partition);
1133:   PetscObjectSetName((PetscObject)*partition, "partition");
1134:   VecGetArray(*partition, &part);
1135:   for (c = cStart; c < cEnd; ++c) {
1136:     PetscScalar *p;

1138:     DMPlexPointLocalRef(*dmCell, c, part, &p);
1139:     p[0] = rank;
1140:   }
1141:   VecRestoreArray(*partition, &part);
1142:   return(0);
1143: }

1145: PetscErrorCode CreateMassMatrix(DM dm, Vec *massMatrix, User user)
1146: {
1147:   DM                dmMass, dmFace, dmCell, dmCoord;
1148:   PetscSection      coordSection;
1149:   Vec               coordinates, facegeom, cellgeom;
1150:   PetscSection      sectionMass;
1151:   PetscScalar       *m;
1152:   const PetscScalar *fgeom, *cgeom, *coords;
1153:   PetscInt          vStart, vEnd, v;
1154:   PetscErrorCode    ierr;

1157:   DMGetCoordinateSection(dm, &coordSection);
1158:   DMGetCoordinatesLocal(dm, &coordinates);
1159:   DMClone(dm, &dmMass);
1160:   DMSetCoordinateSection(dmMass, PETSC_DETERMINE, coordSection);
1161:   DMSetCoordinatesLocal(dmMass, coordinates);
1162:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionMass);
1163:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
1164:   PetscSectionSetChart(sectionMass, vStart, vEnd);
1165:   for (v = vStart; v < vEnd; ++v) {
1166:     PetscInt numFaces;

1168:     DMPlexGetSupportSize(dmMass, v, &numFaces);
1169:     PetscSectionSetDof(sectionMass, v, numFaces*numFaces);
1170:   }
1171:   PetscSectionSetUp(sectionMass);
1172:   DMSetDefaultSection(dmMass, sectionMass);
1173:   PetscSectionDestroy(&sectionMass);
1174:   DMGetLocalVector(dmMass, massMatrix);
1175:   VecGetArray(*massMatrix, &m);
1176:   DMPlexTSGetGeometryFVM(dm, &facegeom, &cellgeom, NULL);
1177:   VecGetDM(facegeom, &dmFace);
1178:   VecGetArrayRead(facegeom, &fgeom);
1179:   VecGetDM(cellgeom, &dmCell);
1180:   VecGetArrayRead(cellgeom, &cgeom);
1181:   DMGetCoordinateDM(dm, &dmCoord);
1182:   VecGetArrayRead(coordinates, &coords);
1183:   for (v = vStart; v < vEnd; ++v) {
1184:     const PetscInt        *faces;
1185:     PetscFVFaceGeom       *fgA, *fgB, *cg;
1186:     PetscScalar           *vertex;
1187:     PetscInt               numFaces, sides[2], f, g;

1189:     DMPlexPointLocalRead(dmCoord, v, coords, &vertex);
1190:     DMPlexGetSupportSize(dmMass, v, &numFaces);
1191:     DMPlexGetSupport(dmMass, v, &faces);
1192:     for (f = 0; f < numFaces; ++f) {
1193:       sides[0] = faces[f];
1194:       DMPlexPointLocalRead(dmFace, faces[f], fgeom, &fgA);
1195:       for (g = 0; g < numFaces; ++g) {
1196:         const PetscInt *cells = NULL;
1197:         PetscReal      area   = 0.0;
1198:         PetscInt       numCells;

1200:         sides[1] = faces[g];
1201:         DMPlexPointLocalRead(dmFace, faces[g], fgeom, &fgB);
1202:         DMPlexGetJoin(dmMass, 2, sides, &numCells, &cells);
1203:         if (numCells != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Invalid join for faces");
1204:         DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cg);
1205:         area += PetscAbsScalar((vertex[0] - cg->centroid[0])*(fgA->centroid[1] - cg->centroid[1]) - (vertex[1] - cg->centroid[1])*(fgA->centroid[0] - cg->centroid[0]));
1206:         area += PetscAbsScalar((vertex[0] - cg->centroid[0])*(fgB->centroid[1] - cg->centroid[1]) - (vertex[1] - cg->centroid[1])*(fgB->centroid[0] - cg->centroid[0]));
1207:         m[f*numFaces+g] = Dot2Real(fgA->normal, fgB->normal)*area*0.5;
1208:         DMPlexRestoreJoin(dmMass, 2, sides, &numCells, &cells);
1209:       }
1210:     }
1211:   }
1212:   VecRestoreArrayRead(facegeom, &fgeom);
1213:   VecRestoreArrayRead(cellgeom, &cgeom);
1214:   VecRestoreArrayRead(coordinates, &coords);
1215:   VecRestoreArray(*massMatrix, &m);
1216:   DMDestroy(&dmMass);
1217:   return(0);
1218: }

1220: /* Behavior will be different for multi-physics or when using non-default boundary conditions */
1221: static PetscErrorCode ModelSolutionSetDefault(Model mod,SolutionFunction func,void *ctx)
1222: {
1224:   mod->solution    = func;
1225:   mod->solutionctx = ctx;
1226:   return(0);
1227: }

1229: static PetscErrorCode ModelFunctionalRegister(Model mod,const char *name,PetscInt *offset,FunctionalFunction func,void *ctx)
1230: {
1232:   FunctionalLink link,*ptr;
1233:   PetscInt       lastoffset = -1;

1236:   for (ptr=&mod->functionalRegistry; *ptr; ptr = &(*ptr)->next) lastoffset = (*ptr)->offset;
1237:   PetscNew(&link);
1238:   PetscStrallocpy(name,&link->name);
1239:   link->offset = lastoffset + 1;
1240:   link->func   = func;
1241:   link->ctx    = ctx;
1242:   link->next   = NULL;
1243:   *ptr         = link;
1244:   *offset      = link->offset;
1245:   return(0);
1246: }

1248: static PetscErrorCode ModelFunctionalSetFromOptions(Model mod,PetscOptionItems *PetscOptionsObject)
1249: {
1251:   PetscInt       i,j;
1252:   FunctionalLink link;
1253:   char           *names[256];

1256:   mod->numMonitored = ALEN(names);
1257:   PetscOptionsStringArray("-monitor","list of functionals to monitor","",names,&mod->numMonitored,NULL);
1258:   /* Create list of functionals that will be computed somehow */
1259:   PetscMalloc1(mod->numMonitored,&mod->functionalMonitored);
1260:   /* Create index of calls that we will have to make to compute these functionals (over-allocation in general). */
1261:   PetscMalloc1(mod->numMonitored,&mod->functionalCall);
1262:   mod->numCall = 0;
1263:   for (i=0; i<mod->numMonitored; i++) {
1264:     for (link=mod->functionalRegistry; link; link=link->next) {
1265:       PetscBool match;
1266:       PetscStrcasecmp(names[i],link->name,&match);
1267:       if (match) break;
1268:     }
1269:     if (!link) SETERRQ1(mod->comm,PETSC_ERR_USER,"No known functional '%s'",names[i]);
1270:     mod->functionalMonitored[i] = link;
1271:     for (j=0; j<i; j++) {
1272:       if (mod->functionalCall[j]->func == link->func && mod->functionalCall[j]->ctx == link->ctx) goto next_name;
1273:     }
1274:     mod->functionalCall[mod->numCall++] = link; /* Just points to the first link using the result. There may be more results. */
1275: next_name:
1276:     PetscFree(names[i]);
1277:   }

1279:   /* Find out the maximum index of any functional computed by a function we will be calling (even if we are not using it) */
1280:   mod->maxComputed = -1;
1281:   for (link=mod->functionalRegistry; link; link=link->next) {
1282:     for (i=0; i<mod->numCall; i++) {
1283:       FunctionalLink call = mod->functionalCall[i];
1284:       if (link->func == call->func && link->ctx == call->ctx) {
1285:         mod->maxComputed = PetscMax(mod->maxComputed,link->offset);
1286:       }
1287:     }
1288:   }
1289:   return(0);
1290: }

1292: static PetscErrorCode FunctionalLinkDestroy(FunctionalLink *link)
1293: {
1295:   FunctionalLink l,next;

1298:   if (!link) return(0);
1299:   l     = *link;
1300:   *link = NULL;
1301:   for (; l; l=next) {
1302:     next = l->next;
1303:     PetscFree(l->name);
1304:     PetscFree(l);
1305:   }
1306:   return(0);
1307: }

1309: /* put the solution callback into a functional callback */
1310: static PetscErrorCode SolutionFunctional(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *modctx)
1311: {
1312:   Model          mod;
1315:   mod  = (Model) modctx;
1316:   (*mod->solution)(mod, time, x, u, mod->solutionctx);
1317:   return(0);
1318: }

1320: PetscErrorCode SetInitialCondition(DM dm, Vec X, User user)
1321: {
1322:   PetscErrorCode     (*func[1]) (PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
1323:   void               *ctx[1];
1324:   Model              mod = user->model;
1325:   PetscErrorCode     ierr;

1328:   func[0] = SolutionFunctional;
1329:   ctx[0]  = (void *) mod;
1330:   DMProjectFunction(dm,0.0,func,ctx,INSERT_ALL_VALUES,X);
1331:   return(0);
1332: }

1334: static PetscErrorCode OutputVTK(DM dm, const char *filename, PetscViewer *viewer)
1335: {

1339:   PetscViewerCreate(PetscObjectComm((PetscObject)dm), viewer);
1340:   PetscViewerSetType(*viewer, PETSCVIEWERVTK);
1341:   PetscViewerFileSetName(*viewer, filename);
1342:   return(0);
1343: }

1345: static PetscErrorCode MonitorVTK(TS ts,PetscInt stepnum,PetscReal time,Vec X,void *ctx)
1346: {
1347:   User           user = (User)ctx;
1348:   DM             dm;
1349:   Vec            cellgeom;
1350:   PetscViewer    viewer;
1351:   char           filename[PETSC_MAX_PATH_LEN],*ftable = NULL;
1352:   PetscReal      xnorm;
1353:   PetscInt       cEndInterior;

1357:   PetscObjectSetName((PetscObject) X, "u");
1358:   VecGetDM(X,&dm);
1359:   DMPlexTSGetGeometryFVM(dm, NULL, &cellgeom, NULL);
1360:   VecNorm(X,NORM_INFINITY,&xnorm);

1362:   if (stepnum >= 0) {
1363:     stepnum += user->monitorStepOffset;
1364:   }
1365:   if (stepnum >= 0) {           /* No summary for final time */
1366:     Model             mod = user->model;
1367:     PetscInt          c,cStart,cEnd,fcount,i;
1368:     size_t            ftableused,ftablealloc;
1369:     const PetscScalar *cgeom,*x;
1370:     DM                dmCell;
1371:     DMLabel           vtkLabel;
1372:     PetscReal         *fmin,*fmax,*fintegral,*ftmp;
1373:     fcount = mod->maxComputed+1;
1374:     PetscMalloc4(fcount,&fmin,fcount,&fmax,fcount,&fintegral,fcount,&ftmp);
1375:     for (i=0; i<fcount; i++) {
1376:       fmin[i]      = PETSC_MAX_REAL;
1377:       fmax[i]      = PETSC_MIN_REAL;
1378:       fintegral[i] = 0;
1379:     }
1380:     VecGetDM(cellgeom,&dmCell);
1381:     DMPlexGetHybridBounds(dmCell, &cEndInterior, NULL, NULL, NULL);
1382:     DMPlexGetHeightStratum(dmCell,0,&cStart,&cEnd);
1383:     VecGetArrayRead(cellgeom,&cgeom);
1384:     VecGetArrayRead(X,&x);
1385:     DMGetLabel(dm,"vtk",&vtkLabel);
1386:     for (c = cStart; c < cEndInterior; ++c) {
1387:       PetscFVCellGeom       *cg;
1388:       const PetscScalar     *cx    = NULL;
1389:       PetscInt              vtkVal = 0;

1391:       /* not that these two routines as currently implemented work for any dm with a
1392:        * defaultSection/defaultGlobalSection */
1393:       DMPlexPointLocalRead(dmCell,c,cgeom,&cg);
1394:       DMPlexPointGlobalRead(dm,c,x,&cx);
1395:       if (vtkLabel) {DMLabelGetValue(vtkLabel,c,&vtkVal);}
1396:       if (!vtkVal || !cx) continue;        /* ghost, or not a global cell */
1397:       for (i=0; i<mod->numCall; i++) {
1398:         FunctionalLink flink = mod->functionalCall[i];
1399:         (*flink->func)(mod,time,cg->centroid,cx,ftmp,flink->ctx);
1400:       }
1401:       for (i=0; i<fcount; i++) {
1402:         fmin[i]       = PetscMin(fmin[i],ftmp[i]);
1403:         fmax[i]       = PetscMax(fmax[i],ftmp[i]);
1404:         fintegral[i] += cg->volume * ftmp[i];
1405:       }
1406:     }
1407:     VecRestoreArrayRead(cellgeom,&cgeom);
1408:     VecRestoreArrayRead(X,&x);
1409:     MPI_Allreduce(MPI_IN_PLACE,fmin,fcount,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)ts));
1410:     MPI_Allreduce(MPI_IN_PLACE,fmax,fcount,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
1411:     MPI_Allreduce(MPI_IN_PLACE,fintegral,fcount,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));

1413:     ftablealloc = fcount * 100;
1414:     ftableused  = 0;
1415:     PetscMalloc1(ftablealloc,&ftable);
1416:     for (i=0; i<mod->numMonitored; i++) {
1417:       size_t         countused;
1418:       char           buffer[256],*p;
1419:       FunctionalLink flink = mod->functionalMonitored[i];
1420:       PetscInt       id    = flink->offset;
1421:       if (i % 3) {
1422:         PetscMemcpy(buffer,"  ",2);
1423:         p    = buffer + 2;
1424:       } else if (i) {
1425:         char newline[] = "\n";
1426:         PetscMemcpy(buffer,newline,sizeof newline-1);
1427:         p    = buffer + sizeof newline - 1;
1428:       } else {
1429:         p = buffer;
1430:       }
1431:       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]);
1432:       countused += p - buffer;
1433:       if (countused > ftablealloc-ftableused-1) { /* reallocate */
1434:         char *ftablenew;
1435:         ftablealloc = 2*ftablealloc + countused;
1436:         PetscMalloc(ftablealloc,&ftablenew);
1437:         PetscMemcpy(ftablenew,ftable,ftableused);
1438:         PetscFree(ftable);
1439:         ftable = ftablenew;
1440:       }
1441:       PetscMemcpy(ftable+ftableused,buffer,countused);
1442:       ftableused += countused;
1443:       ftable[ftableused] = 0;
1444:     }
1445:     PetscFree4(fmin,fmax,fintegral,ftmp);

1447:     PetscPrintf(PetscObjectComm((PetscObject)ts),"% 3D  time %8.4g  |x| %8.4g  %s\n",stepnum,(double)time,(double)xnorm,ftable ? ftable : "");
1448:     PetscFree(ftable);
1449:   }
1450:   if (user->vtkInterval < 1) return(0);
1451:   if ((stepnum == -1) ^ (stepnum % user->vtkInterval == 0)) {
1452:     if (stepnum == -1) {        /* Final time is not multiple of normal time interval, write it anyway */
1453:       TSGetStepNumber(ts,&stepnum);
1454:     }
1455:     PetscSNPrintf(filename,sizeof filename,"%s-%03D.vtu",user->outputBasename,stepnum);
1456:     OutputVTK(dm,filename,&viewer);
1457:     VecView(X,viewer);
1458:     PetscViewerDestroy(&viewer);
1459:   }
1460:   return(0);
1461: }

1463: static PetscErrorCode initializeTS(DM dm, User user, TS *ts)
1464: {

1468:   TSCreate(PetscObjectComm((PetscObject)dm), ts);
1469:   TSSetType(*ts, TSSSP);
1470:   TSSetDM(*ts, dm);
1471:   TSMonitorSet(*ts,MonitorVTK,user,NULL);
1472:   DMTSSetBoundaryLocal(dm, DMPlexTSComputeBoundary, user);
1473:   DMTSSetRHSFunctionLocal(dm, DMPlexTSComputeRHSFunctionFVM, user);
1474:   TSSetMaxTime(*ts,2.0);
1475:   TSSetExactFinalTime(*ts,TS_EXACTFINALTIME_STEPOVER);
1476:   return(0);
1477: }

1479: static PetscErrorCode adaptToleranceFVM(PetscFV fvm, TS ts, Vec sol, VecTagger refineTag, VecTagger coarsenTag, User user, TS *tsNew, Vec *solNew)
1480: {
1481:   DM                dm, gradDM, plex, cellDM, adaptedDM = NULL;
1482:   Vec               cellGeom, faceGeom;
1483:   PetscBool         isForest, computeGradient;
1484:   Vec               grad, locGrad, locX, errVec;
1485:   PetscInt          cStart, cEnd, cEndInterior, c, dim, nRefine, nCoarsen;
1486:   PetscReal         minMaxInd[2] = {PETSC_MAX_REAL, PETSC_MIN_REAL}, minMaxIndGlobal[2], minInd, maxInd, time;
1487:   PetscScalar       *errArray;
1488:   const PetscScalar *pointVals;
1489:   const PetscScalar *pointGrads;
1490:   const PetscScalar *pointGeom;
1491:   DMLabel           adaptLabel = NULL;
1492:   IS                refineIS, coarsenIS;
1493:   PetscErrorCode    ierr;

1496:   TSGetTime(ts,&time);
1497:   VecGetDM(sol, &dm);
1498:   DMGetDimension(dm,&dim);
1499:   PetscFVGetComputeGradients(fvm,&computeGradient);
1500:   PetscFVSetComputeGradients(fvm,PETSC_TRUE);
1501:   DMIsForest(dm, &isForest);
1502:   DMConvert(dm, DMPLEX, &plex);
1503:   DMPlexGetDataFVM(plex, fvm, &cellGeom, &faceGeom, &gradDM);
1504:   DMCreateLocalVector(plex,&locX);
1505:   DMPlexInsertBoundaryValues(plex, PETSC_TRUE, locX, 0.0, faceGeom, cellGeom, NULL);
1506:   DMGlobalToLocalBegin(plex, sol, INSERT_VALUES, locX);
1507:   DMGlobalToLocalEnd  (plex, sol, INSERT_VALUES, locX);
1508:   DMCreateGlobalVector(gradDM, &grad);
1509:   DMPlexReconstructGradientsFVM(plex, locX, grad);
1510:   DMCreateLocalVector(gradDM, &locGrad);
1511:   DMGlobalToLocalBegin(gradDM, grad, INSERT_VALUES, locGrad);
1512:   DMGlobalToLocalEnd(gradDM, grad, INSERT_VALUES, locGrad);
1513:   VecDestroy(&grad);
1514:   DMPlexGetHeightStratum(plex,0,&cStart,&cEnd);
1515:   DMPlexGetHybridBounds(plex,&cEndInterior,NULL,NULL,NULL);
1516:   cEnd = (cEndInterior < 0) ? cEnd : cEndInterior;
1517:   VecGetArrayRead(locGrad,&pointGrads);
1518:   VecGetArrayRead(cellGeom,&pointGeom);
1519:   VecGetArrayRead(locX,&pointVals);
1520:   VecGetDM(cellGeom,&cellDM);
1521:   DMLabelCreate("adapt",&adaptLabel);
1522:   VecCreateMPI(PetscObjectComm((PetscObject)plex),cEnd-cStart,PETSC_DETERMINE,&errVec);
1523:   VecSetUp(errVec);
1524:   VecGetArray(errVec,&errArray);
1525:   for (c = cStart; c < cEnd; c++) {
1526:     PetscReal             errInd = 0.;
1527:     PetscScalar           *pointGrad;
1528:     PetscScalar           *pointVal;
1529:     PetscFVCellGeom       *cg;

1531:     DMPlexPointLocalRead(gradDM,c,pointGrads,&pointGrad);
1532:     DMPlexPointLocalRead(cellDM,c,pointGeom,&cg);
1533:     DMPlexPointLocalRead(plex,c,pointVals,&pointVal);

1535:     (user->model->errorIndicator)(dim,cg->volume,user->model->physics->dof,pointVal,pointGrad,&errInd,user->model->errorCtx);
1536:     errArray[c-cStart] = errInd;
1537:     minMaxInd[0] = PetscMin(minMaxInd[0],errInd);
1538:     minMaxInd[1] = PetscMax(minMaxInd[1],errInd);
1539:   }
1540:   VecRestoreArray(errVec,&errArray);
1541:   VecRestoreArrayRead(locX,&pointVals);
1542:   VecRestoreArrayRead(cellGeom,&pointGeom);
1543:   VecRestoreArrayRead(locGrad,&pointGrads);
1544:   VecDestroy(&locGrad);
1545:   VecDestroy(&locX);
1546:   DMDestroy(&plex);

1548:   VecTaggerComputeIS(refineTag,errVec,&refineIS);
1549:   VecTaggerComputeIS(coarsenTag,errVec,&coarsenIS);
1550:   ISGetSize(refineIS,&nRefine);
1551:   ISGetSize(coarsenIS,&nCoarsen);
1552:   if (nRefine) {DMLabelSetStratumIS(adaptLabel,DM_ADAPT_REFINE,refineIS);}
1553:   if (nCoarsen) {DMLabelSetStratumIS(adaptLabel,DM_ADAPT_COARSEN,coarsenIS);}
1554:   ISDestroy(&coarsenIS);
1555:   ISDestroy(&refineIS);
1556:   VecDestroy(&errVec);

1558:   PetscFVSetComputeGradients(fvm,computeGradient);
1559:   minMaxInd[1] = -minMaxInd[1];
1560:   MPI_Allreduce(minMaxInd,minMaxIndGlobal,2,MPIU_REAL,MPI_MIN,PetscObjectComm((PetscObject)dm));
1561:   minInd = minMaxIndGlobal[0];
1562:   maxInd = -minMaxIndGlobal[1];
1563:   PetscInfo2(ts, "error indicator range (%E, %E)\n", minInd, maxInd);
1564:   if (nRefine || nCoarsen) { /* at least one cell is over the refinement threshold */
1565:     DMAdaptLabel(dm,adaptLabel,&adaptedDM);
1566:   }
1567:   DMLabelDestroy(&adaptLabel);
1568:   if (adaptedDM) {
1569:     PetscInfo2(ts, "Adapted mesh, marking %D cells for refinement, and %D cells for coarsening\n", nRefine, nCoarsen);
1570:     if (tsNew) {initializeTS(adaptedDM, user, tsNew);}
1571:     if (solNew) {
1572:       DMCreateGlobalVector(adaptedDM, solNew);
1573:       PetscObjectSetName((PetscObject) *solNew, "solution");
1574:       DMForestTransferVec(dm, sol, adaptedDM, *solNew, PETSC_TRUE, time);
1575:     }
1576:     if (isForest) {DMForestSetAdaptivityForest(adaptedDM,NULL);} /* clear internal references to the previous dm */
1577:     DMDestroy(&adaptedDM);
1578:   } else {
1579:     if (tsNew)  *tsNew  = NULL;
1580:     if (solNew) *solNew = NULL;
1581:   }
1582:   return(0);
1583: }

1585: int main(int argc, char **argv)
1586: {
1587:   MPI_Comm          comm;
1588:   PetscDS           prob;
1589:   PetscFV           fvm;
1590:   PetscLimiter      limiter = NULL, noneLimiter = NULL;
1591:   User              user;
1592:   Model             mod;
1593:   Physics           phys;
1594:   DM                dm;
1595:   PetscReal         ftime, cfl, dt, minRadius;
1596:   PetscInt          dim, nsteps;
1597:   TS                ts;
1598:   TSConvergedReason reason;
1599:   Vec               X;
1600:   PetscViewer       viewer;
1601:   PetscBool         simplex = PETSC_FALSE, vtkCellGeom, splitFaces, useAMR;
1602:   PetscInt          overlap, adaptInterval;
1603:   char              filename[PETSC_MAX_PATH_LEN] = "";
1604:   char              physname[256]  = "advect";
1605:   VecTagger         refineTag = NULL, coarsenTag = NULL;
1606:   PetscErrorCode    ierr;

1608:   PetscInitialize(&argc, &argv, (char*) 0, help);
1609:   comm = PETSC_COMM_WORLD;

1611:   PetscNew(&user);
1612:   PetscNew(&user->model);
1613:   PetscNew(&user->model->physics);
1614:   mod           = user->model;
1615:   phys          = mod->physics;
1616:   mod->comm     = comm;
1617:   useAMR        = PETSC_FALSE;
1618:   adaptInterval = 1;

1620:   /* Register physical models to be available on the command line */
1621:   PetscFunctionListAdd(&PhysicsList,"advect"          ,PhysicsCreate_Advect);
1622:   PetscFunctionListAdd(&PhysicsList,"sw"              ,PhysicsCreate_SW);
1623:   PetscFunctionListAdd(&PhysicsList,"euler"           ,PhysicsCreate_Euler);

1625:   PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Mesh Options","");
1626:   {
1627:     cfl  = 0.9 * 4; /* default SSPRKS2 with s=5 stages is stable for CFL number s-1 */
1628:     PetscOptionsReal("-ufv_cfl","CFL number per step","",cfl,&cfl,NULL);
1629:     PetscOptionsString("-f","Exodus.II filename to read","",filename,filename,sizeof(filename),NULL);
1630:     PetscOptionsBool("-simplex","Flag to use a simplex mesh","",simplex,&simplex,NULL);
1631:     splitFaces = PETSC_FALSE;
1632:     PetscOptionsBool("-ufv_split_faces","Split faces between cell sets","",splitFaces,&splitFaces,NULL);
1633:     overlap = 1;
1634:     PetscOptionsInt("-ufv_mesh_overlap","Number of cells to overlap partitions","",overlap,&overlap,NULL);
1635:     user->vtkInterval = 1;
1636:     PetscOptionsInt("-ufv_vtk_interval","VTK output interval (0 to disable)","",user->vtkInterval,&user->vtkInterval,NULL);
1637:     vtkCellGeom = PETSC_FALSE;
1638:     PetscStrcpy(user->outputBasename, "ex11");
1639:     PetscOptionsString("-ufv_vtk_basename","VTK output basename","",user->outputBasename,user->outputBasename,PETSC_MAX_PATH_LEN,NULL);
1640:     PetscOptionsBool("-ufv_vtk_cellgeom","Write cell geometry (for debugging)","",vtkCellGeom,&vtkCellGeom,NULL);
1641:     PetscOptionsBool("-ufv_use_amr","use local adaptive mesh refinement","",useAMR,&useAMR,NULL);
1642:     PetscOptionsInt("-ufv_adapt_interval","time steps between AMR","",adaptInterval,&adaptInterval,NULL);
1643:   }
1644:   PetscOptionsEnd();

1646:   if (useAMR) {
1647:     VecTaggerBox refineBox, coarsenBox;

1649:     refineBox.min  = refineBox.max  = PETSC_MAX_REAL;
1650:     coarsenBox.min = coarsenBox.max = PETSC_MIN_REAL;

1652:     VecTaggerCreate(comm,&refineTag);
1653:     PetscObjectSetOptionsPrefix((PetscObject)refineTag,"refine_");
1654:     VecTaggerSetType(refineTag,VECTAGGERABSOLUTE);
1655:     VecTaggerAbsoluteSetBox(refineTag,&refineBox);
1656:     VecTaggerSetFromOptions(refineTag);
1657:     VecTaggerSetUp(refineTag);
1658:     PetscObjectViewFromOptions((PetscObject)refineTag,NULL,"-tag_view");

1660:     VecTaggerCreate(comm,&coarsenTag);
1661:     PetscObjectSetOptionsPrefix((PetscObject)coarsenTag,"coarsen_");
1662:     VecTaggerSetType(coarsenTag,VECTAGGERABSOLUTE);
1663:     VecTaggerAbsoluteSetBox(coarsenTag,&coarsenBox);
1664:     VecTaggerSetFromOptions(coarsenTag);
1665:     VecTaggerSetUp(coarsenTag);
1666:     PetscObjectViewFromOptions((PetscObject)coarsenTag,NULL,"-tag_view");
1667:   }

1669:   PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Physics Options","");
1670:   {
1671:     PetscErrorCode (*physcreate)(Model,Physics,PetscOptionItems*);
1672:     PetscOptionsFList("-physics","Physics module to solve","",PhysicsList,physname,physname,sizeof physname,NULL);
1673:     PetscFunctionListFind(PhysicsList,physname,&physcreate);
1674:     PetscMemzero(phys,sizeof(struct _n_Physics));
1675:     (*physcreate)(mod,phys,PetscOptionsObject);
1676:     /* Count number of fields and dofs */
1677:     for (phys->nfields=0,phys->dof=0; phys->field_desc[phys->nfields].name; phys->nfields++) phys->dof += phys->field_desc[phys->nfields].dof;
1678:     if (phys->dof <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set dof",physname);
1679:     ModelFunctionalSetFromOptions(mod,PetscOptionsObject);
1680:   }
1681:   PetscOptionsEnd();

1683:   /* Create mesh */
1684:   {
1685:     size_t len,i;
1686:     for (i = 0; i < DIM; i++) { mod->bounds[2*i] = 0.; mod->bounds[2*i+1] = 1.;};
1687:     PetscStrlen(filename,&len);
1688:     dim = DIM;
1689:     if (!len) { /* a null name means just do a hex box */
1690:       PetscInt cells[3] = {1, 1, 1}; /* coarse mesh is one cell; refine from there */
1691:       PetscBool flg1, flg2, skew = PETSC_FALSE;
1692:       PetscInt nret1 = DIM;
1693:       PetscInt nret2 = 2*DIM;
1694:       PetscOptionsBegin(comm,NULL,"Rectangular mesh options","");
1695:       PetscOptionsIntArray("-grid_size","number of cells in each direction","",cells,&nret1,&flg1);
1696:       PetscOptionsRealArray("-grid_bounds","bounds of the mesh in each direction (i.e., x_min,x_max,y_min,y_max","",mod->bounds,&nret2,&flg2);
1697:       PetscOptionsBool("-grid_skew_60","Skew grid for 60 degree shock mesh","",skew,&skew,NULL);
1698:       PetscOptionsEnd();
1699:       if (flg1) {
1700:         dim = nret1;
1701:         if (dim != DIM) SETERRQ1(comm,PETSC_ERR_ARG_SIZ,"Dim wrong size %D in -grid_size",dim);
1702:       }
1703:       if (simplex) {
1704:         DMPlexCreateBoxMesh(comm, dim, cells[0], PETSC_TRUE, &dm);
1705:       } else {
1706:         DMPlexCreateHexBoxMesh(comm, dim, cells, mod->bcs[0], mod->bcs[1], mod->bcs[2], &dm);
1707:       }
1708:       if (flg2) {
1709:         PetscInt dimEmbed, i;
1710:         PetscInt nCoords;
1711:         PetscScalar *coords;
1712:         Vec coordinates;

1714:         DMGetCoordinatesLocal(dm,&coordinates);
1715:         DMGetCoordinateDim(dm,&dimEmbed);
1716:         VecGetLocalSize(coordinates,&nCoords);
1717:         if (nCoords % dimEmbed) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Coordinate vector the wrong size");
1718:         VecGetArray(coordinates,&coords);
1719:         for (i = 0; i < nCoords; i += dimEmbed) {
1720:           PetscInt j;

1722:           PetscScalar *coord = &coords[i];
1723:           for (j = 0; j < dimEmbed; j++) {
1724:             coord[j] = mod->bounds[2 * j] + coord[j] * (mod->bounds[2 * j + 1] - mod->bounds[2 * j]);
1725:             if (dim==2 && cells[1]==1 && j==0 && skew) {
1726:               if (cells[0]==2 && i==8) {
1727:                 coord[j] = .57735026918963; /* hack to get 60 deg skewed mesh */
1728:               }
1729:               else if (cells[0]==3) {
1730:                 if(i==2 || i==10) coord[j] = mod->bounds[1]/4.;
1731:                 else if (i==4) coord[j] = mod->bounds[1]/2.;
1732:                 else if (i==12) coord[j] = 1.57735026918963*mod->bounds[1]/2.;
1733:               }
1734:             }
1735:           }
1736:         }
1737:         VecRestoreArray(coordinates,&coords);
1738:         DMSetCoordinatesLocal(dm,coordinates);
1739:       }
1740:     } else {
1741:       DMPlexCreateFromFile(comm, filename, PETSC_TRUE, &dm);
1742:     }
1743:   }
1744:   DMViewFromOptions(dm, NULL, "-orig_dm_view");
1745:   DMGetDimension(dm, &dim);

1747:   /* set up BCs, functions, tags */
1748:   DMCreateLabel(dm, "Face Sets");

1750:   mod->errorIndicator = ErrorIndicator_Simple;

1752:   {
1753:     DM dmDist;

1755:     DMPlexSetAdjacencyUseCone(dm, PETSC_TRUE);
1756:     DMPlexSetAdjacencyUseClosure(dm, PETSC_FALSE);
1757:     DMPlexDistribute(dm, overlap, NULL, &dmDist);
1758:     if (dmDist) {
1759:       DMDestroy(&dm);
1760:       dm   = dmDist;
1761:     }
1762:   }

1764:   DMSetFromOptions(dm);

1766:   {
1767:     DM gdm;

1769:     DMPlexConstructGhostCells(dm, NULL, NULL, &gdm);
1770:     DMDestroy(&dm);
1771:     dm   = gdm;
1772:     DMViewFromOptions(dm, NULL, "-dm_view");
1773:   }
1774:   if (splitFaces) {ConstructCellBoundary(dm, user);}
1775:   SplitFaces(&dm, "split faces", user);

1777:   PetscDSCreate(PetscObjectComm((PetscObject)dm),&prob);
1778:   PetscFVCreate(comm, &fvm);
1779:   PetscFVSetFromOptions(fvm);
1780:   PetscFVSetNumComponents(fvm, phys->dof);
1781:   PetscFVSetSpatialDimension(fvm, dim);
1782:   PetscObjectSetName((PetscObject) fvm,"");
1783:   {
1784:     PetscInt f, dof;
1785:     for (f=0,dof=0; f < phys->nfields; f++) {
1786:       PetscInt newDof = phys->field_desc[f].dof;

1788:       if (newDof == 1) {
1789:         PetscFVSetComponentName(fvm,dof,phys->field_desc[f].name);
1790:       }
1791:       else {
1792:         PetscInt j;

1794:         for (j = 0; j < newDof; j++) {
1795:           char     compName[256]  = "Unknown";

1797:           PetscSNPrintf(compName,sizeof(compName),"%s_%d",phys->field_desc[f].name,j);
1798:           PetscFVSetComponentName(fvm,dof+j,compName);
1799:         }
1800:       }
1801:       dof += newDof;
1802:     }
1803:   }
1804:   /* FV is now structured with one field having all physics as components */
1805:   PetscDSAddDiscretization(prob, (PetscObject) fvm);
1806:   PetscDSSetRiemannSolver(prob, 0, user->model->physics->riemann);
1807:   PetscDSSetContext(prob, 0, user->model->physics);
1808:   (*mod->setupbc)(prob,phys);
1809:   PetscDSSetFromOptions(prob);
1810:   DMSetDS(dm,prob);
1811:   PetscDSDestroy(&prob);
1812:   {
1813:     char      convType[256];
1814:     PetscBool flg;

1816:     PetscOptionsBegin(comm, "", "Mesh conversion options", "DMPLEX");
1817:     PetscOptionsFList("-dm_type","Convert DMPlex to another format","ex12",DMList,DMPLEX,convType,256,&flg);
1818:     PetscOptionsEnd();
1819:     if (flg) {
1820:       DM dmConv;

1822:       DMConvert(dm,convType,&dmConv);
1823:       if (dmConv) {
1824:         DMViewFromOptions(dmConv, NULL, "-dm_conv_view");
1825:         DMDestroy(&dm);
1826:         dm   = dmConv;
1827:         DMSetFromOptions(dm);
1828:       }
1829:     }
1830:   }

1832:   initializeTS(dm, user, &ts);

1834:   DMCreateGlobalVector(dm, &X);
1835:   PetscObjectSetName((PetscObject) X, "solution");
1836:   SetInitialCondition(dm, X, user);
1837:   if (useAMR) {
1838:     PetscInt adaptIter;

1840:     /* use no limiting when reconstructing gradients for adaptivity */
1841:     PetscFVGetLimiter(fvm, &limiter);
1842:     PetscObjectReference((PetscObject) limiter);
1843:     PetscLimiterCreate(PetscObjectComm((PetscObject) fvm), &noneLimiter);
1844:     PetscLimiterSetType(noneLimiter, PETSCLIMITERNONE);

1846:     PetscFVSetLimiter(fvm, noneLimiter);
1847:     for (adaptIter = 0; ; ++adaptIter) {
1848:       PetscLogDouble bytes;
1849:       TS             tsNew = NULL;

1851:       PetscMemoryGetCurrentUsage(&bytes);
1852:       PetscInfo2(ts, "refinement loop %D: memory used %g\n", adaptIter, bytes);
1853:       DMViewFromOptions(dm, NULL, "-initial_dm_view");
1854:       VecViewFromOptions(X, NULL, "-initial_vec_view");
1855: #if 0
1856:       if (viewInitial) {
1857:         PetscViewer viewer;
1858:         char        buf[256];
1859:         PetscBool   isHDF5, isVTK;

1861:         PetscViewerCreate(comm,&viewer);
1862:         PetscViewerSetType(viewer,PETSCVIEWERVTK);
1863:         PetscViewerSetOptionsPrefix(viewer,"initial_");
1864:         PetscViewerSetFromOptions(viewer);
1865:         PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERHDF5,&isHDF5);
1866:         PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERVTK,&isVTK);
1867:         if (isHDF5) {
1868:           PetscSNPrintf(buf, 256, "ex11-initial-%d.h5", adaptIter);
1869:         } else if (isVTK) {
1870:           PetscSNPrintf(buf, 256, "ex11-initial-%d.vtu", adaptIter);
1871:           PetscViewerPushFormat(viewer,PETSC_VIEWER_VTK_VTU);
1872:         }
1873:         PetscViewerFileSetMode(viewer,FILE_MODE_WRITE);
1874:         PetscViewerFileSetName(viewer,buf);
1875:         if (isHDF5) {
1876:           DMView(dm,viewer);
1877:           PetscViewerFileSetMode(viewer,FILE_MODE_UPDATE);
1878:         }
1879:         VecView(X,viewer);
1880:         PetscViewerDestroy(&viewer);
1881:       }
1882: #endif

1884:       adaptToleranceFVM(fvm, ts, X, refineTag, coarsenTag, user, &tsNew, NULL);
1885:       if (!tsNew) {
1886:         break;
1887:       } else {
1888:         DMDestroy(&dm);
1889:         VecDestroy(&X);
1890:         TSDestroy(&ts);
1891:         ts   = tsNew;
1892:         TSGetDM(ts,&dm);
1893:         PetscObjectReference((PetscObject)dm);
1894:         DMCreateGlobalVector(dm,&X);
1895:         PetscObjectSetName((PetscObject) X, "solution");
1896:         SetInitialCondition(dm, X, user);
1897:       }
1898:     }
1899:     /* restore original limiter */
1900:     PetscFVSetLimiter(fvm, limiter);
1901:   }

1903:   if (vtkCellGeom) {
1904:     DM  dmCell;
1905:     Vec cellgeom, partition;

1907:     DMPlexTSGetGeometryFVM(dm, NULL, &cellgeom, NULL);
1908:     OutputVTK(dm, "ex11-cellgeom.vtk", &viewer);
1909:     VecView(cellgeom, viewer);
1910:     PetscViewerDestroy(&viewer);
1911:     CreatePartitionVec(dm, &dmCell, &partition);
1912:     OutputVTK(dmCell, "ex11-partition.vtk", &viewer);
1913:     VecView(partition, viewer);
1914:     PetscViewerDestroy(&viewer);
1915:     VecDestroy(&partition);
1916:     DMDestroy(&dmCell);
1917:   }

1919:   /* collect max maxspeed from all processes -- todo */
1920:   DMPlexTSGetGeometryFVM(dm, NULL, NULL, &minRadius);
1921:   MPI_Allreduce(&phys->maxspeed,&mod->maxspeed,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
1922:   if (mod->maxspeed <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set maxspeed",physname);
1923:   dt   = cfl * minRadius / mod->maxspeed;
1924:   TSSetTimeStep(ts,dt);
1925:   TSSetFromOptions(ts);
1926:   if (!useAMR) {
1927:     TSSolve(ts,X);
1928:     TSGetSolveTime(ts,&ftime);
1929:     TSGetStepNumber(ts,&nsteps);
1930:   } else {
1931:     PetscReal finalTime;
1932:     PetscInt  adaptIter;
1933:     TS        tsNew = NULL;
1934:     Vec       solNew = NULL;

1936:     TSGetMaxTime(ts,&finalTime);
1937:     TSSetMaxSteps(ts,adaptInterval);
1938:     TSSolve(ts,X);
1939:     TSGetSolveTime(ts,&ftime);
1940:     TSGetStepNumber(ts,&nsteps);
1941:     for (adaptIter = 0;ftime < finalTime;adaptIter++) {
1942:       PetscLogDouble bytes;

1944:       PetscMemoryGetCurrentUsage(&bytes);
1945:       PetscInfo2(ts, "AMR time step loop %D: memory used %g\n", adaptIter, bytes);
1946:       PetscFVSetLimiter(fvm,noneLimiter);
1947:       adaptToleranceFVM(fvm,ts,X,refineTag,coarsenTag,user,&tsNew,&solNew);
1948:       PetscFVSetLimiter(fvm,limiter);
1949:       if (tsNew) {
1950:         PetscInfo(ts, "AMR used\n");
1951:         DMDestroy(&dm);
1952:         VecDestroy(&X);
1953:         TSDestroy(&ts);
1954:         ts   = tsNew;
1955:         X    = solNew;
1956:         TSSetFromOptions(ts);
1957:         VecGetDM(X,&dm);
1958:         PetscObjectReference((PetscObject)dm);
1959:         DMPlexTSGetGeometryFVM(dm, NULL, NULL, &minRadius);
1960:         MPI_Allreduce(&phys->maxspeed,&mod->maxspeed,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
1961:         if (mod->maxspeed <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set maxspeed",physname);
1962:         dt   = cfl * minRadius / mod->maxspeed;
1963:         TSSetStepNumber(ts,nsteps);
1964:         TSSetTime(ts,ftime);
1965:         TSSetTimeStep(ts,dt);
1966:       } else {
1967:         PetscInfo(ts, "AMR not used\n");
1968:       }
1969:       user->monitorStepOffset = nsteps;
1970:       TSSetMaxSteps(ts,nsteps+adaptInterval);
1971:       TSSolve(ts,X);
1972:       TSGetSolveTime(ts,&ftime);
1973:       TSGetStepNumber(ts,&nsteps);
1974:     }
1975:   }
1976:   TSGetConvergedReason(ts,&reason);
1977:   PetscPrintf(PETSC_COMM_WORLD,"%s at time %g after %D steps\n",TSConvergedReasons[reason],(double)ftime,nsteps);
1978:   TSDestroy(&ts);

1980:   VecTaggerDestroy(&refineTag);
1981:   VecTaggerDestroy(&coarsenTag);
1982:   PetscFunctionListDestroy(&PhysicsList);
1983:   FunctionalLinkDestroy(&user->model->functionalRegistry);
1984:   PetscFree(user->model->functionalMonitored);
1985:   PetscFree(user->model->functionalCall);
1986:   PetscFree(user->model->physics->data);
1987:   PetscFree(user->model->physics);
1988:   PetscFree(user->model);
1989:   PetscFree(user);
1990:   VecDestroy(&X);
1991:   PetscLimiterDestroy(&limiter);
1992:   PetscLimiterDestroy(&noneLimiter);
1993:   PetscFVDestroy(&fvm);
1994:   DMDestroy(&dm);
1995:   PetscFinalize();
1996:   return ierr;
1997: }

1999: /* Godunov fluxs */
2000: PetscScalar cvmgp_(PetscScalar *a, PetscScalar *b, PetscScalar *test)
2001: {
2002:     /* System generated locals */
2003:     PetscScalar ret_val;

2005:     if (PetscRealPart(*test) > 0.) {
2006:         goto L10;
2007:     }
2008:     ret_val = *b;
2009:     return ret_val;
2010: L10:
2011:     ret_val = *a;
2012:     return ret_val;
2013: } /* cvmgp_ */

2015: PetscScalar cvmgm_(PetscScalar *a, PetscScalar *b, PetscScalar *test)
2016: {
2017:     /* System generated locals */
2018:     PetscScalar ret_val;

2020:     if (PetscRealPart(*test) < 0.) {
2021:         goto L10;
2022:     }
2023:     ret_val = *b;
2024:     return ret_val;
2025: L10:
2026:     ret_val = *a;
2027:     return ret_val;
2028: } /* cvmgm_ */

2030: int riem1mdt( PetscScalar *gaml, PetscScalar *gamr, PetscScalar *rl, PetscScalar *pl,
2031:               PetscScalar *uxl, PetscScalar *rr, PetscScalar *pr,
2032:               PetscScalar *uxr, PetscScalar *rstarl, PetscScalar *rstarr, PetscScalar *
2033:               pstar, PetscScalar *ustar)
2034: {
2035:     /* Initialized data */

2037:     static PetscScalar smallp = 1e-8;

2039:     /* System generated locals */
2040:     int i__1;
2041:     PetscScalar d__1, d__2;

2043:     /* Local variables */
2044:     static int i0;
2045:     static PetscScalar cl, cr, wl, zl, wr, zr, pst, durl, skpr1, skpr2;
2046:     static int iwave;
2047:     static PetscScalar gascl4, gascr4, cstarl, dpstar, cstarr;
2048:     /* static PetscScalar csqrl, csqrr, gascl1, gascl2, gascl3, gascr1, gascr2, gascr3; */
2049:     static int iterno;
2050:     static PetscScalar ustarl, ustarr, rarepr1, rarepr2;



2054:     /* gascl1 = *gaml - 1.; */
2055:     /* gascl2 = (*gaml + 1.) * .5; */
2056:     /* gascl3 = gascl2 / *gaml; */
2057:     gascl4 = 1. / (*gaml - 1.);

2059:     /* gascr1 = *gamr - 1.; */
2060:     /* gascr2 = (*gamr + 1.) * .5; */
2061:     /* gascr3 = gascr2 / *gamr; */
2062:     gascr4 = 1. / (*gamr - 1.);
2063:     iterno = 10;
2064: /*        find pstar: */
2065:     cl = PetscSqrtScalar(*gaml * *pl / *rl);
2066:     cr = PetscSqrtScalar(*gamr * *pr / *rr);
2067:     wl = *rl * cl;
2068:     wr = *rr * cr;
2069:     /* csqrl = wl * wl; */
2070:     /* csqrr = wr * wr; */
2071:     *pstar = (wl * *pr + wr * *pl) / (wl + wr);
2072:     *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
2073:     pst = *pl / *pr;
2074:     skpr1 = cr * (pst - 1.) * PetscSqrtScalar(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
2075:     d__1 = (*gamr - 1.) / (*gamr * 2.);
2076:     rarepr2 = gascr4 * 2. * cr * (1. - PetscPowScalar(pst, d__1));
2077:     pst = *pr / *pl;
2078:     skpr2 = cl * (pst - 1.) * PetscSqrtScalar(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
2079:     d__1 = (*gaml - 1.) / (*gaml * 2.);
2080:     rarepr1 = gascl4 * 2. * cl * (1. - PetscPowScalar(pst, d__1));
2081:     durl = *uxr - *uxl;
2082:     if (PetscRealPart(*pr) < PetscRealPart(*pl)) {
2083:         if (PetscRealPart(durl) >= PetscRealPart(rarepr1)) {
2084:             iwave = 100;
2085:         } else if (PetscRealPart(durl) <= PetscRealPart(-skpr1)) {
2086:             iwave = 300;
2087:         } else {
2088:             iwave = 400;
2089:         }
2090:     } else {
2091:         if (PetscRealPart(durl) >= PetscRealPart(rarepr2)) {
2092:             iwave = 100;
2093:         } else if (PetscRealPart(durl) <= PetscRealPart(-skpr2)) {
2094:             iwave = 300;
2095:         } else {
2096:             iwave = 200;
2097:         }
2098:     }
2099:     if (iwave == 100) {
2100: /*     1-wave: rarefaction wave, 3-wave: rarefaction wave */
2101: /*     case (100) */
2102:         i__1 = iterno;
2103:         for (i0 = 1; i0 <= i__1; ++i0) {
2104:             d__1 = *pstar / *pl;
2105:             d__2 = 1. / *gaml;
2106:             *rstarl = *rl * PetscPowScalar(d__1, d__2);
2107:             cstarl = PetscSqrtScalar(*gaml * *pstar / *rstarl);
2108:             ustarl = *uxl - gascl4 * 2. * (cstarl - cl);
2109:             zl = *rstarl * cstarl;
2110:             d__1 = *pstar / *pr;
2111:             d__2 = 1. / *gamr;
2112:             *rstarr = *rr * PetscPowScalar(d__1, d__2);
2113:             cstarr = PetscSqrtScalar(*gamr * *pstar / *rstarr);
2114:             ustarr = *uxr + gascr4 * 2. * (cstarr - cr);
2115:             zr = *rstarr * cstarr;
2116:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
2117:             *pstar -= dpstar;
2118:             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
2119:             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
2120: #if 0
2121:         break;
2122: #endif
2123:             }
2124:         }
2125: /*     1-wave: shock wave, 3-wave: rarefaction wave */
2126:     } else if (iwave == 200) {
2127: /*     case (200) */
2128:         i__1 = iterno;
2129:         for (i0 = 1; i0 <= i__1; ++i0) {
2130:             pst = *pstar / *pl;
2131:             ustarl = *uxl - (pst - 1.) * cl * PetscSqrtScalar(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
2132:             zl = *pl / cl * PetscSqrtScalar(*gaml * 2. * (*gaml - 1. + (*gaml + 1.) * pst)) * (*gaml - 1. + (*gaml + 1.) * pst) / (*gaml * 3. - 1. + (*gaml + 1.) * pst);
2133:             d__1 = *pstar / *pr;
2134:             d__2 = 1. / *gamr;
2135:             *rstarr = *rr * PetscPowScalar(d__1, d__2);
2136:             cstarr = PetscSqrtScalar(*gamr * *pstar / *rstarr);
2137:             zr = *rstarr * cstarr;
2138:             ustarr = *uxr + gascr4 * 2. * (cstarr - cr);
2139:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
2140:             *pstar -= dpstar;
2141:             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
2142:             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
2143: #if 0
2144:         break;
2145: #endif
2146:             }
2147:         }
2148: /*     1-wave: shock wave, 3-wave: shock */
2149:     } else if (iwave == 300) {
2150: /*     case (300) */
2151:         i__1 = iterno;
2152:         for (i0 = 1; i0 <= i__1; ++i0) {
2153:             pst = *pstar / *pl;
2154:             ustarl = *uxl - (pst - 1.) * cl * PetscSqrtScalar(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
2155:             zl = *pl / cl * PetscSqrtScalar(*gaml * 2. * (*gaml - 1. + (*gaml + 1.) * pst)) * (*gaml - 1. + (*gaml + 1.) * pst) / (*gaml * 3. - 1. + (*gaml + 1.) * pst);
2156:             pst = *pstar / *pr;
2157:             ustarr = *uxr + (pst - 1.) * cr * PetscSqrtScalar(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
2158:             zr = *pr / cr * PetscSqrtScalar(*gamr * 2. * (*gamr - 1. + (*gamr + 1.) * pst)) * (*gamr - 1. + (*gamr + 1.) * pst) / (*gamr * 3. - 1. + (*gamr + 1.) * pst);
2159:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
2160:             *pstar -= dpstar;
2161:             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
2162:             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
2163: #if 0
2164:         break;
2165: #endif
2166:             }
2167:         }
2168: /*     1-wave: rarefaction wave, 3-wave: shock */
2169:     } else if (iwave == 400) {
2170: /*     case (400) */
2171:         i__1 = iterno;
2172:         for (i0 = 1; i0 <= i__1; ++i0) {
2173:             d__1 = *pstar / *pl;
2174:             d__2 = 1. / *gaml;
2175:             *rstarl = *rl * PetscPowScalar(d__1, d__2);
2176:             cstarl = PetscSqrtScalar(*gaml * *pstar / *rstarl);
2177:             ustarl = *uxl - gascl4 * 2. * (cstarl - cl);
2178:             zl = *rstarl * cstarl;
2179:             pst = *pstar / *pr;
2180:             ustarr = *uxr + (pst - 1.) * cr * PetscSqrtScalar(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
2181:             zr = *pr / cr * PetscSqrtScalar(*gamr * 2. * (*gamr - 1. + (*gamr + 1.) * pst)) * (*gamr - 1. + (*gamr + 1.) * pst) / (*gamr * 3. - 1. + (*gamr + 1.) * pst);
2182:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
2183:             *pstar -= dpstar;
2184:             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
2185:             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
2186: #if 0
2187:               break;
2188: #endif
2189:             }
2190:         }
2191:     }

2193:     *ustar = (zl * ustarr + zr * ustarl) / (zl + zr);
2194:     if (PetscRealPart(*pstar) > PetscRealPart(*pl)) {
2195:         pst = *pstar / *pl;
2196:         *rstarl = ((*gaml + 1.) * pst + *gaml - 1.) / ((*gaml - 1.) * pst + *
2197:                 gaml + 1.) * *rl;
2198:     }
2199:     if (PetscRealPart(*pstar) > PetscRealPart(*pr)) {
2200:         pst = *pstar / *pr;
2201:         *rstarr = ((*gamr + 1.) * pst + *gamr - 1.) / ((*gamr - 1.) * pst + *
2202:                 gamr + 1.) * *rr;
2203:     }
2204:     return iwave;
2205: }

2207: PetscScalar sign(PetscScalar x)
2208: {
2209:     if(PetscRealPart(x) > 0) return 1.0;
2210:     if(PetscRealPart(x) < 0) return -1.0;
2211:     return 0.0;
2212: }
2213: /*        Riemann Solver */
2214: /* -------------------------------------------------------------------- */
2215: int riemannsolver(PetscScalar *xcen, PetscScalar *xp,
2216:                    PetscScalar *dtt, PetscScalar *rl, PetscScalar *uxl, PetscScalar *pl,
2217:                    PetscScalar *utl, PetscScalar *ubl, PetscScalar *gaml, PetscScalar *rho1l,
2218:                    PetscScalar *rr, PetscScalar *uxr, PetscScalar *pr, PetscScalar *utr,
2219:                    PetscScalar *ubr, PetscScalar *gamr, PetscScalar *rho1r, PetscScalar *rx,
2220:                    PetscScalar *uxm, PetscScalar *px, PetscScalar *utx, PetscScalar *ubx,
2221:                    PetscScalar *gam, PetscScalar *rho1)
2222: {
2223:     /* System generated locals */
2224:     PetscScalar d__1, d__2;

2226:     /* Local variables */
2227:     static PetscScalar s, c0, p0, r0, u0, w0, x0, x2, ri, cx, sgn0, wsp0, gasc1, gasc2, gasc3, gasc4;
2228:     static PetscScalar cstar, pstar, rstar, ustar, xstar, wspst, ushock, streng, rstarl, rstarr, rstars;
2229:     int iwave;

2231:     if (*rl == *rr && *pr == *pl && *uxl == *uxr && *gaml == *gamr) {
2232:         *rx = *rl;
2233:         *px = *pl;
2234:         *uxm = *uxl;
2235:         *gam = *gaml;
2236:         x2 = *xcen + *uxm * *dtt;

2238:         if (PetscRealPart(*xp) >= PetscRealPart(x2)) {
2239:             *utx = *utr;
2240:             *ubx = *ubr;
2241:             *rho1 = *rho1r;
2242:         } else {
2243:             *utx = *utl;
2244:             *ubx = *ubl;
2245:             *rho1 = *rho1l;
2246:         }
2247:         return 0;
2248:     }
2249:     iwave = riem1mdt(gaml, gamr, rl, pl, uxl, rr, pr, uxr, &rstarl, &rstarr, &pstar, &ustar);

2251:     x2 = *xcen + ustar * *dtt;
2252:     d__1 = *xp - x2;
2253:     sgn0 = sign(d__1);
2254: /*            x is in 3-wave if sgn0 = 1 */
2255: /*            x is in 1-wave if sgn0 = -1 */
2256:     r0 = cvmgm_(rl, rr, &sgn0);
2257:     p0 = cvmgm_(pl, pr, &sgn0);
2258:     u0 = cvmgm_(uxl, uxr, &sgn0);
2259:     *gam = cvmgm_(gaml, gamr, &sgn0);
2260:     gasc1 = *gam - 1.;
2261:     gasc2 = (*gam + 1.) * .5;
2262:     gasc3 = gasc2 / *gam;
2263:     gasc4 = 1. / (*gam - 1.);
2264:     c0 = PetscSqrtScalar(*gam * p0 / r0);
2265:     streng = pstar - p0;
2266:     w0 = *gam * r0 * p0 * (gasc3 * streng / p0 + 1.);
2267:     rstars = r0 / (1. - r0 * streng / w0);
2268:     d__1 = p0 / pstar;
2269:     d__2 = -1. / *gam;
2270:     rstarr = r0 * PetscPowScalar(d__1, d__2);
2271:     rstar = cvmgm_(&rstarr, &rstars, &streng);
2272:     w0 = PetscSqrtScalar(w0);
2273:     cstar = PetscSqrtScalar(*gam * pstar / rstar);
2274:     wsp0 = u0 + sgn0 * c0;
2275:     wspst = ustar + sgn0 * cstar;
2276:     ushock = ustar + sgn0 * w0 / rstar;
2277:     wspst = cvmgp_(&ushock, &wspst, &streng);
2278:     wsp0 = cvmgp_(&ushock, &wsp0, &streng);
2279:     x0 = *xcen + wsp0 * *dtt;
2280:     xstar = *xcen + wspst * *dtt;
2281: /*           using gas formula to evaluate rarefaction wave */
2282: /*            ri : reiman invariant */
2283:     ri = u0 - sgn0 * 2. * gasc4 * c0;
2284:     cx = sgn0 * .5 * gasc1 / gasc2 * ((*xp - *xcen) / *dtt - ri);
2285:     *uxm = ri + sgn0 * 2. * gasc4 * cx;
2286:     s = p0 / PetscPowScalar(r0, *gam);
2287:     d__1 = cx * cx / (*gam * s);
2288:     *rx = PetscPowScalar(d__1, gasc4);
2289:     *px = cx * cx * *rx / *gam;
2290:     d__1 = sgn0 * (x0 - *xp);
2291:     *rx = cvmgp_(rx, &r0, &d__1);
2292:     d__1 = sgn0 * (x0 - *xp);
2293:     *px = cvmgp_(px, &p0, &d__1);
2294:     d__1 = sgn0 * (x0 - *xp);
2295:     *uxm = cvmgp_(uxm, &u0, &d__1);
2296:     d__1 = sgn0 * (xstar - *xp);
2297:     *rx = cvmgm_(rx, &rstar, &d__1);
2298:     d__1 = sgn0 * (xstar - *xp);
2299:     *px = cvmgm_(px, &pstar, &d__1);
2300:     d__1 = sgn0 * (xstar - *xp);
2301:     *uxm = cvmgm_(uxm, &ustar, &d__1);
2302:     if (PetscRealPart(*xp) >= PetscRealPart(x2)) {
2303:         *utx = *utr;
2304:         *ubx = *ubr;
2305:         *rho1 = *rho1r;
2306:     } else {
2307:         *utx = *utl;
2308:         *ubx = *ubl;
2309:         *rho1 = *rho1l;
2310:     }
2311:     return iwave;
2312: }
2313: int godunovflux( const PetscScalar *ul, const PetscScalar *ur,
2314:                  PetscScalar *flux, const PetscReal *nn, const int *ndim,
2315:                  const PetscReal *gamma)
2316: {
2317:     /* System generated locals */
2318:   int i__1,iwave;
2319:     PetscScalar d__1, d__2, d__3;

2321:     /* Local variables */
2322:     static int k;
2323:     static PetscScalar bn[3], fn, ft, tg[3], pl, rl, pm, pr, rr, xp, ubl, ubm,
2324:             ubr, dtt, unm, tmp, utl, utm, uxl, utr, uxr, gaml, gamm, gamr,
2325:             xcen, rhom, rho1l, rho1m, rho1r;
2326:     /* Parameter adjustments */
2327:     --nn;
2328:     --flux;
2329:     --ur;
2330:     --ul;

2332:     /* Function Body */
2333:     xcen = 0.;
2334:     xp = 0.;
2335:     i__1 = *ndim;
2336:     for (k = 1; k <= i__1; ++k) {
2337:         tg[k - 1] = 0.;
2338:         bn[k - 1] = 0.;
2339:     }
2340:     dtt = 1.;
2341:     if (*ndim == 3) {
2342:         if (nn[1] == 0. && nn[2] == 0.) {
2343:             tg[0] = 1.;
2344:         } else {
2345:             tg[0] = -nn[2];
2346:             tg[1] = nn[1];
2347:         }
2348: /*           tmp=dsqrt(tg(1)**2+tg(2)**2) */
2349: /*           tg=tg/tmp */
2350:         bn[0] = -nn[3] * tg[1];
2351:         bn[1] = nn[3] * tg[0];
2352:         bn[2] = nn[1] * tg[1] - nn[2] * tg[0];
2353: /* Computing 2nd power */
2354:         d__1 = bn[0];
2355: /* Computing 2nd power */
2356:         d__2 = bn[1];
2357: /* Computing 2nd power */
2358:         d__3 = bn[2];
2359:         tmp = PetscSqrtScalar(d__1 * d__1 + d__2 * d__2 + d__3 * d__3);
2360:         i__1 = *ndim;
2361:         for (k = 1; k <= i__1; ++k) {
2362:             bn[k - 1] /= tmp;
2363:         }
2364:     } else if (*ndim == 2) {
2365:         tg[0] = -nn[2];
2366:         tg[1] = nn[1];
2367: /*           tmp=dsqrt(tg(1)**2+tg(2)**2) */
2368: /*           tg=tg/tmp */
2369:         bn[0] = 0.;
2370:         bn[1] = 0.;
2371:         bn[2] = 1.;
2372:     }
2373:     rl = ul[1];
2374:     rr = ur[1];
2375:     uxl = 0.;
2376:     uxr = 0.;
2377:     utl = 0.;
2378:     utr = 0.;
2379:     ubl = 0.;
2380:     ubr = 0.;
2381:     i__1 = *ndim;
2382:     for (k = 1; k <= i__1; ++k) {
2383:         uxl += ul[k + 1] * nn[k];
2384:         uxr += ur[k + 1] * nn[k];
2385:         utl += ul[k + 1] * tg[k - 1];
2386:         utr += ur[k + 1] * tg[k - 1];
2387:         ubl += ul[k + 1] * bn[k - 1];
2388:         ubr += ur[k + 1] * bn[k - 1];
2389:     }
2390:     uxl /= rl;
2391:     uxr /= rr;
2392:     utl /= rl;
2393:     utr /= rr;
2394:     ubl /= rl;
2395:     ubr /= rr;

2397:     gaml = *gamma;
2398:     gamr = *gamma;
2399: /* Computing 2nd power */
2400:     d__1 = uxl;
2401: /* Computing 2nd power */
2402:     d__2 = utl;
2403: /* Computing 2nd power */
2404:     d__3 = ubl;
2405:     pl = (*gamma - 1.) * (ul[*ndim + 2] - rl * .5 * (d__1 * d__1 + d__2 * d__2 + d__3 * d__3));
2406: /* Computing 2nd power */
2407:     d__1 = uxr;
2408: /* Computing 2nd power */
2409:     d__2 = utr;
2410: /* Computing 2nd power */
2411:     d__3 = ubr;
2412:     pr = (*gamma - 1.) * (ur[*ndim + 2] - rr * .5 * (d__1 * d__1 + d__2 * d__2 + d__3 * d__3));
2413:     rho1l = rl;
2414:     rho1r = rr;

2416:     iwave = riemannsolver(&xcen, &xp, &dtt, &rl, &uxl, &pl, &utl, &ubl, &gaml, &
2417:                           rho1l, &rr, &uxr, &pr, &utr, &ubr, &gamr, &rho1r, &rhom, &unm, &
2418:                           pm, &utm, &ubm, &gamm, &rho1m);

2420:     flux[1] = rhom * unm;
2421:     fn = rhom * unm * unm + pm;
2422:     ft = rhom * unm * utm;
2423: /*           flux(2)=fn*nn(1)+ft*nn(2) */
2424: /*           flux(3)=fn*tg(1)+ft*tg(2) */
2425:     flux[2] = fn * nn[1] + ft * tg[0];
2426:     flux[3] = fn * nn[2] + ft * tg[1];
2427: /*           flux(2)=rhom*unm*(unm)+pm */
2428: /*           flux(3)=rhom*(unm)*utm */
2429:     if (*ndim == 3) {
2430:         flux[4] = rhom * unm * ubm;
2431:     }
2432:     flux[*ndim + 2] = (rhom * .5 * (unm * unm + utm * utm + ubm * ubm) + gamm / (gamm - 1.) * pm) * unm;
2433:     return iwave;
2434: } /* godunovflux_ */

2436: /* Subroutine to set up the initial conditions for the */
2437: /* Shock Interface interaction or linear wave (Ravi Samtaney,Mark Adams). */
2438: /* ----------------------------------------------------------------------- */
2439: int projecteqstate(PetscReal wc[], const PetscReal ueq[], PetscReal lv[][3])
2440: {
2441:   int j,k;
2442: /*      Wc=matmul(lv,Ueq) 3 vars */
2443:   for (k = 0; k < 3; ++k) {
2444:     wc[k] = 0.;
2445:     for (j = 0; j < 3; ++j) {
2446:       wc[k] += lv[k][j]*ueq[j];
2447:     }
2448:   }
2449:   return 0;
2450: }
2451: /* ----------------------------------------------------------------------- */
2452: int projecttoprim(PetscReal v[], const PetscReal wc[], PetscReal rv[][3])
2453: {
2454:   int k,j;
2455:   /*      V=matmul(rv,WC) 3 vars */
2456:   for (k = 0; k < 3; ++k) {
2457:     v[k] = 0.;
2458:     for (j = 0; j < 3; ++j) {
2459:       v[k] += rv[k][j]*wc[j];
2460:     }
2461:   }
2462:   return 0;
2463: }
2464: /* ---------------------------------------------------------------------- */
2465: int eigenvectors(PetscReal rv[][3], PetscReal lv[][3], const PetscReal ueq[], PetscReal gamma)
2466: {
2467:   int j,k;
2468:   PetscReal rho,csnd,p0;
2469:   /* PetscScalar u; */

2471:   for (k = 0; k < 3; ++k) for (j = 0; j < 3; ++j) { lv[k][j] = 0.; rv[k][j] = 0.; }
2472:   rho = ueq[0];
2473:   /* u = ueq[1]; */
2474:   p0 = ueq[2];
2475:   csnd = PetscSqrtReal(gamma * p0 / rho);
2476:   lv[0][1] = rho * .5;
2477:   lv[0][2] = -.5 / csnd;
2478:   lv[1][0] = csnd;
2479:   lv[1][2] = -1. / csnd;
2480:   lv[2][1] = rho * .5;
2481:   lv[2][2] = .5 / csnd;
2482:   rv[0][0] = -1. / csnd;
2483:   rv[1][0] = 1. / rho;
2484:   rv[2][0] = -csnd;
2485:   rv[0][1] = 1. / csnd;
2486:   rv[0][2] = 1. / csnd;
2487:   rv[1][2] = 1. / rho;
2488:   rv[2][2] = csnd;
2489:   return 0;
2490: }

2492: int initLinearWave(EulerNode *ux, const PetscReal gamma, const PetscReal coord[], const PetscReal Lx)
2493: {
2494:   PetscReal p0,u0,wcp[3],wc[3];
2495:   PetscReal lv[3][3];
2496:   PetscReal vp[3];
2497:   PetscReal rv[3][3];
2498:   PetscReal eps, ueq[3], rho0, twopi;

2500:   /* Function Body */
2501:   twopi = 2.*PETSC_PI;
2502:   eps = 1e-4; /* perturbation */
2503:   rho0 = 1e3;   /* density of water */
2504:   p0 = 101325.; /* init pressure of 1 atm (?) */
2505:   u0 = 0.;
2506:   ueq[0] = rho0;
2507:   ueq[1] = u0;
2508:   ueq[2] = p0;
2509:   /* Project initial state to characteristic variables */
2510:   eigenvectors(rv, lv, ueq, gamma);
2511:   projecteqstate(wc, ueq, lv);
2512:   wcp[0] = wc[0];
2513:   wcp[1] = wc[1];
2514:   wcp[2] = wc[2] + eps * PetscCosReal(coord[0] * 2. * twopi / Lx);
2515:   projecttoprim(vp, wcp, rv);
2516:   ux->r = vp[0]; /* density */
2517:   ux->ru[0] = vp[0] * vp[1]; /* x momentum */
2518:   ux->ru[1] = 0.;
2519: #if defined DIM > 2
2520:   if (dim>2) ux->ru[2] = 0.;
2521: #endif
2522:   /* E = rho * e + rho * v^2/2 = p/(gam-1) + rho*v^2/2 */
2523:   ux->E = vp[2]/(gamma - 1.) + 0.5*vp[0]*vp[1]*vp[1];
2524:   return 0;
2525: }

2527: /*TEST

2529:   # 2D Advection 0-10
2530:   test:
2531:     suffix: 0
2532:     requires: exodusii
2533:     args: -ufv_vtk_interval 0 -f ${PETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo
2534:   test:
2535:     suffix: 1
2536:     requires: exodusii
2537:     args: -ufv_vtk_interval 0 -f ${PETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo
2538:   test:
2539:     suffix: 2
2540:     requires: exodusii
2541:     nsize: 2
2542:     args: -ufv_vtk_interval 0 -f ${PETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo
2543:   test:
2544:     suffix: 3
2545:     requires: exodusii
2546:     nsize: 2
2547:     args: -ufv_vtk_interval 0 -f ${PETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo
2548:   test:
2549:     suffix: 4
2550:     requires: exodusii
2551:     nsize: 8
2552:     args: -ufv_vtk_interval 0 -f ${PETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad.exo
2553:   test:
2554:     suffix: 5
2555:     requires: exodusii
2556:     args: -ufv_vtk_interval 0 -f ${PETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo -ts_type rosw -ts_adapt_reject_safety 1
2557:   test:
2558:     suffix: 6
2559:     requires: exodusii
2560:     args: -ufv_vtk_interval 0 -f ${PETSC_DIR}/share/petsc/datafiles/meshes/squaremotor-30.exo -ufv_split_faces
2561:   test:
2562:     suffix: 7
2563:     requires: exodusii
2564:     args: -ufv_vtk_interval 0 -f ${PETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 1
2565:   test:
2566:     suffix: 8
2567:     requires: exodusii
2568:     nsize: 2
2569:     args: -ufv_vtk_interval 0 -f ${PETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 2
2570:   test:
2571:     suffix: 9
2572:     requires: exodusii
2573:     nsize: 8
2574:     args: -ufv_vtk_interval 0 -f ${PETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 2
2575:   test:
2576:     suffix: 10
2577:     requires: exodusii
2578:     args: -ufv_vtk_interval 0 -f ${PETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad.exo
2579:   # 2D Shallow water
2580:   test:
2581:     suffix: sw_0
2582:     requires: exodusii
2583:     args: -ufv_vtk_interval 0 -f ${PETSC_DIR}/share/petsc/datafiles/meshes/annulus-20.exo -bc_wall 100,101 -physics sw -ufv_cfl 5 -petscfv_type leastsquares -petsclimiter_type sin -ts_final_time 1 -ts_ssp_type rks2 -ts_ssp_nstages 10 -monitor height,energy
2584:   # 2D Advection: p4est
2585:   test:
2586:     suffix: p4est_advec_2d
2587:     requires: p4est
2588:     args: -ufv_vtk_interval 0 -f -dm_type p4est -dm_forest_minimum_refinement 1 -dm_forest_initial_refinement 2 -dm_p4est_refine_pattern hash -dm_forest_maximum_refinement 5
2589:   # Advection in a box
2590:   test:
2591:     suffix: adv_2d_quad_0
2592:     args: -ufv_vtk_interval 0 -dm_refine 5 -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3
2593:   test:
2594:     suffix: adv_2d_quad_1
2595:     args: -ufv_vtk_interval 0 -dm_refine 5 -dm_plex_separate_marker -grid_bounds -0.5,0.5,-0.5,0.5 -bc_inflow 1,2,4 -bc_outflow 3 -advect_sol_type bump -advect_bump_center 0.25,0 -advect_bump_radius 0.1
2596:   test:
2597:     suffix: adv_2d_quad_p4est_0
2598:     requires: p4est
2599:     args: -ufv_vtk_interval 0 -dm_refine 5 -dm_type p4est -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3
2600:   test:
2601:     suffix: adv_2d_quad_p4est_1
2602:     requires: p4est
2603:     args: -ufv_vtk_interval 0 -dm_refine 5 -dm_type p4est -dm_plex_separate_marker -grid_bounds -0.5,0.5,-0.5,0.5 -bc_inflow 1,2,4 -bc_outflow 3 -advect_sol_type bump -advect_bump_center 0.25,0 -advect_bump_radius 0.1
2604:   test:
2605:     suffix: adv_2d_quad_p4est_adapt_0
2606:     requires: p4est
2607:     args: -ufv_vtk_interval 0 -dm_refine 3 -dm_type p4est -dm_plex_separate_marker -grid_bounds -0.5,0.5,-0.5,0.5 -bc_inflow 1,2,4 -bc_outflow 3 -advect_sol_type bump -advect_bump_center 0.25,0 -advect_bump_radius 0.1 -ufv_use_amr -refine_vec_tagger_box 0.005,inf -coarsen_vec_tagger_box 0,1.e-5 -petscfv_type leastsquares -ts_final_time 0.01
2608:   test:
2609:     suffix: adv_2d_tri_0
2610:     requires: triangle
2611:     args: -ufv_vtk_interval 0 -simplex -dm_refine 3 -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3
2612:   test:
2613:     suffix: adv_2d_tri_1
2614:     requires: triangle
2615:     args: -ufv_vtk_interval 0 -simplex -dm_refine 5 -dm_plex_separate_marker -grid_bounds -0.5,0.5,-0.5,0.5 -bc_inflow 1,2,4 -bc_outflow 3 -advect_sol_type bump -advect_bump_center 0.25,0 -advect_bump_radius 0.1
2616:   test:
2617:     suffix: adv_0
2618:     TODO: broken
2619:     args: -ufv_vtk_interval 0 -f ${PETSC_DIR}/share/petsc/datafiles/meshes/blockcylinder-50.exo -bc_inflow 100,101,200 -bc_outflow 201

2621: TEST*/