Actual source code: ex11.c

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


We use a second order TVD finite volume method to evolve a system of PDEs. Our simple upwinded residual evaluation loops
over all mesh faces and uses a Riemann solver to produce the flux given the face geometry and cell values,

f_i = \mathrm{riemann}(\mathrm{phys}, p_\mathrm{centroid}, \hat n, x^L, x^R)

and then update the cell values given the cell volume.
\begin{eqnarray}
f^L_i &-=& \frac{f_i}{vol^L} \\
f^R_i &+=& \frac{f_i}{vol^R}
\end{eqnarray}

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

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

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

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

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

45: static PetscFunctionList PhysicsList, PhysicsRiemannList_SW;

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

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

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

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

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

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

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

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

113: PETSC_STATIC_INLINE PetscReal DotDIMReal(const PetscReal *x,const PetscReal *y)
114: {
115:   PetscInt  i;
116:   PetscReal prod=0.0;

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

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

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

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

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

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

159: static PetscErrorCode PhysicsBoundary_Advect_Inflow(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
160: {
161:   Physics        phys    = (Physics)ctx;
162:   Physics_Advect *advect = (Physics_Advect*)phys->data;

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

169: static PetscErrorCode PhysicsBoundary_Advect_Outflow(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
170: {
172:   xG[0] = xI[0];
173:   return(0);
174: }

176: 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)
177: {
178:   Physics_Advect *advect = (Physics_Advect*)phys->data;
179:   PetscReal      wind[DIM],wn;

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

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

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

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

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

235:   switch (advect->soltype) {
236:   case ADVECT_SOL_TILTED: {
237:     PetscReal             x0[DIM];
238:     Physics_Advect_Tilted *tilted = &advect->sol.tilted;
239:     Waxpy2Real(-time,tilted->wind,x,x0);
240:     if (x0[1] > 0) u[0] = 1.*x[0] + 3.*x[1];
241:     else u[0] = advect->inflowState;
242:   } break;
243:   case ADVECT_SOL_BUMP_CAVITY:
244:   case ADVECT_SOL_BUMP: {
245:     Physics_Advect_Bump *bump = &advect->sol.bump;
246:     PetscReal           x0[DIM],v[DIM],r,cost,sint;
247:     cost  = PetscCosReal(time);
248:     sint  = PetscSinReal(time);
249:     x0[0] = cost*x[0] + sint*x[1];
250:     x0[1] = -sint*x[0] + cost*x[1];
251:     Waxpy2Real(-1,bump->center,x0,v);
252:     r = Norm2Real(v);
253:     switch (bump->type) {
254:     case ADVECT_SOL_BUMP_CONE:
255:       u[0] = PetscMax(1 - r/bump->radius,0);
256:       break;
257:     case ADVECT_SOL_BUMP_COS:
258:       u[0] = 0.5 + 0.5*PetscCosReal(PetscMin(r/bump->radius,1)*PETSC_PI);
259:       break;
260:     }
261:   } break;
262:   default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unknown solution type");
263:   }
264:   return(0);
265: }

267: static PetscErrorCode PhysicsFunctional_Advect(Model mod,PetscReal time,const PetscReal *x,const PetscScalar *y,PetscReal *f,void *ctx)
268: {
269:   Physics        phys    = (Physics)ctx;
270:   Physics_Advect *advect = (Physics_Advect*)phys->data;
271:   PetscScalar    yexact[1] = {0.0};

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

281: static PetscErrorCode SetUpBC_Advect(DM dm, PetscDS prob, Physics phys)
282: {
284:   const PetscInt inflowids[] = {100,200,300},outflowids[] = {101};
285:   DMLabel        label;

288:   /* Register "canned" boundary conditions and defaults for where to apply. */
289:   DMGetLabel(dm, "Face Sets", &label);
290:   PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "inflow",  label, ALEN(inflowids),  inflowids,  0, 0, NULL, (void (*)(void)) PhysicsBoundary_Advect_Inflow, NULL,  phys, NULL);
291:   PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "outflow", label, ALEN(outflowids), outflowids, 0, 0, NULL, (void (*)(void)) PhysicsBoundary_Advect_Outflow, NULL, phys, NULL);
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:   return(0);
345: }

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

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

368: /*
369:  * h_t + div(uh) = 0
370:  * (uh)_t + div (u\otimes uh + g h^2 / 2 I) = 0
371:  *
372:  * */
373: static PetscErrorCode SWFlux(Physics phys,const PetscReal *n,const SWNode *x,SWNode *f)
374: {
375:   Physics_SW  *sw = (Physics_SW*)phys->data;
376:   PetscReal   uhn,u[DIM];
377:   PetscInt     i;

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

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

396: static void PhysicsRiemann_SW_HLL(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)
397: {
398:   Physics_SW *sw = (Physics_SW *) phys->data;
399:   PetscReal aL, aR;
400:   PetscReal nn[DIM];
401: #if !defined(PETSC_USE_COMPLEX)
402:   const SWNode *uL = (const SWNode *) xL, *uR = (const SWNode *) xR;
403: #else
404:   SWNodeUnion  uLreal, uRreal;
405:   const SWNode *uL = &uLreal.swnode;
406:   const SWNode *uR = &uRreal.swnode;
407: #endif
408:   SWNodeUnion fL, fR;
409:   PetscInt i;
410:   PetscReal zero = 0.;

412: #if defined(PETSC_USE_COMPLEX)
413:   uLreal.swnode.h = 0; uRreal.swnode.h = 0;
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) {
418:     for (i = 0; i < 1 + dim; i++) flux[i] = zero;
419:     return;
420:   } /* SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Reconstructed thickness is negative"); */
421:   nn[0] = n[0];
422:   nn[1] = n[1];
423:   Normalize2Real(nn);
424:   SWFlux(phys, nn, uL, &(fL.swnode));
425:   SWFlux(phys, nn, uR, &(fR.swnode));
426:   /* gravity wave speed */
427:   aL = PetscSqrtReal(sw->gravity * uL->h);
428:   aR = PetscSqrtReal(sw->gravity * uR->h);
429:   // Defining u_tilda and v_tilda as u and v
430:   PetscReal u_L, u_R;
431:   u_L = Dot2Real(uL->uh,nn)/uL->h;
432:   u_R = Dot2Real(uR->uh,nn)/uR->h;
433:   PetscReal sL, sR;
434:   sL = PetscMin(u_L - aL, u_R - aR);
435:   sR = PetscMax(u_L + aL, u_R + aR);
436:   if (sL > zero) {
437:     for (i = 0; i < dim + 1; i++) {
438:       flux[i] = fL.vals[i] * Norm2Real(n);
439:     }
440:   } else if (sR < zero) {
441:     for (i = 0; i < dim + 1; i++) {
442:       flux[i] = fR.vals[i] * Norm2Real(n);
443:     }
444:   } else {
445:     for (i = 0; i < dim + 1; i++) {
446:       flux[i] = ((sR * fL.vals[i] - sL * fR.vals[i] + sR * sL * (xR[i] - xL[i])) / (sR - sL)) * Norm2Real(n);
447:     }
448:   }
449: }

451: static void PhysicsRiemann_SW_Rusanov(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)
452: {
453:   Physics_SW   *sw = (Physics_SW*)phys->data;
454:   PetscReal    cL,cR,speed;
455:   PetscReal    nn[DIM];
456: #if !defined(PETSC_USE_COMPLEX)
457:   const SWNode *uL = (const SWNode*)xL,*uR = (const SWNode*)xR;
458: #else
459:   SWNodeUnion  uLreal, uRreal;
460:   const SWNode *uL = &uLreal.swnode;
461:   const SWNode *uR = &uRreal.swnode;
462: #endif
463:   SWNodeUnion  fL,fR;
464:   PetscInt     i;
465:   PetscReal    zero=0.;

467: #if defined(PETSC_USE_COMPLEX)
468:   uLreal.swnode.h = 0; uRreal.swnode.h = 0;
469:   for (i = 0; i < 1+dim; i++) uLreal.vals[i] = PetscRealPart(xL[i]);
470:   for (i = 0; i < 1+dim; i++) uRreal.vals[i] = PetscRealPart(xR[i]);
471: #endif
472:   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"); */
473:   nn[0] = n[0];
474:   nn[1] = n[1];
475:   Normalize2Real(nn);
476:   SWFlux(phys,nn,uL,&(fL.swnode));
477:   SWFlux(phys,nn,uR,&(fR.swnode));
478:   cL    = PetscSqrtReal(sw->gravity*uL->h);
479:   cR    = PetscSqrtReal(sw->gravity*uR->h); /* gravity wave speed */
480:   speed = PetscMax(PetscAbsReal(Dot2Real(uL->uh,nn)/uL->h) + cL,PetscAbsReal(Dot2Real(uR->uh,nn)/uR->h) + cR);
481:   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);
482: }

484: static PetscErrorCode PhysicsSolution_SW(Model mod,PetscReal time,const PetscReal *x,PetscScalar *u,void *ctx)
485: {
486:   PetscReal dx[2],r,sigma;

489:   if (time != 0.0) SETERRQ1(mod->comm,PETSC_ERR_SUP,"No solution known for time %g",(double)time);
490:   dx[0] = x[0] - 1.5;
491:   dx[1] = x[1] - 1.0;
492:   r     = Norm2Real(dx);
493:   sigma = 0.5;
494:   u[0]  = 1 + 2*PetscExpReal(-PetscSqr(r)/(2*PetscSqr(sigma)));
495:   u[1]  = 0.0;
496:   u[2]  = 0.0;
497:   return(0);
498: }

500: static PetscErrorCode PhysicsFunctional_SW(Model mod,PetscReal time,const PetscReal *coord,const PetscScalar *xx,PetscReal *f,void *ctx)
501: {
502:   Physics      phys = (Physics)ctx;
503:   Physics_SW   *sw  = (Physics_SW*)phys->data;
504:   const SWNode *x   = (const SWNode*)xx;
505:   PetscReal  u[2];
506:   PetscReal    h;

509:   h = x->h;
510:   Scale2Real(1./x->h,x->uh,u);
511:   f[sw->functional.Height] = h;
512:   f[sw->functional.Speed]  = Norm2Real(u) + PetscSqrtReal(sw->gravity*h);
513:   f[sw->functional.Energy] = 0.5*(Dot2Real(x->uh,u) + sw->gravity*PetscSqr(h));
514:   return(0);
515: }

517: static PetscErrorCode SetUpBC_SW(DM dm, PetscDS prob,Physics phys)
518: {
520:   const PetscInt wallids[] = {100,101,200,300};
521:   DMLabel        label;

524:   DMGetLabel(dm, "Face Sets", &label);
525:   PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "wall", label, ALEN(wallids), wallids, 0, 0, NULL, (void (*)(void)) PhysicsBoundary_SW_Wall, NULL, phys, NULL);
526:   return(0);
527: }

529: static PetscErrorCode PhysicsCreate_SW(Model mod,Physics phys,PetscOptionItems *PetscOptionsObject)
530: {
531:   Physics_SW     *sw;
532:   char           sw_riemann[64] = "rusanov";

536:   phys->field_desc = PhysicsFields_SW;
537:   PetscNew(&sw);
538:   phys->data    = sw;
539:   mod->setupbc  = SetUpBC_SW;

541:   PetscFunctionListAdd(&PhysicsRiemannList_SW, "rusanov", PhysicsRiemann_SW_Rusanov);
542:   PetscFunctionListAdd(&PhysicsRiemannList_SW, "hll", PhysicsRiemann_SW_HLL);

544:   PetscOptionsHead(PetscOptionsObject,"SW options");
545:   {
546:     void (*PhysicsRiemann_SW)(PetscInt, PetscInt, const PetscReal *, const PetscReal *, const PetscScalar *, const PetscScalar *, PetscInt, const PetscScalar, PetscScalar *, Physics);
547:     sw->gravity = 1.0;
548:     PetscOptionsReal("-sw_gravity","Gravitational constant","",sw->gravity,&sw->gravity,NULL);
549:     PetscOptionsFList("-sw_riemann","Riemann solver","",PhysicsRiemannList_SW,sw_riemann,sw_riemann,sizeof sw_riemann,NULL);
550:     PetscFunctionListFind(PhysicsRiemannList_SW,sw_riemann,&PhysicsRiemann_SW);
551:     phys->riemann = (PetscRiemannFunc) PhysicsRiemann_SW;
552:   }
553:   PetscOptionsTail();
554:   phys->maxspeed = PetscSqrtReal(2.0*sw->gravity); /* Mach 1 for depth of 2 */

556:   ModelSolutionSetDefault(mod,PhysicsSolution_SW,phys);
557:   ModelFunctionalRegister(mod,"Height",&sw->functional.Height,PhysicsFunctional_SW,phys);
558:   ModelFunctionalRegister(mod,"Speed",&sw->functional.Speed,PhysicsFunctional_SW,phys);
559:   ModelFunctionalRegister(mod,"Energy",&sw->functional.Energy,PhysicsFunctional_SW,phys);

561:   return(0);
562: }

564: /******************* Euler Density Shock (EULER_IV_SHOCK,EULER_SS_SHOCK) ********************/
565: /* An initial-value and self-similar solutions of the compressible Euler equations */
566: /* Ravi Samtaney and D. I. Pullin */
567: /* Phys. Fluids 8, 2650 (1996); http://dx.doi.org/10.1063/1.869050 */
568: typedef enum {EULER_PAR_GAMMA,EULER_PAR_RHOR,EULER_PAR_AMACH,EULER_PAR_ITANA,EULER_PAR_SIZE} EulerParamIdx;
569: typedef enum {EULER_IV_SHOCK,EULER_SS_SHOCK,EULER_SHOCK_TUBE,EULER_LINEAR_WAVE} EulerType;
570: typedef struct {
571:   PetscReal r;
572:   PetscReal ru[DIM];
573:   PetscReal E;
574: } EulerNode;
575: typedef union {
576:   EulerNode eulernode;
577:   PetscReal vals[DIM+2];
578: } EulerNodeUnion;
579: typedef PetscErrorCode (*EquationOfState)(const PetscReal*, const EulerNode*, PetscReal*);
580: typedef struct {
581:   EulerType       type;
582:   PetscReal       pars[EULER_PAR_SIZE];
583:   EquationOfState sound;
584:   struct {
585:     PetscInt Density;
586:     PetscInt Momentum;
587:     PetscInt Energy;
588:     PetscInt Pressure;
589:     PetscInt Speed;
590:   } monitor;
591: } Physics_Euler;

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

595: /* initial condition */
596: int initLinearWave(EulerNode *ux, const PetscReal gamma, const PetscReal coord[], const PetscReal Lx);
597: static PetscErrorCode PhysicsSolution_Euler(Model mod, PetscReal time, const PetscReal *x, PetscScalar *u, void *ctx)
598: {
599:   PetscInt i;
600:   Physics         phys = (Physics)ctx;
601:   Physics_Euler   *eu  = (Physics_Euler*)phys->data;
602:   EulerNode       *uu  = (EulerNode*)u;
603:   PetscReal        p0,gamma,c;
605:   if (time != 0.0) SETERRQ1(mod->comm,PETSC_ERR_SUP,"No solution known for time %g",(double)time);

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

611:   if (eu->type==EULER_IV_SHOCK || eu->type==EULER_SS_SHOCK) {
612:     /******************* Euler Density Shock ********************/
613:     /* On initial-value and self-similar solutions of the compressible Euler equations */
614:     /* Ravi Samtaney and D. I. Pullin */
615:     /* Phys. Fluids 8, 2650 (1996); http://dx.doi.org/10.1063/1.869050 */
616:     /* initial conditions 1: left of shock, 0: left of discontinuity 2: right of discontinuity,  */
617:     p0 = 1.;
618:     if (x[0] < 0.0 + x[1]*eu->pars[EULER_PAR_ITANA]) {
619:       if (x[0] < mod->bounds[0]*0.5) { /* left of shock (1) */
620:         PetscReal amach,rho,press,gas1,p1;
621:         amach = eu->pars[EULER_PAR_AMACH];
622:         rho = 1.;
623:         press = p0;
624:         p1 = press*(1.0+2.0*gamma/(gamma+1.0)*(amach*amach-1.0));
625:         gas1 = (gamma-1.0)/(gamma+1.0);
626:         uu->r = rho*(p1/press+gas1)/(gas1*p1/press+1.0);
627:         uu->ru[0]   = ((uu->r - rho)*PetscSqrtReal(gamma*press/rho)*amach);
628:         uu->E = p1/(gamma-1.0) + .5/uu->r*uu->ru[0]*uu->ru[0];
629:       }
630:       else { /* left of discontinuity (0) */
631:         uu->r = 1.; /* rho = 1 */
632:         uu->E = p0/(gamma-1.0);
633:       }
634:     }
635:     else { /* right of discontinuity (2) */
636:       uu->r = eu->pars[EULER_PAR_RHOR];
637:       uu->E = p0/(gamma-1.0);
638:     }
639:   }
640:   else if (eu->type==EULER_SHOCK_TUBE) {
641:     /* 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. */
642:     if (x[0] < 0.0) {
643:       uu->r = 8.;
644:       uu->E = 10./(gamma-1.);
645:     }
646:     else {
647:       uu->r = 1.;
648:       uu->E = 1./(gamma-1.);
649:     }
650:   }
651:   else if (eu->type==EULER_LINEAR_WAVE) {
652:     initLinearWave( uu, gamma, x, mod->bounds[1] - mod->bounds[0]);
653:   }
654:   else SETERRQ1(mod->comm,PETSC_ERR_SUP,"Unknown type %d",eu->type);

656:   /* set phys->maxspeed: (mod->maxspeed = phys->maxspeed) in main; */
657:   eu->sound(&gamma,uu,&c);
658:   c = (uu->ru[0]/uu->r) + c;
659:   if (c > phys->maxspeed) phys->maxspeed = c;

661:   return(0);
662: }

664: static PetscErrorCode Pressure_PG(const PetscReal gamma,const EulerNode *x,PetscReal *p)
665: {
666:   PetscReal ru2;

669:   ru2  = DotDIMReal(x->ru,x->ru);
670:   (*p)=(x->E - 0.5*ru2/x->r)*(gamma - 1.0); /* (E - rho V^2/2)(gamma-1) = e rho (gamma-1) */
671:   return(0);
672: }

674: static PetscErrorCode SpeedOfSound_PG(const PetscReal *gamma, const EulerNode *x, PetscReal *c)
675: {
676:   PetscReal p;

679:   Pressure_PG(*gamma,x,&p);
680:   if (p<0.) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"negative pressure time %g -- NEED TO FIX!!!!!!",(double) p);
681:   /* pars[EULER_PAR_GAMMA] = heat capacity ratio */
682:   (*c)=PetscSqrtReal(*gamma * p / x->r);
683:   return(0);
684: }

686: /*
687:  * x = (rho,rho*(u_1),...,rho*e)^T
688:  * x_t+div(f_1(x))+...+div(f_DIM(x)) = 0
689:  *
690:  * f_i(x) = u_i*x+(0,0,...,p,...,p*u_i)^T
691:  *
692:  */
693: static PetscErrorCode EulerFlux(Physics phys,const PetscReal *n,const EulerNode *x,EulerNode *f)
694: {
695:   Physics_Euler *eu = (Physics_Euler*)phys->data;
696:   PetscReal     nu,p;
697:   PetscInt      i;

700:   Pressure_PG(eu->pars[EULER_PAR_GAMMA],x,&p);
701:   nu = DotDIMReal(x->ru,n);
702:   f->r = nu;   /* A rho u */
703:   nu /= x->r;  /* A u */
704:   for (i=0; i<DIM; i++) f->ru[i] = nu * x->ru[i] + n[i]*p;  /* r u^2 + p */
705:   f->E = nu * (x->E + p); /* u(e+p) */
706:   return(0);
707: }

709: /* PetscReal* => EulerNode* conversion */
710: static PetscErrorCode PhysicsBoundary_Euler_Wall(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *a_xI, PetscScalar *a_xG, void *ctx)
711: {
712:   PetscInt    i;
713:   const EulerNode *xI = (const EulerNode*)a_xI;
714:   EulerNode       *xG = (EulerNode*)a_xG;
715:   Physics         phys = (Physics)ctx;
716:   Physics_Euler   *eu  = (Physics_Euler*)phys->data;
718:   xG->r = xI->r;           /* ghost cell density - same */
719:   xG->E = xI->E;           /* ghost cell energy - same */
720:   if (n[1] != 0.) {        /* top and bottom */
721:     xG->ru[0] =  xI->ru[0]; /* copy tang to wall */
722:     xG->ru[1] = -xI->ru[1]; /* reflect perp to t/b wall */
723:   }
724:   else { /* sides */
725:     for (i=0; i<DIM; i++) xG->ru[i] = xI->ru[i]; /* copy */
726:   }
727:   if (eu->type == EULER_LINEAR_WAVE) { /* debug */
728: #if 0
729:     PetscPrintf(PETSC_COMM_WORLD,"%s coord=%g,%g\n",PETSC_FUNCTION_NAME,c[0],c[1]);
730: #endif
731:   }
732:   return(0);
733: }
734: int godunovflux( const PetscScalar *ul, const PetscScalar *ur, PetscScalar *flux, const PetscReal *nn, const int *ndim, const PetscReal *gamma);
735: /* PetscReal* => EulerNode* conversion */
736: static void PhysicsRiemann_Euler_Godunov( PetscInt dim, PetscInt Nf, const PetscReal *qp, const PetscReal *n,
737:                                           const PetscScalar *xL, const PetscScalar *xR, PetscInt numConstants, const PetscScalar constants[], PetscScalar *flux, Physics phys)
738: {
739:   Physics_Euler   *eu = (Physics_Euler*)phys->data;
740:   PetscReal       cL,cR,speed,velL,velR,nn[DIM],s2;
741:   PetscInt        i;
742:   PetscErrorCode  ierr;

745:   for (i=0,s2=0.; i<DIM; i++) {
746:     nn[i] = n[i];
747:     s2 += nn[i]*nn[i];
748:   }
749:   s2 = PetscSqrtReal(s2); /* |n|_2 = sum(n^2)^1/2 */
750:   for (i=0.; i<DIM; i++) nn[i] /= s2;
751:   if (0) { /* Rusanov */
752:     const EulerNode *uL = (const EulerNode*)xL,*uR = (const EulerNode*)xR;
753:     EulerNodeUnion  fL,fR;
754:     EulerFlux(phys,nn,uL,&(fL.eulernode));
755:     EulerFlux(phys,nn,uR,&(fR.eulernode));
756:     eu->sound(&eu->pars[EULER_PAR_GAMMA],uL,&cL);if (ierr) exit(13);
757:     eu->sound(&eu->pars[EULER_PAR_GAMMA],uR,&cR);if (ierr) exit(14);
758:     velL = DotDIMReal(uL->ru,nn)/uL->r;
759:     velR = DotDIMReal(uR->ru,nn)/uR->r;
760:     speed = PetscMax(velR + cR, velL + cL);
761:     for (i=0; i<2+dim; i++) flux[i] = 0.5*((fL.vals[i]+fR.vals[i]) + speed*(xL[i] - xR[i]))*s2;
762:   }
763:   else {
764:     int dim = DIM;
765:     /* int iwave =  */
766:     godunovflux(xL, xR, flux, nn, &dim, &eu->pars[EULER_PAR_GAMMA]);
767:     for (i=0; i<2+dim; i++) flux[i] *= s2;
768:   }
769:   PetscFunctionReturnVoid();
770: }

772: static PetscErrorCode PhysicsFunctional_Euler(Model mod,PetscReal time,const PetscReal *coord,const PetscScalar *xx,PetscReal *f,void *ctx)
773: {
774:   Physics         phys = (Physics)ctx;
775:   Physics_Euler   *eu  = (Physics_Euler*)phys->data;
776:   const EulerNode *x   = (const EulerNode*)xx;
777:   PetscReal       p;

780:   f[eu->monitor.Density]  = x->r;
781:   f[eu->monitor.Momentum] = NormDIM(x->ru);
782:   f[eu->monitor.Energy]   = x->E;
783:   f[eu->monitor.Speed]    = NormDIM(x->ru)/x->r;
784:   Pressure_PG(eu->pars[EULER_PAR_GAMMA], x, &p);
785:   f[eu->monitor.Pressure] = p;
786:   return(0);
787: }

789: static PetscErrorCode SetUpBC_Euler(DM dm, PetscDS prob,Physics phys)
790: {
791:   PetscErrorCode  ierr;
792:   Physics_Euler   *eu = (Physics_Euler *) phys->data;
793:   DMLabel         label;

796:   DMGetLabel(dm, "Face Sets", &label);
797:   if (eu->type == EULER_LINEAR_WAVE) {
798:     const PetscInt wallids[] = {100,101};
799:     PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "wall", label, ALEN(wallids), wallids, 0, 0, NULL, (void (*)(void)) PhysicsBoundary_Euler_Wall, NULL, phys, NULL);
800:   }
801:   else {
802:     const PetscInt wallids[] = {100,101,200,300};
803:     PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "wall", label, ALEN(wallids), wallids, 0, 0, NULL, (void (*)(void)) PhysicsBoundary_Euler_Wall, NULL, phys, NULL);
804:   }
805:   return(0);
806: }

808: static PetscErrorCode PhysicsCreate_Euler(Model mod,Physics phys,PetscOptionItems *PetscOptionsObject)
809: {
810:   Physics_Euler   *eu;
811:   PetscErrorCode  ierr;

814:   phys->field_desc = PhysicsFields_Euler;
815:   phys->riemann = (PetscRiemannFunc) PhysicsRiemann_Euler_Godunov;
816:   PetscNew(&eu);
817:   phys->data    = eu;
818:   mod->setupbc = SetUpBC_Euler;
819:   PetscOptionsHead(PetscOptionsObject,"Euler options");
820:   {
821:     PetscReal alpha;
822:     char type[64] = "linear_wave";
823:     PetscBool  is;
824:     eu->pars[EULER_PAR_GAMMA] = 1.4;
825:     eu->pars[EULER_PAR_AMACH] = 2.02;
826:     eu->pars[EULER_PAR_RHOR] = 3.0;
827:     eu->pars[EULER_PAR_ITANA] = 0.57735026918963; /* angle of Euler self similar (SS) shock */
828:     PetscOptionsReal("-eu_gamma","Heat capacity ratio","",eu->pars[EULER_PAR_GAMMA],&eu->pars[EULER_PAR_GAMMA],NULL);
829:     PetscOptionsReal("-eu_amach","Shock speed (Mach)","",eu->pars[EULER_PAR_AMACH],&eu->pars[EULER_PAR_AMACH],NULL);
830:     PetscOptionsReal("-eu_rho2","Density right of discontinuity","",eu->pars[EULER_PAR_RHOR],&eu->pars[EULER_PAR_RHOR],NULL);
831:     alpha = 60.;
832:     PetscOptionsReal("-eu_alpha","Angle of discontinuity","",alpha,&alpha,NULL);
833:     if (alpha<=0. || alpha>90.) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Alpha bust be > 0 and <= 90 (%g)",alpha);
834:     eu->pars[EULER_PAR_ITANA] = 1./PetscTanReal( alpha * PETSC_PI / 180.0);
835:     PetscOptionsString("-eu_type","Type of Euler test","",type,type,sizeof(type),NULL);
836:     PetscStrcmp(type,"linear_wave", &is);
837:     if (is) {
838:       /* Remember this should be periodic */
839:       eu->type = EULER_LINEAR_WAVE;
840:       PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",PETSC_FUNCTION_NAME,"linear_wave");
841:     }
842:     else {
843:       if (DIM != 2) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"DIM must be 2 unless linear wave test %s",type);
844:       PetscStrcmp(type,"iv_shock", &is);
845:       if (is) {
846:         eu->type = EULER_IV_SHOCK;
847:         PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",PETSC_FUNCTION_NAME,"iv_shock");
848:       }
849:       else {
850:         PetscStrcmp(type,"ss_shock", &is);
851:         if (is) {
852:           eu->type = EULER_SS_SHOCK;
853:           PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",PETSC_FUNCTION_NAME,"ss_shock");
854:         }
855:         else {
856:           PetscStrcmp(type,"shock_tube", &is);
857:           if (is) eu->type = EULER_SHOCK_TUBE;
858:           else SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Unknown Euler type %s",type);
859:           PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",PETSC_FUNCTION_NAME,"shock_tube");
860:         }
861:       }
862:     }
863:   }
864:   PetscOptionsTail();
865:   eu->sound = SpeedOfSound_PG;
866:   phys->maxspeed = 0.; /* will get set in solution */
867:   ModelSolutionSetDefault(mod,PhysicsSolution_Euler,phys);
868:   ModelFunctionalRegister(mod,"Speed",&eu->monitor.Speed,PhysicsFunctional_Euler,phys);
869:   ModelFunctionalRegister(mod,"Energy",&eu->monitor.Energy,PhysicsFunctional_Euler,phys);
870:   ModelFunctionalRegister(mod,"Density",&eu->monitor.Density,PhysicsFunctional_Euler,phys);
871:   ModelFunctionalRegister(mod,"Momentum",&eu->monitor.Momentum,PhysicsFunctional_Euler,phys);
872:   ModelFunctionalRegister(mod,"Pressure",&eu->monitor.Pressure,PhysicsFunctional_Euler,phys);

874:   return(0);
875: }

877: static PetscErrorCode ErrorIndicator_Simple(PetscInt dim, PetscReal volume, PetscInt numComps, const PetscScalar u[], const PetscScalar grad[], PetscReal *error, void *ctx)
878: {
879:   PetscReal      err = 0.;
880:   PetscInt       i, j;

883:   for (i = 0; i < numComps; i++) {
884:     for (j = 0; j < dim; j++) {
885:       err += PetscSqr(PetscRealPart(grad[i * dim + j]));
886:     }
887:   }
888:   *error = volume * err;
889:   return(0);
890: }

892: PetscErrorCode CreatePartitionVec(DM dm, DM *dmCell, Vec *partition)
893: {
894:   PetscSF        sfPoint;
895:   PetscSection   coordSection;
896:   Vec            coordinates;
897:   PetscSection   sectionCell;
898:   PetscScalar    *part;
899:   PetscInt       cStart, cEnd, c;
900:   PetscMPIInt    rank;

904:   DMGetCoordinateSection(dm, &coordSection);
905:   DMGetCoordinatesLocal(dm, &coordinates);
906:   DMClone(dm, dmCell);
907:   DMGetPointSF(dm, &sfPoint);
908:   DMSetPointSF(*dmCell, sfPoint);
909:   DMSetCoordinateSection(*dmCell, PETSC_DETERMINE, coordSection);
910:   DMSetCoordinatesLocal(*dmCell, coordinates);
911:   MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);
912:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionCell);
913:   DMPlexGetHeightStratum(*dmCell, 0, &cStart, &cEnd);
914:   PetscSectionSetChart(sectionCell, cStart, cEnd);
915:   for (c = cStart; c < cEnd; ++c) {
916:     PetscSectionSetDof(sectionCell, c, 1);
917:   }
918:   PetscSectionSetUp(sectionCell);
919:   DMSetLocalSection(*dmCell, sectionCell);
920:   PetscSectionDestroy(&sectionCell);
921:   DMCreateLocalVector(*dmCell, partition);
922:   PetscObjectSetName((PetscObject)*partition, "partition");
923:   VecGetArray(*partition, &part);
924:   for (c = cStart; c < cEnd; ++c) {
925:     PetscScalar *p;

927:     DMPlexPointLocalRef(*dmCell, c, part, &p);
928:     p[0] = rank;
929:   }
930:   VecRestoreArray(*partition, &part);
931:   return(0);
932: }

934: PetscErrorCode CreateMassMatrix(DM dm, Vec *massMatrix, User user)
935: {
936:   DM                plex, dmMass, dmFace, dmCell, dmCoord;
937:   PetscSection      coordSection;
938:   Vec               coordinates, facegeom, cellgeom;
939:   PetscSection      sectionMass;
940:   PetscScalar       *m;
941:   const PetscScalar *fgeom, *cgeom, *coords;
942:   PetscInt          vStart, vEnd, v;
943:   PetscErrorCode    ierr;

946:   DMConvert(dm, DMPLEX, &plex);
947:   DMGetCoordinateSection(dm, &coordSection);
948:   DMGetCoordinatesLocal(dm, &coordinates);
949:   DMClone(dm, &dmMass);
950:   DMSetCoordinateSection(dmMass, PETSC_DETERMINE, coordSection);
951:   DMSetCoordinatesLocal(dmMass, coordinates);
952:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionMass);
953:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
954:   PetscSectionSetChart(sectionMass, vStart, vEnd);
955:   for (v = vStart; v < vEnd; ++v) {
956:     PetscInt numFaces;

958:     DMPlexGetSupportSize(dmMass, v, &numFaces);
959:     PetscSectionSetDof(sectionMass, v, numFaces*numFaces);
960:   }
961:   PetscSectionSetUp(sectionMass);
962:   DMSetLocalSection(dmMass, sectionMass);
963:   PetscSectionDestroy(&sectionMass);
964:   DMGetLocalVector(dmMass, massMatrix);
965:   VecGetArray(*massMatrix, &m);
966:   DMPlexGetGeometryFVM(plex, &facegeom, &cellgeom, NULL);
967:   VecGetDM(facegeom, &dmFace);
968:   VecGetArrayRead(facegeom, &fgeom);
969:   VecGetDM(cellgeom, &dmCell);
970:   VecGetArrayRead(cellgeom, &cgeom);
971:   DMGetCoordinateDM(dm, &dmCoord);
972:   VecGetArrayRead(coordinates, &coords);
973:   for (v = vStart; v < vEnd; ++v) {
974:     const PetscInt        *faces;
975:     PetscFVFaceGeom       *fgA, *fgB, *cg;
976:     PetscScalar           *vertex;
977:     PetscInt               numFaces, sides[2], f, g;

979:     DMPlexPointLocalRead(dmCoord, v, coords, &vertex);
980:     DMPlexGetSupportSize(dmMass, v, &numFaces);
981:     DMPlexGetSupport(dmMass, v, &faces);
982:     for (f = 0; f < numFaces; ++f) {
983:       sides[0] = faces[f];
984:       DMPlexPointLocalRead(dmFace, faces[f], fgeom, &fgA);
985:       for (g = 0; g < numFaces; ++g) {
986:         const PetscInt *cells = NULL;
987:         PetscReal      area   = 0.0;
988:         PetscInt       numCells;

990:         sides[1] = faces[g];
991:         DMPlexPointLocalRead(dmFace, faces[g], fgeom, &fgB);
992:         DMPlexGetJoin(dmMass, 2, sides, &numCells, &cells);
993:         if (numCells != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Invalid join for faces");
994:         DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cg);
995:         area += PetscAbsScalar((vertex[0] - cg->centroid[0])*(fgA->centroid[1] - cg->centroid[1]) - (vertex[1] - cg->centroid[1])*(fgA->centroid[0] - cg->centroid[0]));
996:         area += PetscAbsScalar((vertex[0] - cg->centroid[0])*(fgB->centroid[1] - cg->centroid[1]) - (vertex[1] - cg->centroid[1])*(fgB->centroid[0] - cg->centroid[0]));
997:         m[f*numFaces+g] = Dot2Real(fgA->normal, fgB->normal)*area*0.5;
998:         DMPlexRestoreJoin(dmMass, 2, sides, &numCells, &cells);
999:       }
1000:     }
1001:   }
1002:   VecRestoreArrayRead(facegeom, &fgeom);
1003:   VecRestoreArrayRead(cellgeom, &cgeom);
1004:   VecRestoreArrayRead(coordinates, &coords);
1005:   VecRestoreArray(*massMatrix, &m);
1006:   DMDestroy(&dmMass);
1007:   DMDestroy(&plex);
1008:   return(0);
1009: }

1011: /* Behavior will be different for multi-physics or when using non-default boundary conditions */
1012: static PetscErrorCode ModelSolutionSetDefault(Model mod,SolutionFunction func,void *ctx)
1013: {
1015:   mod->solution    = func;
1016:   mod->solutionctx = ctx;
1017:   return(0);
1018: }

1020: static PetscErrorCode ModelFunctionalRegister(Model mod,const char *name,PetscInt *offset,FunctionalFunction func,void *ctx)
1021: {
1023:   FunctionalLink link,*ptr;
1024:   PetscInt       lastoffset = -1;

1027:   for (ptr=&mod->functionalRegistry; *ptr; ptr = &(*ptr)->next) lastoffset = (*ptr)->offset;
1028:   PetscNew(&link);
1029:   PetscStrallocpy(name,&link->name);
1030:   link->offset = lastoffset + 1;
1031:   link->func   = func;
1032:   link->ctx    = ctx;
1033:   link->next   = NULL;
1034:   *ptr         = link;
1035:   *offset      = link->offset;
1036:   return(0);
1037: }

1039: static PetscErrorCode ModelFunctionalSetFromOptions(Model mod,PetscOptionItems *PetscOptionsObject)
1040: {
1042:   PetscInt       i,j;
1043:   FunctionalLink link;
1044:   char           *names[256];

1047:   mod->numMonitored = ALEN(names);
1048:   PetscOptionsStringArray("-monitor","list of functionals to monitor","",names,&mod->numMonitored,NULL);
1049:   /* Create list of functionals that will be computed somehow */
1050:   PetscMalloc1(mod->numMonitored,&mod->functionalMonitored);
1051:   /* Create index of calls that we will have to make to compute these functionals (over-allocation in general). */
1052:   PetscMalloc1(mod->numMonitored,&mod->functionalCall);
1053:   mod->numCall = 0;
1054:   for (i=0; i<mod->numMonitored; i++) {
1055:     for (link=mod->functionalRegistry; link; link=link->next) {
1056:       PetscBool match;
1057:       PetscStrcasecmp(names[i],link->name,&match);
1058:       if (match) break;
1059:     }
1060:     if (!link) SETERRQ1(mod->comm,PETSC_ERR_USER,"No known functional '%s'",names[i]);
1061:     mod->functionalMonitored[i] = link;
1062:     for (j=0; j<i; j++) {
1063:       if (mod->functionalCall[j]->func == link->func && mod->functionalCall[j]->ctx == link->ctx) goto next_name;
1064:     }
1065:     mod->functionalCall[mod->numCall++] = link; /* Just points to the first link using the result. There may be more results. */
1066: next_name:
1067:     PetscFree(names[i]);
1068:   }

1070:   /* Find out the maximum index of any functional computed by a function we will be calling (even if we are not using it) */
1071:   mod->maxComputed = -1;
1072:   for (link=mod->functionalRegistry; link; link=link->next) {
1073:     for (i=0; i<mod->numCall; i++) {
1074:       FunctionalLink call = mod->functionalCall[i];
1075:       if (link->func == call->func && link->ctx == call->ctx) {
1076:         mod->maxComputed = PetscMax(mod->maxComputed,link->offset);
1077:       }
1078:     }
1079:   }
1080:   return(0);
1081: }

1083: static PetscErrorCode FunctionalLinkDestroy(FunctionalLink *link)
1084: {
1086:   FunctionalLink l,next;

1089:   if (!link) return(0);
1090:   l     = *link;
1091:   *link = NULL;
1092:   for (; l; l=next) {
1093:     next = l->next;
1094:     PetscFree(l->name);
1095:     PetscFree(l);
1096:   }
1097:   return(0);
1098: }

1100: /* put the solution callback into a functional callback */
1101: static PetscErrorCode SolutionFunctional(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *modctx)
1102: {
1103:   Model          mod;
1106:   mod  = (Model) modctx;
1107:   (*mod->solution)(mod, time, x, u, mod->solutionctx);
1108:   return(0);
1109: }

1111: PetscErrorCode SetInitialCondition(DM dm, Vec X, User user)
1112: {
1113:   PetscErrorCode     (*func[1]) (PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
1114:   void               *ctx[1];
1115:   Model              mod = user->model;
1116:   PetscErrorCode     ierr;

1119:   func[0] = SolutionFunctional;
1120:   ctx[0]  = (void *) mod;
1121:   DMProjectFunction(dm,0.0,func,ctx,INSERT_ALL_VALUES,X);
1122:   return(0);
1123: }

1125: static PetscErrorCode OutputVTK(DM dm, const char *filename, PetscViewer *viewer)
1126: {

1130:   PetscViewerCreate(PetscObjectComm((PetscObject)dm), viewer);
1131:   PetscViewerSetType(*viewer, PETSCVIEWERVTK);
1132:   PetscViewerFileSetName(*viewer, filename);
1133:   return(0);
1134: }

1136: static PetscErrorCode MonitorVTK(TS ts,PetscInt stepnum,PetscReal time,Vec X,void *ctx)
1137: {
1138:   User           user = (User)ctx;
1139:   DM             dm, plex;
1140:   PetscViewer    viewer;
1141:   char           filename[PETSC_MAX_PATH_LEN],*ftable = NULL;
1142:   PetscReal      xnorm;

1146:   PetscObjectSetName((PetscObject) X, "u");
1147:   VecGetDM(X,&dm);
1148:   VecNorm(X,NORM_INFINITY,&xnorm);

1150:   if (stepnum >= 0) {
1151:     stepnum += user->monitorStepOffset;
1152:   }
1153:   if (stepnum >= 0) {           /* No summary for final time */
1154:     Model             mod = user->model;
1155:     Vec               cellgeom;
1156:     PetscInt          c,cStart,cEnd,fcount,i;
1157:     size_t            ftableused,ftablealloc;
1158:     const PetscScalar *cgeom,*x;
1159:     DM                dmCell;
1160:     DMLabel           vtkLabel;
1161:     PetscReal         *fmin,*fmax,*fintegral,*ftmp;

1163:     DMConvert(dm, DMPLEX, &plex);
1164:     DMPlexGetGeometryFVM(plex, NULL, &cellgeom, NULL);
1165:     fcount = mod->maxComputed+1;
1166:     PetscMalloc4(fcount,&fmin,fcount,&fmax,fcount,&fintegral,fcount,&ftmp);
1167:     for (i=0; i<fcount; i++) {
1168:       fmin[i]      = PETSC_MAX_REAL;
1169:       fmax[i]      = PETSC_MIN_REAL;
1170:       fintegral[i] = 0;
1171:     }
1172:     VecGetDM(cellgeom,&dmCell);
1173:     DMPlexGetSimplexOrBoxCells(dmCell,0,&cStart,&cEnd);
1174:     VecGetArrayRead(cellgeom,&cgeom);
1175:     VecGetArrayRead(X,&x);
1176:     DMGetLabel(dm,"vtk",&vtkLabel);
1177:     for (c = cStart; c < cEnd; ++c) {
1178:       PetscFVCellGeom       *cg;
1179:       const PetscScalar     *cx    = NULL;
1180:       PetscInt              vtkVal = 0;

1182:       /* not that these two routines as currently implemented work for any dm with a
1183:        * localSection/globalSection */
1184:       DMPlexPointLocalRead(dmCell,c,cgeom,&cg);
1185:       DMPlexPointGlobalRead(dm,c,x,&cx);
1186:       if (vtkLabel) {DMLabelGetValue(vtkLabel,c,&vtkVal);}
1187:       if (!vtkVal || !cx) continue;        /* ghost, or not a global cell */
1188:       for (i=0; i<mod->numCall; i++) {
1189:         FunctionalLink flink = mod->functionalCall[i];
1190:         (*flink->func)(mod,time,cg->centroid,cx,ftmp,flink->ctx);
1191:       }
1192:       for (i=0; i<fcount; i++) {
1193:         fmin[i]       = PetscMin(fmin[i],ftmp[i]);
1194:         fmax[i]       = PetscMax(fmax[i],ftmp[i]);
1195:         fintegral[i] += cg->volume * ftmp[i];
1196:       }
1197:     }
1198:     VecRestoreArrayRead(cellgeom,&cgeom);
1199:     VecRestoreArrayRead(X,&x);
1200:     DMDestroy(&plex);
1201:     MPI_Allreduce(MPI_IN_PLACE,fmin,fcount,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)ts));
1202:     MPI_Allreduce(MPI_IN_PLACE,fmax,fcount,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
1203:     MPI_Allreduce(MPI_IN_PLACE,fintegral,fcount,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));

1205:     ftablealloc = fcount * 100;
1206:     ftableused  = 0;
1207:     PetscMalloc1(ftablealloc,&ftable);
1208:     for (i=0; i<mod->numMonitored; i++) {
1209:       size_t         countused;
1210:       char           buffer[256],*p;
1211:       FunctionalLink flink = mod->functionalMonitored[i];
1212:       PetscInt       id    = flink->offset;
1213:       if (i % 3) {
1214:         PetscArraycpy(buffer,"  ",2);
1215:         p    = buffer + 2;
1216:       } else if (i) {
1217:         char newline[] = "\n";
1218:         PetscMemcpy(buffer,newline,sizeof(newline)-1);
1219:         p    = buffer + sizeof(newline) - 1;
1220:       } else {
1221:         p = buffer;
1222:       }
1223:       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]);
1224:       countused--;
1225:       countused += p - buffer;
1226:       if (countused > ftablealloc-ftableused-1) { /* reallocate */
1227:         char *ftablenew;
1228:         ftablealloc = 2*ftablealloc + countused;
1229:         PetscMalloc(ftablealloc,&ftablenew);
1230:         PetscArraycpy(ftablenew,ftable,ftableused);
1231:         PetscFree(ftable);
1232:         ftable = ftablenew;
1233:       }
1234:       PetscArraycpy(ftable+ftableused,buffer,countused);
1235:       ftableused += countused;
1236:       ftable[ftableused] = 0;
1237:     }
1238:     PetscFree4(fmin,fmax,fintegral,ftmp);

1240:     PetscPrintf(PetscObjectComm((PetscObject)ts),"% 3D  time %8.4g  |x| %8.4g  %s\n",stepnum,(double)time,(double)xnorm,ftable ? ftable : "");
1241:     PetscFree(ftable);
1242:   }
1243:   if (user->vtkInterval < 1) return(0);
1244:   if ((stepnum == -1) ^ (stepnum % user->vtkInterval == 0)) {
1245:     if (stepnum == -1) {        /* Final time is not multiple of normal time interval, write it anyway */
1246:       TSGetStepNumber(ts,&stepnum);
1247:     }
1248:     PetscSNPrintf(filename,sizeof filename,"%s-%03D.vtu",user->outputBasename,stepnum);
1249:     OutputVTK(dm,filename,&viewer);
1250:     VecView(X,viewer);
1251:     PetscViewerDestroy(&viewer);
1252:   }
1253:   return(0);
1254: }

1256: static PetscErrorCode initializeTS(DM dm, User user, TS *ts)
1257: {

1261:   TSCreate(PetscObjectComm((PetscObject)dm), ts);
1262:   TSSetType(*ts, TSSSP);
1263:   TSSetDM(*ts, dm);
1264:   if (user->vtkmon) {
1265:     TSMonitorSet(*ts,MonitorVTK,user,NULL);
1266:   }
1267:   DMTSSetBoundaryLocal(dm, DMPlexTSComputeBoundary, user);
1268:   DMTSSetRHSFunctionLocal(dm, DMPlexTSComputeRHSFunctionFVM, user);
1269:   TSSetMaxTime(*ts,2.0);
1270:   TSSetExactFinalTime(*ts,TS_EXACTFINALTIME_STEPOVER);
1271:   return(0);
1272: }

1274: static PetscErrorCode adaptToleranceFVM(PetscFV fvm, TS ts, Vec sol, VecTagger refineTag, VecTagger coarsenTag, User user, TS *tsNew, Vec *solNew)
1275: {
1276:   DM                dm, gradDM, plex, cellDM, adaptedDM = NULL;
1277:   Vec               cellGeom, faceGeom;
1278:   PetscBool         isForest, computeGradient;
1279:   Vec               grad, locGrad, locX, errVec;
1280:   PetscInt          cStart, cEnd, c, dim, nRefine, nCoarsen;
1281:   PetscReal         minMaxInd[2] = {PETSC_MAX_REAL, PETSC_MIN_REAL}, minMaxIndGlobal[2], minInd, maxInd, time;
1282:   PetscScalar       *errArray;
1283:   const PetscScalar *pointVals;
1284:   const PetscScalar *pointGrads;
1285:   const PetscScalar *pointGeom;
1286:   DMLabel           adaptLabel = NULL;
1287:   IS                refineIS, coarsenIS;
1288:   PetscErrorCode    ierr;

1291:   TSGetTime(ts,&time);
1292:   VecGetDM(sol, &dm);
1293:   DMGetDimension(dm,&dim);
1294:   PetscFVGetComputeGradients(fvm,&computeGradient);
1295:   PetscFVSetComputeGradients(fvm,PETSC_TRUE);
1296:   DMIsForest(dm, &isForest);
1297:   DMConvert(dm, DMPLEX, &plex);
1298:   DMPlexGetDataFVM(plex, fvm, &cellGeom, &faceGeom, &gradDM);
1299:   DMCreateLocalVector(plex,&locX);
1300:   DMPlexInsertBoundaryValues(plex, PETSC_TRUE, locX, 0.0, faceGeom, cellGeom, NULL);
1301:   DMGlobalToLocalBegin(plex, sol, INSERT_VALUES, locX);
1302:   DMGlobalToLocalEnd  (plex, sol, INSERT_VALUES, locX);
1303:   DMCreateGlobalVector(gradDM, &grad);
1304:   DMPlexReconstructGradientsFVM(plex, locX, grad);
1305:   DMCreateLocalVector(gradDM, &locGrad);
1306:   DMGlobalToLocalBegin(gradDM, grad, INSERT_VALUES, locGrad);
1307:   DMGlobalToLocalEnd(gradDM, grad, INSERT_VALUES, locGrad);
1308:   VecDestroy(&grad);
1309:   DMPlexGetSimplexOrBoxCells(plex,0,&cStart,&cEnd);
1310:   VecGetArrayRead(locGrad,&pointGrads);
1311:   VecGetArrayRead(cellGeom,&pointGeom);
1312:   VecGetArrayRead(locX,&pointVals);
1313:   VecGetDM(cellGeom,&cellDM);
1314:   DMLabelCreate(PETSC_COMM_SELF,"adapt",&adaptLabel);
1315:   VecCreateMPI(PetscObjectComm((PetscObject)plex),cEnd-cStart,PETSC_DETERMINE,&errVec);
1316:   VecSetUp(errVec);
1317:   VecGetArray(errVec,&errArray);
1318:   for (c = cStart; c < cEnd; c++) {
1319:     PetscReal             errInd = 0.;
1320:     PetscScalar           *pointGrad;
1321:     PetscScalar           *pointVal;
1322:     PetscFVCellGeom       *cg;

1324:     DMPlexPointLocalRead(gradDM,c,pointGrads,&pointGrad);
1325:     DMPlexPointLocalRead(cellDM,c,pointGeom,&cg);
1326:     DMPlexPointLocalRead(plex,c,pointVals,&pointVal);

1328:     (user->model->errorIndicator)(dim,cg->volume,user->model->physics->dof,pointVal,pointGrad,&errInd,user->model->errorCtx);
1329:     errArray[c-cStart] = errInd;
1330:     minMaxInd[0] = PetscMin(minMaxInd[0],errInd);
1331:     minMaxInd[1] = PetscMax(minMaxInd[1],errInd);
1332:   }
1333:   VecRestoreArray(errVec,&errArray);
1334:   VecRestoreArrayRead(locX,&pointVals);
1335:   VecRestoreArrayRead(cellGeom,&pointGeom);
1336:   VecRestoreArrayRead(locGrad,&pointGrads);
1337:   VecDestroy(&locGrad);
1338:   VecDestroy(&locX);
1339:   DMDestroy(&plex);

1341:   VecTaggerComputeIS(refineTag,errVec,&refineIS);
1342:   VecTaggerComputeIS(coarsenTag,errVec,&coarsenIS);
1343:   ISGetSize(refineIS,&nRefine);
1344:   ISGetSize(coarsenIS,&nCoarsen);
1345:   if (nRefine) {DMLabelSetStratumIS(adaptLabel,DM_ADAPT_REFINE,refineIS);}
1346:   if (nCoarsen) {DMLabelSetStratumIS(adaptLabel,DM_ADAPT_COARSEN,coarsenIS);}
1347:   ISDestroy(&coarsenIS);
1348:   ISDestroy(&refineIS);
1349:   VecDestroy(&errVec);

1351:   PetscFVSetComputeGradients(fvm,computeGradient);
1352:   minMaxInd[1] = -minMaxInd[1];
1353:   MPI_Allreduce(minMaxInd,minMaxIndGlobal,2,MPIU_REAL,MPI_MIN,PetscObjectComm((PetscObject)dm));
1354:   minInd = minMaxIndGlobal[0];
1355:   maxInd = -minMaxIndGlobal[1];
1356:   PetscInfo2(ts, "error indicator range (%E, %E)\n", minInd, maxInd);
1357:   if (nRefine || nCoarsen) { /* at least one cell is over the refinement threshold */
1358:     DMAdaptLabel(dm,adaptLabel,&adaptedDM);
1359:   }
1360:   DMLabelDestroy(&adaptLabel);
1361:   if (adaptedDM) {
1362:     PetscInfo2(ts, "Adapted mesh, marking %D cells for refinement, and %D cells for coarsening\n", nRefine, nCoarsen);
1363:     if (tsNew) {initializeTS(adaptedDM, user, tsNew);}
1364:     if (solNew) {
1365:       DMCreateGlobalVector(adaptedDM, solNew);
1366:       PetscObjectSetName((PetscObject) *solNew, "solution");
1367:       DMForestTransferVec(dm, sol, adaptedDM, *solNew, PETSC_TRUE, time);
1368:     }
1369:     if (isForest) {DMForestSetAdaptivityForest(adaptedDM,NULL);} /* clear internal references to the previous dm */
1370:     DMDestroy(&adaptedDM);
1371:   } else {
1372:     if (tsNew)  *tsNew  = NULL;
1373:     if (solNew) *solNew = NULL;
1374:   }
1375:   return(0);
1376: }

1378: int main(int argc, char **argv)
1379: {
1380:   MPI_Comm          comm;
1381:   PetscDS           prob;
1382:   PetscFV           fvm;
1383:   PetscLimiter      limiter = NULL, noneLimiter = NULL;
1384:   User              user;
1385:   Model             mod;
1386:   Physics           phys;
1387:   DM                dm, plex;
1388:   PetscReal         ftime, cfl, dt, minRadius;
1389:   PetscInt          dim, nsteps;
1390:   TS                ts;
1391:   TSConvergedReason reason;
1392:   Vec               X;
1393:   PetscViewer       viewer;
1394:   PetscBool         vtkCellGeom, useAMR;
1395:   PetscInt          adaptInterval;
1396:   char              physname[256]  = "advect";
1397:   VecTagger         refineTag = NULL, coarsenTag = NULL;
1398:   PetscErrorCode    ierr;

1400:   PetscInitialize(&argc, &argv, (char*) 0, help);if (ierr) return ierr;
1401:   comm = PETSC_COMM_WORLD;

1403:   PetscNew(&user);
1404:   PetscNew(&user->model);
1405:   PetscNew(&user->model->physics);
1406:   mod           = user->model;
1407:   phys          = mod->physics;
1408:   mod->comm     = comm;
1409:   useAMR        = PETSC_FALSE;
1410:   adaptInterval = 1;

1412:   /* Register physical models to be available on the command line */
1413:   PetscFunctionListAdd(&PhysicsList,"advect"          ,PhysicsCreate_Advect);
1414:   PetscFunctionListAdd(&PhysicsList,"sw"              ,PhysicsCreate_SW);
1415:   PetscFunctionListAdd(&PhysicsList,"euler"           ,PhysicsCreate_Euler);

1417:   PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Mesh Options","");
1418:   {
1419:     cfl  = 0.9 * 4; /* default SSPRKS2 with s=5 stages is stable for CFL number s-1 */
1420:     PetscOptionsReal("-ufv_cfl","CFL number per step","",cfl,&cfl,NULL);
1421:     user->vtkInterval = 1;
1422:     PetscOptionsInt("-ufv_vtk_interval","VTK output interval (0 to disable)","",user->vtkInterval,&user->vtkInterval,NULL);
1423:     user->vtkmon = PETSC_TRUE;
1424:     PetscOptionsBool("-ufv_vtk_monitor","Use VTKMonitor routine","",user->vtkmon,&user->vtkmon,NULL);
1425:     vtkCellGeom = PETSC_FALSE;
1426:     PetscStrcpy(user->outputBasename, "ex11");
1427:     PetscOptionsString("-ufv_vtk_basename","VTK output basename","",user->outputBasename,user->outputBasename,sizeof(user->outputBasename),NULL);
1428:     PetscOptionsBool("-ufv_vtk_cellgeom","Write cell geometry (for debugging)","",vtkCellGeom,&vtkCellGeom,NULL);
1429:     PetscOptionsBool("-ufv_use_amr","use local adaptive mesh refinement","",useAMR,&useAMR,NULL);
1430:     PetscOptionsInt("-ufv_adapt_interval","time steps between AMR","",adaptInterval,&adaptInterval,NULL);
1431:   }
1432:   PetscOptionsEnd();

1434:   if (useAMR) {
1435:     VecTaggerBox refineBox, coarsenBox;

1437:     refineBox.min  = refineBox.max  = PETSC_MAX_REAL;
1438:     coarsenBox.min = coarsenBox.max = PETSC_MIN_REAL;

1440:     VecTaggerCreate(comm,&refineTag);
1441:     PetscObjectSetOptionsPrefix((PetscObject)refineTag,"refine_");
1442:     VecTaggerSetType(refineTag,VECTAGGERABSOLUTE);
1443:     VecTaggerAbsoluteSetBox(refineTag,&refineBox);
1444:     VecTaggerSetFromOptions(refineTag);
1445:     VecTaggerSetUp(refineTag);
1446:     PetscObjectViewFromOptions((PetscObject)refineTag,NULL,"-tag_view");

1448:     VecTaggerCreate(comm,&coarsenTag);
1449:     PetscObjectSetOptionsPrefix((PetscObject)coarsenTag,"coarsen_");
1450:     VecTaggerSetType(coarsenTag,VECTAGGERABSOLUTE);
1451:     VecTaggerAbsoluteSetBox(coarsenTag,&coarsenBox);
1452:     VecTaggerSetFromOptions(coarsenTag);
1453:     VecTaggerSetUp(coarsenTag);
1454:     PetscObjectViewFromOptions((PetscObject)coarsenTag,NULL,"-tag_view");
1455:   }

1457:   PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Physics Options","");
1458:   {
1459:     PetscErrorCode (*physcreate)(Model,Physics,PetscOptionItems*);
1460:     PetscOptionsFList("-physics","Physics module to solve","",PhysicsList,physname,physname,sizeof physname,NULL);
1461:     PetscFunctionListFind(PhysicsList,physname,&physcreate);
1462:     PetscMemzero(phys,sizeof(struct _n_Physics));
1463:     (*physcreate)(mod,phys,PetscOptionsObject);
1464:     /* Count number of fields and dofs */
1465:     for (phys->nfields=0,phys->dof=0; phys->field_desc[phys->nfields].name; phys->nfields++) phys->dof += phys->field_desc[phys->nfields].dof;
1466:     if (phys->dof <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set dof",physname);
1467:     ModelFunctionalSetFromOptions(mod,PetscOptionsObject);
1468:   }
1469:   PetscOptionsEnd();

1471:   /* Create mesh */
1472:   {
1473:     PetscInt i;

1475:     DMCreate(comm, &dm);
1476:     DMSetType(dm, DMPLEX);
1477:     DMSetFromOptions(dm);
1478:     for (i = 0; i < DIM; i++) { mod->bounds[2*i] = 0.; mod->bounds[2*i+1] = 1.;};
1479:     dim = DIM;
1480:     { /* a null name means just do a hex box */
1481:       PetscInt  cells[3] = {1, 1, 1}, n = 3;
1482:       PetscBool flg2, skew = PETSC_FALSE;
1483:       PetscInt nret2 = 2*DIM;
1484:       PetscOptionsBegin(comm,NULL,"Rectangular mesh options","");
1485:       PetscOptionsRealArray("-grid_bounds","bounds of the mesh in each direction (i.e., x_min,x_max,y_min,y_max","",mod->bounds,&nret2,&flg2);
1486:       PetscOptionsBool("-grid_skew_60","Skew grid for 60 degree shock mesh","",skew,&skew,NULL);
1487:       PetscOptionsIntArray("-dm_plex_box_faces", "Number of faces along each dimension", "", cells, &n, NULL);
1488:       PetscOptionsEnd();
1489:       /* TODO Rewrite this with Mark, and remove grid_bounds at that time */
1490:       if (flg2) {
1491:         PetscInt dimEmbed, i;
1492:         PetscInt nCoords;
1493:         PetscScalar *coords;
1494:         Vec coordinates;

1496:         DMGetCoordinatesLocal(dm,&coordinates);
1497:         DMGetCoordinateDim(dm,&dimEmbed);
1498:         VecGetLocalSize(coordinates,&nCoords);
1499:         if (nCoords % dimEmbed) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Coordinate vector the wrong size");
1500:         VecGetArray(coordinates,&coords);
1501:         for (i = 0; i < nCoords; i += dimEmbed) {
1502:           PetscInt j;

1504:           PetscScalar *coord = &coords[i];
1505:           for (j = 0; j < dimEmbed; j++) {
1506:             coord[j] = mod->bounds[2 * j] + coord[j] * (mod->bounds[2 * j + 1] - mod->bounds[2 * j]);
1507:             if (dim==2 && cells[1]==1 && j==0 && skew) {
1508:               if (cells[0] == 2 && i == 8) {
1509:                 coord[j] = .57735026918963; /* hack to get 60 deg skewed mesh */
1510:               } else if (cells[0] == 3) {
1511:                 if (i==2 || i==10) coord[j] = mod->bounds[1]/4.;
1512:                 else if (i==4) coord[j] = mod->bounds[1]/2.;
1513:                 else if (i==12) coord[j] = 1.57735026918963*mod->bounds[1]/2.;
1514:               }
1515:             }
1516:           }
1517:         }
1518:         VecRestoreArray(coordinates,&coords);
1519:         DMSetCoordinatesLocal(dm,coordinates);
1520:       }
1521:     }
1522:   }
1523:   DMViewFromOptions(dm, NULL, "-orig_dm_view");
1524:   DMGetDimension(dm, &dim);

1526:   /* set up BCs, functions, tags */
1527:   DMCreateLabel(dm, "Face Sets");
1528:   mod->errorIndicator = ErrorIndicator_Simple;

1530:   {
1531:     DM gdm;

1533:     DMPlexConstructGhostCells(dm, NULL, NULL, &gdm);
1534:     DMDestroy(&dm);
1535:     dm   = gdm;
1536:     DMViewFromOptions(dm, NULL, "-dm_view");
1537:   }

1539:   PetscFVCreate(comm, &fvm);
1540:   PetscFVSetFromOptions(fvm);
1541:   PetscFVSetNumComponents(fvm, phys->dof);
1542:   PetscFVSetSpatialDimension(fvm, dim);
1543:   PetscObjectSetName((PetscObject) fvm,"");
1544:   {
1545:     PetscInt f, dof;
1546:     for (f=0,dof=0; f < phys->nfields; f++) {
1547:       PetscInt newDof = phys->field_desc[f].dof;

1549:       if (newDof == 1) {
1550:         PetscFVSetComponentName(fvm,dof,phys->field_desc[f].name);
1551:       }
1552:       else {
1553:         PetscInt j;

1555:         for (j = 0; j < newDof; j++) {
1556:           char     compName[256]  = "Unknown";

1558:           PetscSNPrintf(compName,sizeof(compName),"%s_%d",phys->field_desc[f].name,j);
1559:           PetscFVSetComponentName(fvm,dof+j,compName);
1560:         }
1561:       }
1562:       dof += newDof;
1563:     }
1564:   }
1565:   /* FV is now structured with one field having all physics as components */
1566:   DMAddField(dm, NULL, (PetscObject) fvm);
1567:   DMCreateDS(dm);
1568:   DMGetDS(dm, &prob);
1569:   PetscDSSetRiemannSolver(prob, 0, user->model->physics->riemann);
1570:   PetscDSSetContext(prob, 0, user->model->physics);
1571:   (*mod->setupbc)(dm, prob,phys);
1572:   PetscDSSetFromOptions(prob);
1573:   {
1574:     char      convType[256];
1575:     PetscBool flg;

1577:     PetscOptionsBegin(comm, "", "Mesh conversion options", "DMPLEX");
1578:     PetscOptionsFList("-dm_type","Convert DMPlex to another format","ex12",DMList,DMPLEX,convType,256,&flg);
1579:     PetscOptionsEnd();
1580:     if (flg) {
1581:       DM dmConv;

1583:       DMConvert(dm,convType,&dmConv);
1584:       if (dmConv) {
1585:         DMViewFromOptions(dmConv, NULL, "-dm_conv_view");
1586:         DMDestroy(&dm);
1587:         dm   = dmConv;
1588:         DMSetFromOptions(dm);
1589:       }
1590:     }
1591:   }

1593:   initializeTS(dm, user, &ts);

1595:   DMCreateGlobalVector(dm, &X);
1596:   PetscObjectSetName((PetscObject) X, "solution");
1597:   SetInitialCondition(dm, X, user);
1598:   if (useAMR) {
1599:     PetscInt adaptIter;

1601:     /* use no limiting when reconstructing gradients for adaptivity */
1602:     PetscFVGetLimiter(fvm, &limiter);
1603:     PetscObjectReference((PetscObject) limiter);
1604:     PetscLimiterCreate(PetscObjectComm((PetscObject) fvm), &noneLimiter);
1605:     PetscLimiterSetType(noneLimiter, PETSCLIMITERNONE);

1607:     PetscFVSetLimiter(fvm, noneLimiter);
1608:     for (adaptIter = 0; ; ++adaptIter) {
1609:       PetscLogDouble bytes;
1610:       TS             tsNew = NULL;

1612:       PetscMemoryGetCurrentUsage(&bytes);
1613:       PetscInfo2(ts, "refinement loop %D: memory used %g\n", adaptIter, bytes);
1614:       DMViewFromOptions(dm, NULL, "-initial_dm_view");
1615:       VecViewFromOptions(X, NULL, "-initial_vec_view");
1616: #if 0
1617:       if (viewInitial) {
1618:         PetscViewer viewer;
1619:         char        buf[256];
1620:         PetscBool   isHDF5, isVTK;

1622:         PetscViewerCreate(comm,&viewer);
1623:         PetscViewerSetType(viewer,PETSCVIEWERVTK);
1624:         PetscViewerSetOptionsPrefix(viewer,"initial_");
1625:         PetscViewerSetFromOptions(viewer);
1626:         PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERHDF5,&isHDF5);
1627:         PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERVTK,&isVTK);
1628:         if (isHDF5) {
1629:           PetscSNPrintf(buf, 256, "ex11-initial-%d.h5", adaptIter);
1630:         } else if (isVTK) {
1631:           PetscSNPrintf(buf, 256, "ex11-initial-%d.vtu", adaptIter);
1632:           PetscViewerPushFormat(viewer,PETSC_VIEWER_VTK_VTU);
1633:         }
1634:         PetscViewerFileSetMode(viewer,FILE_MODE_WRITE);
1635:         PetscViewerFileSetName(viewer,buf);
1636:         if (isHDF5) {
1637:           DMView(dm,viewer);
1638:           PetscViewerFileSetMode(viewer,FILE_MODE_UPDATE);
1639:         }
1640:         VecView(X,viewer);
1641:         PetscViewerDestroy(&viewer);
1642:       }
1643: #endif

1645:       adaptToleranceFVM(fvm, ts, X, refineTag, coarsenTag, user, &tsNew, NULL);
1646:       if (!tsNew) {
1647:         break;
1648:       } else {
1649:         DMDestroy(&dm);
1650:         VecDestroy(&X);
1651:         TSDestroy(&ts);
1652:         ts   = tsNew;
1653:         TSGetDM(ts,&dm);
1654:         PetscObjectReference((PetscObject)dm);
1655:         DMCreateGlobalVector(dm,&X);
1656:         PetscObjectSetName((PetscObject) X, "solution");
1657:         SetInitialCondition(dm, X, user);
1658:       }
1659:     }
1660:     /* restore original limiter */
1661:     PetscFVSetLimiter(fvm, limiter);
1662:   }

1664:   DMConvert(dm, DMPLEX, &plex);
1665:   if (vtkCellGeom) {
1666:     DM  dmCell;
1667:     Vec cellgeom, partition;

1669:     DMPlexGetGeometryFVM(plex, NULL, &cellgeom, NULL);
1670:     OutputVTK(dm, "ex11-cellgeom.vtk", &viewer);
1671:     VecView(cellgeom, viewer);
1672:     PetscViewerDestroy(&viewer);
1673:     CreatePartitionVec(dm, &dmCell, &partition);
1674:     OutputVTK(dmCell, "ex11-partition.vtk", &viewer);
1675:     VecView(partition, viewer);
1676:     PetscViewerDestroy(&viewer);
1677:     VecDestroy(&partition);
1678:     DMDestroy(&dmCell);
1679:   }
1680:   /* collect max maxspeed from all processes -- todo */
1681:   DMPlexGetGeometryFVM(plex, NULL, NULL, &minRadius);
1682:   DMDestroy(&plex);
1683:   MPI_Allreduce(&phys->maxspeed,&mod->maxspeed,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
1684:   if (mod->maxspeed <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set maxspeed",physname);
1685:   dt   = cfl * minRadius / mod->maxspeed;
1686:   TSSetTimeStep(ts,dt);
1687:   TSSetFromOptions(ts);
1688:   if (!useAMR) {
1689:     TSSolve(ts,X);
1690:     TSGetSolveTime(ts,&ftime);
1691:     TSGetStepNumber(ts,&nsteps);
1692:   } else {
1693:     PetscReal finalTime;
1694:     PetscInt  adaptIter;
1695:     TS        tsNew = NULL;
1696:     Vec       solNew = NULL;

1698:     TSGetMaxTime(ts,&finalTime);
1699:     TSSetMaxSteps(ts,adaptInterval);
1700:     TSSolve(ts,X);
1701:     TSGetSolveTime(ts,&ftime);
1702:     TSGetStepNumber(ts,&nsteps);
1703:     for (adaptIter = 0;ftime < finalTime;adaptIter++) {
1704:       PetscLogDouble bytes;

1706:       PetscMemoryGetCurrentUsage(&bytes);
1707:       PetscInfo2(ts, "AMR time step loop %D: memory used %g\n", adaptIter, bytes);
1708:       PetscFVSetLimiter(fvm,noneLimiter);
1709:       adaptToleranceFVM(fvm,ts,X,refineTag,coarsenTag,user,&tsNew,&solNew);
1710:       PetscFVSetLimiter(fvm,limiter);
1711:       if (tsNew) {
1712:         PetscInfo(ts, "AMR used\n");
1713:         DMDestroy(&dm);
1714:         VecDestroy(&X);
1715:         TSDestroy(&ts);
1716:         ts   = tsNew;
1717:         X    = solNew;
1718:         TSSetFromOptions(ts);
1719:         VecGetDM(X,&dm);
1720:         PetscObjectReference((PetscObject)dm);
1721:         DMConvert(dm, DMPLEX, &plex);
1722:         DMPlexGetGeometryFVM(dm, NULL, NULL, &minRadius);
1723:         DMDestroy(&plex);
1724:         MPI_Allreduce(&phys->maxspeed,&mod->maxspeed,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
1725:         if (mod->maxspeed <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set maxspeed",physname);
1726:         dt   = cfl * minRadius / mod->maxspeed;
1727:         TSSetStepNumber(ts,nsteps);
1728:         TSSetTime(ts,ftime);
1729:         TSSetTimeStep(ts,dt);
1730:       } else {
1731:         PetscInfo(ts, "AMR not used\n");
1732:       }
1733:       user->monitorStepOffset = nsteps;
1734:       TSSetMaxSteps(ts,nsteps+adaptInterval);
1735:       TSSolve(ts,X);
1736:       TSGetSolveTime(ts,&ftime);
1737:       TSGetStepNumber(ts,&nsteps);
1738:     }
1739:   }
1740:   TSGetConvergedReason(ts,&reason);
1741:   PetscPrintf(PETSC_COMM_WORLD,"%s at time %g after %D steps\n",TSConvergedReasons[reason],(double)ftime,nsteps);
1742:   TSDestroy(&ts);

1744:   VecTaggerDestroy(&refineTag);
1745:   VecTaggerDestroy(&coarsenTag);
1746:   PetscFunctionListDestroy(&PhysicsList);
1747:   PetscFunctionListDestroy(&PhysicsRiemannList_SW);
1748:   FunctionalLinkDestroy(&user->model->functionalRegistry);
1749:   PetscFree(user->model->functionalMonitored);
1750:   PetscFree(user->model->functionalCall);
1751:   PetscFree(user->model->physics->data);
1752:   PetscFree(user->model->physics);
1753:   PetscFree(user->model);
1754:   PetscFree(user);
1755:   VecDestroy(&X);
1756:   PetscLimiterDestroy(&limiter);
1757:   PetscLimiterDestroy(&noneLimiter);
1758:   PetscFVDestroy(&fvm);
1759:   DMDestroy(&dm);
1760:   PetscFinalize();
1761:   return ierr;
1762: }

1764: /* Godunov fluxs */
1765: PetscScalar cvmgp_(PetscScalar *a, PetscScalar *b, PetscScalar *test)
1766: {
1767:     /* System generated locals */
1768:     PetscScalar ret_val;

1770:     if (PetscRealPart(*test) > 0.) {
1771:         goto L10;
1772:     }
1773:     ret_val = *b;
1774:     return ret_val;
1775: L10:
1776:     ret_val = *a;
1777:     return ret_val;
1778: } /* cvmgp_ */

1780: PetscScalar cvmgm_(PetscScalar *a, PetscScalar *b, PetscScalar *test)
1781: {
1782:     /* System generated locals */
1783:     PetscScalar ret_val;

1785:     if (PetscRealPart(*test) < 0.) {
1786:         goto L10;
1787:     }
1788:     ret_val = *b;
1789:     return ret_val;
1790: L10:
1791:     ret_val = *a;
1792:     return ret_val;
1793: } /* cvmgm_ */

1795: int riem1mdt( PetscScalar *gaml, PetscScalar *gamr, PetscScalar *rl, PetscScalar *pl,
1796:               PetscScalar *uxl, PetscScalar *rr, PetscScalar *pr,
1797:               PetscScalar *uxr, PetscScalar *rstarl, PetscScalar *rstarr, PetscScalar *
1798:               pstar, PetscScalar *ustar)
1799: {
1800:     /* Initialized data */

1802:     static PetscScalar smallp = 1e-8;

1804:     /* System generated locals */
1805:     int i__1;
1806:     PetscScalar d__1, d__2;

1808:     /* Local variables */
1809:     static int i0;
1810:     static PetscScalar cl, cr, wl, zl, wr, zr, pst, durl, skpr1, skpr2;
1811:     static int iwave;
1812:     static PetscScalar gascl4, gascr4, cstarl, dpstar, cstarr;
1813:     /* static PetscScalar csqrl, csqrr, gascl1, gascl2, gascl3, gascr1, gascr2, gascr3; */
1814:     static int iterno;
1815:     static PetscScalar ustarl, ustarr, rarepr1, rarepr2;

1817:     /* gascl1 = *gaml - 1.; */
1818:     /* gascl2 = (*gaml + 1.) * .5; */
1819:     /* gascl3 = gascl2 / *gaml; */
1820:     gascl4 = 1. / (*gaml - 1.);

1822:     /* gascr1 = *gamr - 1.; */
1823:     /* gascr2 = (*gamr + 1.) * .5; */
1824:     /* gascr3 = gascr2 / *gamr; */
1825:     gascr4 = 1. / (*gamr - 1.);
1826:     iterno = 10;
1827: /*        find pstar: */
1828:     cl = PetscSqrtScalar(*gaml * *pl / *rl);
1829:     cr = PetscSqrtScalar(*gamr * *pr / *rr);
1830:     wl = *rl * cl;
1831:     wr = *rr * cr;
1832:     /* csqrl = wl * wl; */
1833:     /* csqrr = wr * wr; */
1834:     *pstar = (wl * *pr + wr * *pl) / (wl + wr);
1835:     *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
1836:     pst = *pl / *pr;
1837:     skpr1 = cr * (pst - 1.) * PetscSqrtScalar(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
1838:     d__1 = (*gamr - 1.) / (*gamr * 2.);
1839:     rarepr2 = gascr4 * 2. * cr * (1. - PetscPowScalar(pst, d__1));
1840:     pst = *pr / *pl;
1841:     skpr2 = cl * (pst - 1.) * PetscSqrtScalar(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
1842:     d__1 = (*gaml - 1.) / (*gaml * 2.);
1843:     rarepr1 = gascl4 * 2. * cl * (1. - PetscPowScalar(pst, d__1));
1844:     durl = *uxr - *uxl;
1845:     if (PetscRealPart(*pr) < PetscRealPart(*pl)) {
1846:         if (PetscRealPart(durl) >= PetscRealPart(rarepr1)) {
1847:             iwave = 100;
1848:         } else if (PetscRealPart(durl) <= PetscRealPart(-skpr1)) {
1849:             iwave = 300;
1850:         } else {
1851:             iwave = 400;
1852:         }
1853:     } else {
1854:         if (PetscRealPart(durl) >= PetscRealPart(rarepr2)) {
1855:             iwave = 100;
1856:         } else if (PetscRealPart(durl) <= PetscRealPart(-skpr2)) {
1857:             iwave = 300;
1858:         } else {
1859:             iwave = 200;
1860:         }
1861:     }
1862:     if (iwave == 100) {
1863: /*     1-wave: rarefaction wave, 3-wave: rarefaction wave */
1864: /*     case (100) */
1865:         i__1 = iterno;
1866:         for (i0 = 1; i0 <= i__1; ++i0) {
1867:             d__1 = *pstar / *pl;
1868:             d__2 = 1. / *gaml;
1869:             *rstarl = *rl * PetscPowScalar(d__1, d__2);
1870:             cstarl = PetscSqrtScalar(*gaml * *pstar / *rstarl);
1871:             ustarl = *uxl - gascl4 * 2. * (cstarl - cl);
1872:             zl = *rstarl * cstarl;
1873:             d__1 = *pstar / *pr;
1874:             d__2 = 1. / *gamr;
1875:             *rstarr = *rr * PetscPowScalar(d__1, d__2);
1876:             cstarr = PetscSqrtScalar(*gamr * *pstar / *rstarr);
1877:             ustarr = *uxr + gascr4 * 2. * (cstarr - cr);
1878:             zr = *rstarr * cstarr;
1879:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
1880:             *pstar -= dpstar;
1881:             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
1882:             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
1883: #if 0
1884:         break;
1885: #endif
1886:             }
1887:         }
1888: /*     1-wave: shock wave, 3-wave: rarefaction wave */
1889:     } else if (iwave == 200) {
1890: /*     case (200) */
1891:         i__1 = iterno;
1892:         for (i0 = 1; i0 <= i__1; ++i0) {
1893:             pst = *pstar / *pl;
1894:             ustarl = *uxl - (pst - 1.) * cl * PetscSqrtScalar(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
1895:             zl = *pl / cl * PetscSqrtScalar(*gaml * 2. * (*gaml - 1. + (*gaml + 1.) * pst)) * (*gaml - 1. + (*gaml + 1.) * pst) / (*gaml * 3. - 1. + (*gaml + 1.) * pst);
1896:             d__1 = *pstar / *pr;
1897:             d__2 = 1. / *gamr;
1898:             *rstarr = *rr * PetscPowScalar(d__1, d__2);
1899:             cstarr = PetscSqrtScalar(*gamr * *pstar / *rstarr);
1900:             zr = *rstarr * cstarr;
1901:             ustarr = *uxr + gascr4 * 2. * (cstarr - cr);
1902:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
1903:             *pstar -= dpstar;
1904:             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
1905:             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
1906: #if 0
1907:         break;
1908: #endif
1909:             }
1910:         }
1911: /*     1-wave: shock wave, 3-wave: shock */
1912:     } else if (iwave == 300) {
1913: /*     case (300) */
1914:         i__1 = iterno;
1915:         for (i0 = 1; i0 <= i__1; ++i0) {
1916:             pst = *pstar / *pl;
1917:             ustarl = *uxl - (pst - 1.) * cl * PetscSqrtScalar(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
1918:             zl = *pl / cl * PetscSqrtScalar(*gaml * 2. * (*gaml - 1. + (*gaml + 1.) * pst)) * (*gaml - 1. + (*gaml + 1.) * pst) / (*gaml * 3. - 1. + (*gaml + 1.) * pst);
1919:             pst = *pstar / *pr;
1920:             ustarr = *uxr + (pst - 1.) * cr * PetscSqrtScalar(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
1921:             zr = *pr / cr * PetscSqrtScalar(*gamr * 2. * (*gamr - 1. + (*gamr + 1.) * pst)) * (*gamr - 1. + (*gamr + 1.) * pst) / (*gamr * 3. - 1. + (*gamr + 1.) * pst);
1922:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
1923:             *pstar -= dpstar;
1924:             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
1925:             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
1926: #if 0
1927:         break;
1928: #endif
1929:             }
1930:         }
1931: /*     1-wave: rarefaction wave, 3-wave: shock */
1932:     } else if (iwave == 400) {
1933: /*     case (400) */
1934:         i__1 = iterno;
1935:         for (i0 = 1; i0 <= i__1; ++i0) {
1936:             d__1 = *pstar / *pl;
1937:             d__2 = 1. / *gaml;
1938:             *rstarl = *rl * PetscPowScalar(d__1, d__2);
1939:             cstarl = PetscSqrtScalar(*gaml * *pstar / *rstarl);
1940:             ustarl = *uxl - gascl4 * 2. * (cstarl - cl);
1941:             zl = *rstarl * cstarl;
1942:             pst = *pstar / *pr;
1943:             ustarr = *uxr + (pst - 1.) * cr * PetscSqrtScalar(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
1944:             zr = *pr / cr * PetscSqrtScalar(*gamr * 2. * (*gamr - 1. + (*gamr + 1.) * pst)) * (*gamr - 1. + (*gamr + 1.) * pst) / (*gamr * 3. - 1. + (*gamr + 1.) * pst);
1945:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
1946:             *pstar -= dpstar;
1947:             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
1948:             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
1949: #if 0
1950:               break;
1951: #endif
1952:             }
1953:         }
1954:     }

1956:     *ustar = (zl * ustarr + zr * ustarl) / (zl + zr);
1957:     if (PetscRealPart(*pstar) > PetscRealPart(*pl)) {
1958:         pst = *pstar / *pl;
1959:         *rstarl = ((*gaml + 1.) * pst + *gaml - 1.) / ((*gaml - 1.) * pst + *
1960:                 gaml + 1.) * *rl;
1961:     }
1962:     if (PetscRealPart(*pstar) > PetscRealPart(*pr)) {
1963:         pst = *pstar / *pr;
1964:         *rstarr = ((*gamr + 1.) * pst + *gamr - 1.) / ((*gamr - 1.) * pst + *
1965:                 gamr + 1.) * *rr;
1966:     }
1967:     return iwave;
1968: }

1970: PetscScalar sign(PetscScalar x)
1971: {
1972:     if (PetscRealPart(x) > 0) return 1.0;
1973:     if (PetscRealPart(x) < 0) return -1.0;
1974:     return 0.0;
1975: }
1976: /*        Riemann Solver */
1977: /* -------------------------------------------------------------------- */
1978: int riemannsolver(PetscScalar *xcen, PetscScalar *xp,
1979:                    PetscScalar *dtt, PetscScalar *rl, PetscScalar *uxl, PetscScalar *pl,
1980:                    PetscScalar *utl, PetscScalar *ubl, PetscScalar *gaml, PetscScalar *rho1l,
1981:                    PetscScalar *rr, PetscScalar *uxr, PetscScalar *pr, PetscScalar *utr,
1982:                    PetscScalar *ubr, PetscScalar *gamr, PetscScalar *rho1r, PetscScalar *rx,
1983:                    PetscScalar *uxm, PetscScalar *px, PetscScalar *utx, PetscScalar *ubx,
1984:                    PetscScalar *gam, PetscScalar *rho1)
1985: {
1986:     /* System generated locals */
1987:     PetscScalar d__1, d__2;

1989:     /* Local variables */
1990:     static PetscScalar s, c0, p0, r0, u0, w0, x0, x2, ri, cx, sgn0, wsp0, gasc1, gasc2, gasc3, gasc4;
1991:     static PetscScalar cstar, pstar, rstar, ustar, xstar, wspst, ushock, streng, rstarl, rstarr, rstars;
1992:     int iwave;

1994:     if (*rl == *rr && *pr == *pl && *uxl == *uxr && *gaml == *gamr) {
1995:         *rx = *rl;
1996:         *px = *pl;
1997:         *uxm = *uxl;
1998:         *gam = *gaml;
1999:         x2 = *xcen + *uxm * *dtt;

2001:         if (PetscRealPart(*xp) >= PetscRealPart(x2)) {
2002:             *utx = *utr;
2003:             *ubx = *ubr;
2004:             *rho1 = *rho1r;
2005:         } else {
2006:             *utx = *utl;
2007:             *ubx = *ubl;
2008:             *rho1 = *rho1l;
2009:         }
2010:         return 0;
2011:     }
2012:     iwave = riem1mdt(gaml, gamr, rl, pl, uxl, rr, pr, uxr, &rstarl, &rstarr, &pstar, &ustar);

2014:     x2 = *xcen + ustar * *dtt;
2015:     d__1 = *xp - x2;
2016:     sgn0 = sign(d__1);
2017: /*            x is in 3-wave if sgn0 = 1 */
2018: /*            x is in 1-wave if sgn0 = -1 */
2019:     r0 = cvmgm_(rl, rr, &sgn0);
2020:     p0 = cvmgm_(pl, pr, &sgn0);
2021:     u0 = cvmgm_(uxl, uxr, &sgn0);
2022:     *gam = cvmgm_(gaml, gamr, &sgn0);
2023:     gasc1 = *gam - 1.;
2024:     gasc2 = (*gam + 1.) * .5;
2025:     gasc3 = gasc2 / *gam;
2026:     gasc4 = 1. / (*gam - 1.);
2027:     c0 = PetscSqrtScalar(*gam * p0 / r0);
2028:     streng = pstar - p0;
2029:     w0 = *gam * r0 * p0 * (gasc3 * streng / p0 + 1.);
2030:     rstars = r0 / (1. - r0 * streng / w0);
2031:     d__1 = p0 / pstar;
2032:     d__2 = -1. / *gam;
2033:     rstarr = r0 * PetscPowScalar(d__1, d__2);
2034:     rstar = cvmgm_(&rstarr, &rstars, &streng);
2035:     w0 = PetscSqrtScalar(w0);
2036:     cstar = PetscSqrtScalar(*gam * pstar / rstar);
2037:     wsp0 = u0 + sgn0 * c0;
2038:     wspst = ustar + sgn0 * cstar;
2039:     ushock = ustar + sgn0 * w0 / rstar;
2040:     wspst = cvmgp_(&ushock, &wspst, &streng);
2041:     wsp0 = cvmgp_(&ushock, &wsp0, &streng);
2042:     x0 = *xcen + wsp0 * *dtt;
2043:     xstar = *xcen + wspst * *dtt;
2044: /*           using gas formula to evaluate rarefaction wave */
2045: /*            ri : reiman invariant */
2046:     ri = u0 - sgn0 * 2. * gasc4 * c0;
2047:     cx = sgn0 * .5 * gasc1 / gasc2 * ((*xp - *xcen) / *dtt - ri);
2048:     *uxm = ri + sgn0 * 2. * gasc4 * cx;
2049:     s = p0 / PetscPowScalar(r0, *gam);
2050:     d__1 = cx * cx / (*gam * s);
2051:     *rx = PetscPowScalar(d__1, gasc4);
2052:     *px = cx * cx * *rx / *gam;
2053:     d__1 = sgn0 * (x0 - *xp);
2054:     *rx = cvmgp_(rx, &r0, &d__1);
2055:     d__1 = sgn0 * (x0 - *xp);
2056:     *px = cvmgp_(px, &p0, &d__1);
2057:     d__1 = sgn0 * (x0 - *xp);
2058:     *uxm = cvmgp_(uxm, &u0, &d__1);
2059:     d__1 = sgn0 * (xstar - *xp);
2060:     *rx = cvmgm_(rx, &rstar, &d__1);
2061:     d__1 = sgn0 * (xstar - *xp);
2062:     *px = cvmgm_(px, &pstar, &d__1);
2063:     d__1 = sgn0 * (xstar - *xp);
2064:     *uxm = cvmgm_(uxm, &ustar, &d__1);
2065:     if (PetscRealPart(*xp) >= PetscRealPart(x2)) {
2066:         *utx = *utr;
2067:         *ubx = *ubr;
2068:         *rho1 = *rho1r;
2069:     } else {
2070:         *utx = *utl;
2071:         *ubx = *ubl;
2072:         *rho1 = *rho1l;
2073:     }
2074:     return iwave;
2075: }
2076: int godunovflux( const PetscScalar *ul, const PetscScalar *ur,
2077:                  PetscScalar *flux, const PetscReal *nn, const int *ndim,
2078:                  const PetscReal *gamma)
2079: {
2080:     /* System generated locals */
2081:   int i__1,iwave;
2082:     PetscScalar d__1, d__2, d__3;

2084:     /* Local variables */
2085:     static int k;
2086:     static PetscScalar bn[3], fn, ft, tg[3], pl, rl, pm, pr, rr, xp, ubl, ubm,
2087:             ubr, dtt, unm, tmp, utl, utm, uxl, utr, uxr, gaml, gamm, gamr,
2088:             xcen, rhom, rho1l, rho1m, rho1r;

2090:     /* Function Body */
2091:     xcen = 0.;
2092:     xp = 0.;
2093:     i__1 = *ndim;
2094:     for (k = 1; k <= i__1; ++k) {
2095:         tg[k - 1] = 0.;
2096:         bn[k - 1] = 0.;
2097:     }
2098:     dtt = 1.;
2099:     if (*ndim == 3) {
2100:         if (nn[0] == 0. && nn[1] == 0.) {
2101:             tg[0] = 1.;
2102:         } else {
2103:             tg[0] = -nn[1];
2104:             tg[1] = nn[0];
2105:         }
2106: /*           tmp=dsqrt(tg(1)**2+tg(2)**2) */
2107: /*           tg=tg/tmp */
2108:         bn[0] = -nn[2] * tg[1];
2109:         bn[1] = nn[2] * tg[0];
2110:         bn[2] = nn[0] * tg[1] - nn[1] * tg[0];
2111: /* Computing 2nd power */
2112:         d__1 = bn[0];
2113: /* Computing 2nd power */
2114:         d__2 = bn[1];
2115: /* Computing 2nd power */
2116:         d__3 = bn[2];
2117:         tmp = PetscSqrtScalar(d__1 * d__1 + d__2 * d__2 + d__3 * d__3);
2118:         i__1 = *ndim;
2119:         for (k = 1; k <= i__1; ++k) {
2120:             bn[k - 1] /= tmp;
2121:         }
2122:     } else if (*ndim == 2) {
2123:         tg[0] = -nn[1];
2124:         tg[1] = nn[0];
2125: /*           tmp=dsqrt(tg(1)**2+tg(2)**2) */
2126: /*           tg=tg/tmp */
2127:         bn[0] = 0.;
2128:         bn[1] = 0.;
2129:         bn[2] = 1.;
2130:     }
2131:     rl = ul[0];
2132:     rr = ur[0];
2133:     uxl = 0.;
2134:     uxr = 0.;
2135:     utl = 0.;
2136:     utr = 0.;
2137:     ubl = 0.;
2138:     ubr = 0.;
2139:     i__1 = *ndim;
2140:     for (k = 1; k <= i__1; ++k) {
2141:         uxl += ul[k] * nn[k-1];
2142:         uxr += ur[k] * nn[k-1];
2143:         utl += ul[k] * tg[k - 1];
2144:         utr += ur[k] * tg[k - 1];
2145:         ubl += ul[k] * bn[k - 1];
2146:         ubr += ur[k] * bn[k - 1];
2147:     }
2148:     uxl /= rl;
2149:     uxr /= rr;
2150:     utl /= rl;
2151:     utr /= rr;
2152:     ubl /= rl;
2153:     ubr /= rr;

2155:     gaml = *gamma;
2156:     gamr = *gamma;
2157: /* Computing 2nd power */
2158:     d__1 = uxl;
2159: /* Computing 2nd power */
2160:     d__2 = utl;
2161: /* Computing 2nd power */
2162:     d__3 = ubl;
2163:     pl = (*gamma - 1.) * (ul[*ndim + 1] - rl * .5 * (d__1 * d__1 + d__2 * d__2 + d__3 * d__3));
2164: /* Computing 2nd power */
2165:     d__1 = uxr;
2166: /* Computing 2nd power */
2167:     d__2 = utr;
2168: /* Computing 2nd power */
2169:     d__3 = ubr;
2170:     pr = (*gamma - 1.) * (ur[*ndim + 1] - rr * .5 * (d__1 * d__1 + d__2 * d__2 + d__3 * d__3));
2171:     rho1l = rl;
2172:     rho1r = rr;

2174:     iwave = riemannsolver(&xcen, &xp, &dtt, &rl, &uxl, &pl, &utl, &ubl, &gaml, &
2175:                           rho1l, &rr, &uxr, &pr, &utr, &ubr, &gamr, &rho1r, &rhom, &unm, &
2176:                           pm, &utm, &ubm, &gamm, &rho1m);

2178:     flux[0] = rhom * unm;
2179:     fn = rhom * unm * unm + pm;
2180:     ft = rhom * unm * utm;
2181: /*           flux(2)=fn*nn(1)+ft*nn(2) */
2182: /*           flux(3)=fn*tg(1)+ft*tg(2) */
2183:     flux[1] = fn * nn[0] + ft * tg[0];
2184:     flux[2] = fn * nn[1] + ft * tg[1];
2185: /*           flux(2)=rhom*unm*(unm)+pm */
2186: /*           flux(3)=rhom*(unm)*utm */
2187:     if (*ndim == 3) {
2188:         flux[3] = rhom * unm * ubm;
2189:     }
2190:     flux[*ndim + 1] = (rhom * .5 * (unm * unm + utm * utm + ubm * ubm) + gamm / (gamm - 1.) * pm) * unm;
2191:     return iwave;
2192: } /* godunovflux_ */

2194: /* Subroutine to set up the initial conditions for the */
2195: /* Shock Interface interaction or linear wave (Ravi Samtaney,Mark Adams). */
2196: /* ----------------------------------------------------------------------- */
2197: int projecteqstate(PetscReal wc[], const PetscReal ueq[], PetscReal lv[][3])
2198: {
2199:   int j,k;
2200: /*      Wc=matmul(lv,Ueq) 3 vars */
2201:   for (k = 0; k < 3; ++k) {
2202:     wc[k] = 0.;
2203:     for (j = 0; j < 3; ++j) {
2204:       wc[k] += lv[k][j]*ueq[j];
2205:     }
2206:   }
2207:   return 0;
2208: }
2209: /* ----------------------------------------------------------------------- */
2210: int projecttoprim(PetscReal v[], const PetscReal wc[], PetscReal rv[][3])
2211: {
2212:   int k,j;
2213:   /*      V=matmul(rv,WC) 3 vars */
2214:   for (k = 0; k < 3; ++k) {
2215:     v[k] = 0.;
2216:     for (j = 0; j < 3; ++j) {
2217:       v[k] += rv[k][j]*wc[j];
2218:     }
2219:   }
2220:   return 0;
2221: }
2222: /* ---------------------------------------------------------------------- */
2223: int eigenvectors(PetscReal rv[][3], PetscReal lv[][3], const PetscReal ueq[], PetscReal gamma)
2224: {
2225:   int j,k;
2226:   PetscReal rho,csnd,p0;
2227:   /* PetscScalar u; */

2229:   for (k = 0; k < 3; ++k) for (j = 0; j < 3; ++j) { lv[k][j] = 0.; rv[k][j] = 0.; }
2230:   rho = ueq[0];
2231:   /* u = ueq[1]; */
2232:   p0 = ueq[2];
2233:   csnd = PetscSqrtReal(gamma * p0 / rho);
2234:   lv[0][1] = rho * .5;
2235:   lv[0][2] = -.5 / csnd;
2236:   lv[1][0] = csnd;
2237:   lv[1][2] = -1. / csnd;
2238:   lv[2][1] = rho * .5;
2239:   lv[2][2] = .5 / csnd;
2240:   rv[0][0] = -1. / csnd;
2241:   rv[1][0] = 1. / rho;
2242:   rv[2][0] = -csnd;
2243:   rv[0][1] = 1. / csnd;
2244:   rv[0][2] = 1. / csnd;
2245:   rv[1][2] = 1. / rho;
2246:   rv[2][2] = csnd;
2247:   return 0;
2248: }

2250: int initLinearWave(EulerNode *ux, const PetscReal gamma, const PetscReal coord[], const PetscReal Lx)
2251: {
2252:   PetscReal p0,u0,wcp[3],wc[3];
2253:   PetscReal lv[3][3];
2254:   PetscReal vp[3];
2255:   PetscReal rv[3][3];
2256:   PetscReal eps, ueq[3], rho0, twopi;

2258:   /* Function Body */
2259:   twopi = 2.*PETSC_PI;
2260:   eps = 1e-4; /* perturbation */
2261:   rho0 = 1e3;   /* density of water */
2262:   p0 = 101325.; /* init pressure of 1 atm (?) */
2263:   u0 = 0.;
2264:   ueq[0] = rho0;
2265:   ueq[1] = u0;
2266:   ueq[2] = p0;
2267:   /* Project initial state to characteristic variables */
2268:   eigenvectors(rv, lv, ueq, gamma);
2269:   projecteqstate(wc, ueq, lv);
2270:   wcp[0] = wc[0];
2271:   wcp[1] = wc[1];
2272:   wcp[2] = wc[2] + eps * PetscCosReal(coord[0] * 2. * twopi / Lx);
2273:   projecttoprim(vp, wcp, rv);
2274:   ux->r = vp[0]; /* density */
2275:   ux->ru[0] = vp[0] * vp[1]; /* x momentum */
2276:   ux->ru[1] = 0.;
2277: #if defined DIM > 2
2278:   if (dim>2) ux->ru[2] = 0.;
2279: #endif
2280:   /* E = rho * e + rho * v^2/2 = p/(gam-1) + rho*v^2/2 */
2281:   ux->E = vp[2]/(gamma - 1.) + 0.5*vp[0]*vp[1]*vp[1];
2282:   return 0;
2283: }

2285: /*TEST

2287:   testset:
2288:     args: -dm_plex_adj_cone -dm_plex_adj_closure 0

2290:     test:
2291:       suffix: adv_2d_tri_0
2292:       requires: triangle
2293:       TODO: how did this ever get in main when there is no support for this
2294:       args: -ufv_vtk_interval 0 -simplex -dm_refine 3 -dm_plex_faces 1,1 -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3

2296:     test:
2297:       suffix: adv_2d_tri_1
2298:       requires: triangle
2299:       TODO: how did this ever get in main when there is no support for this
2300:       args: -ufv_vtk_interval 0 -simplex -dm_refine 5 -dm_plex_faces 1,1 -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

2302:     test:
2303:       suffix: tut_1
2304:       requires: exodusii
2305:       nsize: 1
2306:       args: -dm_plex_filename ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo 2308: test: 2309: suffix: tut_2 2310: requires: exodusii 2311: nsize: 1 2312: args: -dm_plex_filename${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo -ts_type rosw

2314:     test:
2315:       suffix: tut_3
2316:       requires: exodusii
2317:       nsize: 4
2318:       args: -dm_distribute -dm_distribute_overlap 1 -dm_plex_filename ${wPETSC_DIR}/share/petsc/datafiles/meshes/annulus-20.exo -monitor Error -advect_sol_type bump -petscfv_type leastsquares -petsclimiter_type sin 2320: test: 2321: suffix: tut_4 2322: requires: exodusii 2323: nsize: 4 2324: args: -dm_distribute -dm_distribute_overlap 1 -dm_plex_filename${wPETSC_DIR}/share/petsc/datafiles/meshes/annulus-20.exo -physics sw -monitor Height,Energy -petscfv_type leastsquares -petsclimiter_type minmod

2326:   testset:
2327:     args: -dm_plex_adj_cone -dm_plex_adj_closure 0 -dm_plex_simplex 0 -dm_plex_box_faces 1,1,1

2329:     # 2D Advection 0-10
2330:     test:
2331:       suffix: 0
2332:       requires: exodusii
2333:       args: -ufv_vtk_interval 0 -dm_plex_filename ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo 2335: test: 2336: suffix: 1 2337: requires: exodusii 2338: args: -ufv_vtk_interval 0 -dm_plex_filename${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo

2340:     test:
2341:       suffix: 2
2342:       requires: exodusii
2343:       nsize: 2
2344:       args: -dm_distribute -dm_distribute_overlap 1 -ufv_vtk_interval 0 -dm_plex_filename ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo 2346: test: 2347: suffix: 3 2348: requires: exodusii 2349: nsize: 2 2350: args: -dm_distribute -dm_distribute_overlap 1 -ufv_vtk_interval 0 -dm_plex_filename${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo

2352:     test:
2353:       suffix: 4
2354:       requires: exodusii
2355:       nsize: 8
2356:       args: -dm_distribute -dm_distribute_overlap 1 -ufv_vtk_interval 0 -dm_plex_filename ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad.exo 2358: test: 2359: suffix: 5 2360: requires: exodusii 2361: args: -ufv_vtk_interval 0 -dm_plex_filename${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo -ts_type rosw -ts_adapt_reject_safety 1

2363:     test:
2364:       suffix: 7
2365:       requires: exodusii
2366:       args: -ufv_vtk_interval 0 -dm_plex_filename ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 1 2368: test: 2369: suffix: 8 2370: requires: exodusii 2371: nsize: 2 2372: args: -dm_distribute -dm_distribute_overlap 1 -ufv_vtk_interval 0 -dm_plex_filename${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 1

2374:     test:
2375:       suffix: 9
2376:       requires: exodusii
2377:       nsize: 8
2378:       args: -dm_distribute -dm_distribute_overlap 1 -ufv_vtk_interval 0 -dm_plex_filename ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 1 2380: test: 2381: suffix: 10 2382: requires: exodusii 2383: args: -ufv_vtk_interval 0 -dm_plex_filename${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad.exo

2385:     # 2D Shallow water
2386:     test:
2387:       suffix: sw_0
2388:       requires: exodusii
2389:       args: -ufv_vtk_interval 0 -dm_plex_filename ${wPETSC_DIR}/share/petsc/datafiles/meshes/annulus-20.exo -bc_wall 100,101 -physics sw -ufv_cfl 5 -petscfv_type leastsquares -petsclimiter_type sin -ts_max_time 1 -ts_ssp_type rks2 -ts_ssp_nstages 10 -monitor height,energy 2391: test: 2392: suffix: sw_hll 2393: args: -ufv_vtk_interval 0 -bc_wall 1,2,3,4 -physics sw -ufv_cfl 3 -petscfv_type leastsquares -petsclimiter_type sin -ts_max_steps 5 -ts_ssp_type rks2 -ts_ssp_nstages 10 -monitor height,energy -grid_bounds 0,5,0,5 -dm_plex_box_faces 25,25 -sw_riemann hll 2395: # 2D Advection: p4est 2396: test: 2397: suffix: p4est_advec_2d 2398: requires: p4est 2399: args: -ufv_vtk_interval 0 -dm_type p4est -dm_forest_minimum_refinement 1 -dm_forest_initial_refinement 2 -dm_p4est_refine_pattern hash -dm_forest_maximum_refinement 5 2401: # Advection in a box 2402: test: 2403: suffix: adv_2d_quad_0 2404: args: -ufv_vtk_interval 0 -dm_refine 3 -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3 2406: test: 2407: suffix: adv_2d_quad_1 2408: args: -ufv_vtk_interval 0 -dm_refine 3 -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 2409: timeoutfactor: 3 2411: test: 2412: suffix: adv_2d_quad_p4est_0 2413: requires: p4est 2414: args: -ufv_vtk_interval 0 -dm_refine 5 -dm_type p4est -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3 2416: test: 2417: suffix: adv_2d_quad_p4est_1 2418: requires: p4est 2419: 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 2420: timeoutfactor: 3 2422: test: 2423: suffix: adv_2d_quad_p4est_adapt_0 2424: requires: p4est !__float128 #broken for quad precision 2425: 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_max_time 0.01 2426: timeoutfactor: 3 2428: test: 2429: suffix: adv_0 2430: requires: exodusii 2431: args: -ufv_vtk_interval 0 -dm_plex_filename${wPETSC_DIR}/share/petsc/datafiles/meshes/blockcylinder-50.exo -bc_inflow 100,101,200 -bc_outflow 201

2433:     test:
2434:       suffix: shock_0
2435:       requires: p4est !single !complex
2436:       args: -dm_plex_box_faces 2,1 -grid_bounds -1,1.,0.,1 -grid_skew_60 \
2437:       -dm_type p4est -dm_forest_partition_overlap 1 -dm_forest_maximum_refinement 6 -dm_forest_minimum_refinement 2 -dm_forest_initial_refinement 2 \
2438:       -ufv_use_amr -refine_vec_tagger_box 0.5,inf -coarsen_vec_tagger_box 0,1.e-2 -refine_tag_view -coarsen_tag_view \
2439:       -bc_wall 1,2,3,4 -physics euler -eu_type iv_shock -ufv_cfl 10 -eu_alpha 60. -eu_gamma 1.4 -eu_amach 2.02 -eu_rho2 3. \
2440:       -petscfv_type leastsquares -petsclimiter_type minmod -petscfv_compute_gradients 0 \
2441:       -ts_max_time 0.5 -ts_ssp_type rks2 -ts_ssp_nstages 10 \
2442:       -ufv_vtk_basename ${wPETSC_DIR}/ex11 -ufv_vtk_interval 0 -monitor density,energy 2443: timeoutfactor: 3 2445: # Test GLVis visualization of PetscFV fields 2446: test: 2447: suffix: glvis_adv_2d_tet 2448: args: -ufv_vtk_interval 0 -ufv_vtk_monitor 0 \ 2449: -dm_plex_filename${wPETSC_DIR}/share/petsc/datafiles/meshes/square_periodic.msh -dm_plex_gmsh_periodic 0 \
2450:             -ts_monitor_solution glvis: -ts_max_steps 0

2452:     test:
2453:       suffix: glvis_adv_2d_quad
2454:       args: -ufv_vtk_interval 0 -ufv_vtk_monitor 0 -bc_inflow 1,2,4 -bc_outflow 3 \
2455:             -dm_refine 5 -dm_plex_separate_marker \
2456:             -ts_monitor_solution glvis: -ts_max_steps 0

2458: TEST*/