Actual source code: ex11.c

petsc-3.11.2 2019-05-18
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  1: static char help[] = "Second Order TVD Finite Volume Example.\n";

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

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

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

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

The mesh is read in from an ExodusII file, usually generated by Cubit.
 37:  #include <petscdmplex.h>
 38:  #include <petscdmforest.h>
 39:  #include <petscds.h>
 40:  #include <petscts.h>
 41: #include <petscsf.h> /* For SplitFaces() */

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

 46: static PetscFunctionList PhysicsList;

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

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

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

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

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

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

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

107: struct _n_User {
108:   PetscInt numSplitFaces;
109:   PetscInt vtkInterval;   /* For monitor */
110:   char outputBasename[PETSC_MAX_PATH_LEN]; /* Basename for output files */
111:   PetscInt monitorStepOffset;
112:   Model    model;
113:   PetscBool vtkmon;
114: };

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

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

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

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

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

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

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

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

168:   xG[0] = advect->inflowState;
169:   return(0);
170: }

172: static PetscErrorCode PhysicsBoundary_Advect_Outflow(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
173: {
175:   xG[0] = xI[0];
176:   return(0);
177: }

179: 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)
180: {
181:   Physics_Advect *advect = (Physics_Advect*)phys->data;
182:   PetscReal      wind[DIM],wn;

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

199:       rad2 = 0.;
200:       for (i = 0; i < dim; i++) {
201:         comp2[i] = qp[i] * qp[i];
202:         rad2    += comp2[i];
203:       }

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

211:         for (i = 1; i < dim; i++) {
212:           if (comp2[i] > maxComp2) {
213:             maxI     = i;
214:             maxComp2 = comp2[i];
215:           }
216:         }
217:         wind[maxI] = 0.;
218:       }
219:     }
220:     break;
221:   default:
222:   {
223:     PetscInt i;
224:     for (i = 0; i < DIM; ++i) wind[i] = 0.0;
225:   }
226:   /* default: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for solution type %s",AdvectSolBumpTypes[advect->soltype]); */
227:   }
228:   wn      = Dot2Real(wind, n);
229:   flux[0] = (wn > 0 ? xL[0] : xR[0]) * wn;
230: }

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

238:   switch (advect->soltype) {
239:   case ADVECT_SOL_TILTED: {
240:     PetscReal             x0[DIM];
241:     Physics_Advect_Tilted *tilted = &advect->sol.tilted;
242:     Waxpy2Real(-time,tilted->wind,x,x0);
243:     if (x0[1] > 0) u[0] = 1.*x[0] + 3.*x[1];
244:     else u[0] = advect->inflowState;
245:   } break;
246:   case ADVECT_SOL_BUMP_CAVITY:
247:   case ADVECT_SOL_BUMP: {
248:     Physics_Advect_Bump *bump = &advect->sol.bump;
249:     PetscReal           x0[DIM],v[DIM],r,cost,sint;
250:     cost  = PetscCosReal(time);
251:     sint  = PetscSinReal(time);
252:     x0[0] = cost*x[0] + sint*x[1];
253:     x0[1] = -sint*x[0] + cost*x[1];
254:     Waxpy2Real(-1,bump->center,x0,v);
255:     r = Norm2Real(v);
256:     switch (bump->type) {
257:     case ADVECT_SOL_BUMP_CONE:
258:       u[0] = PetscMax(1 - r/bump->radius,0);
259:       break;
260:     case ADVECT_SOL_BUMP_COS:
261:       u[0] = 0.5 + 0.5*PetscCosReal(PetscMin(r/bump->radius,1)*PETSC_PI);
262:       break;
263:     }
264:   } break;
265:   default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unknown solution type");
266:   }
267:   return(0);
268: }

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

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

284: static PetscErrorCode SetUpBC_Advect(PetscDS prob, Physics phys)
285: {
287:   const PetscInt inflowids[] = {100,200,300},outflowids[] = {101};

290:   /* Register "canned" boundary conditions and defaults for where to apply. */
291:   PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "inflow",  "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_Advect_Inflow,  ALEN(inflowids),  inflowids,  phys);
292:   PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "outflow", "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_Advect_Outflow, ALEN(outflowids), outflowids, phys);
293:   return(0);
294: }

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

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

308:   PetscOptionsHead(PetscOptionsObject,"Advect options");
309:   {
310:     PetscInt two = 2,dof = 1;
311:     advect->soltype = ADVECT_SOL_TILTED;
312:     PetscOptionsEnum("-advect_sol_type","solution type","",AdvectSolTypes,(PetscEnum)advect->soltype,(PetscEnum*)&advect->soltype,NULL);
313:     switch (advect->soltype) {
314:     case ADVECT_SOL_TILTED: {
315:       Physics_Advect_Tilted *tilted = &advect->sol.tilted;
316:       two = 2;
317:       tilted->wind[0] = 0.0;
318:       tilted->wind[1] = 1.0;
319:       PetscOptionsRealArray("-advect_tilted_wind","background wind vx,vy","",tilted->wind,&two,NULL);
320:       advect->inflowState = -2.0;
321:       PetscOptionsRealArray("-advect_tilted_inflow","Inflow state","",&advect->inflowState,&dof,NULL);
322:       phys->maxspeed = Norm2Real(tilted->wind);
323:     } break;
324:     case ADVECT_SOL_BUMP_CAVITY:
325:     case ADVECT_SOL_BUMP: {
326:       Physics_Advect_Bump *bump = &advect->sol.bump;
327:       two = 2;
328:       bump->center[0] = 2.;
329:       bump->center[1] = 0.;
330:       PetscOptionsRealArray("-advect_bump_center","location of center of bump x,y","",bump->center,&two,NULL);
331:       bump->radius = 0.9;
332:       PetscOptionsReal("-advect_bump_radius","radius of bump","",bump->radius,&bump->radius,NULL);
333:       bump->type = ADVECT_SOL_BUMP_CONE;
334:       PetscOptionsEnum("-advect_bump_type","type of bump","",AdvectSolBumpTypes,(PetscEnum)bump->type,(PetscEnum*)&bump->type,NULL);
335:       phys->maxspeed = 3.;       /* radius of mesh, kludge */
336:     } break;
337:     }
338:   }
339:   PetscOptionsTail();
340:   /* Initial/transient solution with default boundary conditions */
341:   ModelSolutionSetDefault(mod,PhysicsSolution_Advect,phys);
342:   /* Register "canned" functionals */
343:   ModelFunctionalRegister(mod,"Solution",&advect->functional.Solution,PhysicsFunctional_Advect,phys);
344:   ModelFunctionalRegister(mod,"Error",&advect->functional.Error,PhysicsFunctional_Advect,phys);
345:   mod->bcs[0] = mod->bcs[1] = mod->bcs[2] = DM_BOUNDARY_GHOSTED;
346:   return(0);
347: }

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

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

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

382:   Scale2Real(1./x->h,x->uh,u);
383:   uhn  = x->uh[0] * n[0] + x->uh[1] * n[1];
384:   f->h = uhn;
385:   for (i=0; i<DIM; i++) f->uh[i] = u[i] * uhn + sw->gravity * PetscSqr(x->h) * n[i];
386:   return(0);
387: }

389: static PetscErrorCode PhysicsBoundary_SW_Wall(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
390: {
392:   xG[0] = xI[0];
393:   xG[1] = -xI[1];
394:   xG[2] = -xI[2];
395:   return(0);
396: }

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

414: #if defined(PETSC_USE_COMPLEX)
415:   uLreal.swnode.h = 0; uRreal.swnode.h = 0;
416:   for (i = 0; i < 1+dim; i++) uLreal.vals[i] = PetscRealPart(xL[i]);
417:   for (i = 0; i < 1+dim; i++) uRreal.vals[i] = PetscRealPart(xR[i]);
418: #endif
419:   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"); */
420:   nn[0] = n[0];
421:   nn[1] = n[1];
422:   Normalize2Real(nn);
423:   SWFlux(phys,nn,uL,&(fL.swnode));
424:   SWFlux(phys,nn,uR,&(fR.swnode));
425:   cL    = PetscSqrtReal(sw->gravity*uL->h);
426:   cR    = PetscSqrtReal(sw->gravity*uR->h); /* gravity wave speed */
427:   speed = PetscMax(PetscAbsReal(Dot2Real(uL->uh,nn)/uL->h) + cL,PetscAbsReal(Dot2Real(uR->uh,nn)/uR->h) + cR);
428:   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);
429: }

431: static PetscErrorCode PhysicsSolution_SW(Model mod,PetscReal time,const PetscReal *x,PetscScalar *u,void *ctx)
432: {
433:   PetscReal dx[2],r,sigma;

436:   if (time != 0.0) SETERRQ1(mod->comm,PETSC_ERR_SUP,"No solution known for time %g",(double)time);
437:   dx[0] = x[0] - 1.5;
438:   dx[1] = x[1] - 1.0;
439:   r     = Norm2Real(dx);
440:   sigma = 0.5;
441:   u[0]  = 1 + 2*PetscExpReal(-PetscSqr(r)/(2*PetscSqr(sigma)));
442:   u[1]  = 0.0;
443:   u[2]  = 0.0;
444:   return(0);
445: }

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

456:   h = x->h;
457:   Scale2Real(1./x->h,x->uh,u);
458:   f[sw->functional.Height] = h;
459:   f[sw->functional.Speed]  = Norm2Real(u) + PetscSqrtReal(sw->gravity*h);
460:   f[sw->functional.Energy] = 0.5*(Dot2Real(x->uh,u) + sw->gravity*PetscSqr(h));
461:   return(0);
462: }

464: static PetscErrorCode SetUpBC_SW(PetscDS prob,Physics phys)
465: {
467:   const PetscInt wallids[] = {100,101,200,300};
469:   PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "wall", "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_SW_Wall, ALEN(wallids), wallids, phys);
470:   return(0);
471: }

473: static PetscErrorCode PhysicsCreate_SW(Model mod,Physics phys,PetscOptionItems *PetscOptionsObject)
474: {
475:   Physics_SW     *sw;

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

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

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

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

500:   return(0);
501: }

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

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

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

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

550:   if (eu->type==EULER_IV_SHOCK || eu->type==EULER_SS_SHOCK) {
551:     /******************* Euler Density Shock ********************/
552:     /* On initial-value and self-similar solutions of the compressible Euler equations */
553:     /* Ravi Samtaney and D. I. Pullin */
554:     /* Phys. Fluids 8, 2650 (1996); http://dx.doi.org/10.1063/1.869050 */
555:     /* initial conditions 1: left of shock, 0: left of discontinuity 2: right of discontinuity,  */
556:     p0 = 1.;
557:     if (x[0] < 0.0 + x[1]*eu->pars[EULER_PAR_ITANA]) {
558:       if (x[0] < mod->bounds[0]*0.5) { /* left of shock (1) */
559:         PetscReal amach,rho,press,gas1,p1;
560:         amach = eu->pars[EULER_PAR_AMACH];
561:         rho = 1.;
562:         press = p0;
563:         p1 = press*(1.0+2.0*gamma/(gamma+1.0)*(amach*amach-1.0));
564:         gas1 = (gamma-1.0)/(gamma+1.0);
565:         uu->r = rho*(p1/press+gas1)/(gas1*p1/press+1.0);
566:         uu->ru[0]   = ((uu->r - rho)*PetscSqrtReal(gamma*press/rho)*amach);
567:         uu->E = p1/(gamma-1.0) + .5/uu->r*uu->ru[0]*uu->ru[0];
568:       }
569:       else { /* left of discontinuity (0) */
570:         uu->r = 1.; /* rho = 1 */
571:         uu->E = p0/(gamma-1.0);
572:       }
573:     }
574:     else { /* right of discontinuity (2) */
575:       uu->r = eu->pars[EULER_PAR_RHOR];
576:       uu->E = p0/(gamma-1.0);
577:     }
578:   }
579:   else if (eu->type==EULER_SHOCK_TUBE) {
580:     /* 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. */
581:     if (x[0] < 0.0 ) {
582:       uu->r = 8.;
583:       uu->E = 10./(gamma-1.);
584:     }
585:     else {
586:       uu->r = 1.;
587:       uu->E = 1./(gamma-1.);
588:     }
589:   }
590:   else if (eu->type==EULER_LINEAR_WAVE) {
591:     initLinearWave( uu, gamma, x, mod->bounds[1] - mod->bounds[0]);
592:   }
593:   else SETERRQ1(mod->comm,PETSC_ERR_SUP,"Unknown type %d",eu->type);

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

600:   return(0);
601: }

603: static PetscErrorCode Pressure_PG(const PetscReal gamma,const EulerNode *x,PetscReal *p)
604: {
605:   PetscReal ru2;

608:   ru2  = DotDIMReal(x->ru,x->ru);
609:   (*p)=(x->E - 0.5*ru2/x->r)*(gamma - 1.0); /* (E - rho V^2/2)(gamma-1) = e rho (gamma-1) */
610:   return(0);
611: }

613: static PetscErrorCode SpeedOfSound_PG(const PetscReal *gamma, const EulerNode *x, PetscReal *c)
614: {
615:   PetscReal p;

618:   Pressure_PG(*gamma,x,&p);
619:   if (p<0.) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"negative pressure time %g -- NEED TO FIX!!!!!!",(double) p);
620:   /* pars[EULER_PAR_GAMMA] = heat capacity ratio */
621:   (*c)=PetscSqrtReal(*gamma * p / x->r);
622:   return(0);
623: }

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

639:   Pressure_PG(eu->pars[EULER_PAR_GAMMA],x,&p);
640:   nu = DotDIMReal(x->ru,n);
641:   f->r = nu;   /* A rho u */
642:   nu /= x->r;  /* A u */
643:   for (i=0; i<DIM; i++) f->ru[i] = nu * x->ru[i] + n[i]*p;  /* r u^2 + p */
644:   f->E = nu * (x->E + p); /* u(e+p) */
645:   return(0);
646: }

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

684:   for (i=0,s2=0.; i<DIM; i++) {
685:     nn[i] = n[i];
686:     s2 += nn[i]*nn[i];
687:   }
688:   s2 = PetscSqrtReal(s2); /* |n|_2 = sum(n^2)^1/2 */
689:   for (i=0.; i<DIM; i++) nn[i] /= s2;
690:   if (0) { /* Rusanov */
691:     const EulerNode *uL = (const EulerNode*)xL,*uR = (const EulerNode*)xR;
692:     EulerNodeUnion  fL,fR;
693:     EulerFlux(phys,nn,uL,&(fL.eulernode));
694:     EulerFlux(phys,nn,uR,&(fR.eulernode));
695:     eu->sound(&eu->pars[EULER_PAR_GAMMA],uL,&cL);if (ierr) exit(13);
696:     eu->sound(&eu->pars[EULER_PAR_GAMMA],uR,&cR);if (ierr) exit(14);
697:     velL = DotDIMReal(uL->ru,nn)/uL->r;
698:     velR = DotDIMReal(uR->ru,nn)/uR->r;
699:     speed = PetscMax(velR + cR, velL + cL);
700:     for (i=0; i<2+dim; i++) flux[i] = 0.5*((fL.vals[i]+fR.vals[i]) + speed*(xL[i] - xR[i]))*s2;
701:   }
702:   else {
703:     int dim = DIM;
704:     /* int iwave =  */
705:     godunovflux(xL, xR, flux, nn, &dim, &eu->pars[EULER_PAR_GAMMA]);
706:     for (i=0; i<2+dim; i++) flux[i] *= s2;
707:   }
708:   PetscFunctionReturnVoid();
709: }

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

719:   f[eu->monitor.Density]  = x->r;
720:   f[eu->monitor.Momentum] = NormDIM(x->ru);
721:   f[eu->monitor.Energy]   = x->E;
722:   f[eu->monitor.Speed]    = NormDIM(x->ru)/x->r;
723:   Pressure_PG(eu->pars[EULER_PAR_GAMMA], x, &p);
724:   f[eu->monitor.Pressure] = p;
725:   return(0);
726: }

728: static PetscErrorCode SetUpBC_Euler(PetscDS prob,Physics phys)
729: {
730:   PetscErrorCode  ierr;
731:   Physics_Euler   *eu = (Physics_Euler *) phys->data;
732:   if (eu->type == EULER_LINEAR_WAVE) {
733:     const PetscInt wallids[] = {100,101};
734:     PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "wall", "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_Euler_Wall, ALEN(wallids), wallids, phys);
735:   }
736:   else {
737:     const PetscInt wallids[] = {100,101,200,300};
738:     PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "wall", "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_Euler_Wall, ALEN(wallids), wallids, phys);
739:   }
740:   return(0);
741: }

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

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

811:   return(0);
812: }

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

820:   for (i = 0; i < numComps; i++) {
821:     for (j = 0; j < dim; j++) {
822:       err += PetscSqr(PetscRealPart(grad[i * dim + j]));
823:     }
824:   }
825:   *error = volume * err;
826:   return(0);
827: }

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

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

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

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

873:       if ((face < fStart) || (face >= fEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Got invalid point %d which is not a face", face);
874:       DMPlexGetSupportSize(dm, face, &nC);
875:       if (nC != 2) continue;
876:       DMPlexGetSupport(dm, face, &neighbors);
877:       if ((neighbors[0] >= cEndInterior) || (neighbors[1] >= cEndInterior)) continue;
878:       if ((neighbors[0] < cStart) || (neighbors[0] >= cEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Got invalid point %d which is not a cell", neighbors[0]);
879:       if ((neighbors[1] < cStart) || (neighbors[1] >= cEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Got invalid point %d which is not a cell", neighbors[1]);
880:       DMGetLabelValue(dm, name, neighbors[0], &regionA);
881:       DMGetLabelValue(dm, name, neighbors[1], &regionB);
882:       if (regionA < 0) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Invalid label %s: Cell %d has no value", name, neighbors[0]);
883:       if (regionB < 0) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Invalid label %s: Cell %d has no value", name, neighbors[1]);
884:       if (regionA != regionB) {
885:         DMSetLabelValue(dm, bdname, faces[f], 1);
886:       }
887:     }
888:   }
889:   ISRestoreIndices(innerIS, &cells);
890:   ISDestroy(&innerIS);
891:   {
892:     DMLabel label;

894:     DMGetLabel(dm, bdname, &label);
895:     DMLabelView(label, PETSC_VIEWER_STDOUT_WORLD);
896:   }
897:   return(0);
898: }

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

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

926:   DMGetLabelIdIS(dm, labelName, &idIS);
927:   ISGetLocalSize(idIS, &numFS);
928:   ISGetIndices(idIS, &ids);

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

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

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

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

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

987:     DMPlexGetConeSize(dm, p, &size);
988:     DMPlexGetCone(dm, p, &points);
989:     DMPlexGetConeOrientation(dm, p, &orientations);
990:     for (i = 0; i < size; ++i) newpoints[i] = points[i];
991:     DMPlexSetCone(sdm, newp, newpoints);
992:     DMPlexSetConeOrientation(sdm, newp, orientations);
993:     DMPlexGetSupportSize(dm, p, &size);
994:     DMPlexGetSupport(dm, p, &points);
995:     for (i = 0; i < size; ++i) newpoints[i] = points[i];
996:     DMPlexSetSupport(sdm, newp, newpoints);
997:   }
998:   PetscFree(newpoints);
999:   for (fs = 0, newf = fEnd; fs < numFS; ++fs) {
1000:     IS             faceIS;
1001:     const PetscInt *faces;
1002:     PetscInt       numFaces, f;

1004:     DMGetStratumIS(dm, labelName, ids[fs], &faceIS);
1005:     ISGetLocalSize(faceIS, &numFaces);
1006:     ISGetIndices(faceIS, &faces);
1007:     for (f = 0; f < numFaces; ++f, ++newf) {
1008:       const PetscInt *points;

1010:       DMPlexGetCone(dm, faces[f], &points);
1011:       DMPlexSetCone(sdm, newf, points);
1012:       DMPlexGetSupport(dm, faces[f], &points);
1013:       DMPlexSetSupport(sdm, newf, points);
1014:     }
1015:     ISRestoreIndices(faceIS, &faces);
1016:     ISDestroy(&faceIS);
1017:   }
1018:   ISRestoreIndices(idIS, &ids);
1019:   ISDestroy(&idIS);
1020:   DMPlexStratify(sdm);
1021:   DMPlexSetHybridBounds(sdm, cEndInterior, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_DETERMINE);
1022:   /* Convert coordinates */
1023:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
1024:   DMGetCoordinateSection(dm, &coordSection);
1025:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &newCoordSection);
1026:   PetscSectionSetNumFields(newCoordSection, 1);
1027:   PetscSectionSetFieldComponents(newCoordSection, 0, dim);
1028:   PetscSectionSetChart(newCoordSection, vStart, vEnd);
1029:   for (v = vStart; v < vEnd; ++v) {
1030:     PetscSectionSetDof(newCoordSection, v, dim);
1031:     PetscSectionSetFieldDof(newCoordSection, v, 0, dim);
1032:   }
1033:   PetscSectionSetUp(newCoordSection);
1034:   DMSetCoordinateSection(sdm, PETSC_DETERMINE, newCoordSection);
1035:   PetscSectionDestroy(&newCoordSection); /* relinquish our reference */
1036:   DMGetCoordinatesLocal(dm, &coordinates);
1037:   DMSetCoordinatesLocal(sdm, coordinates);
1038:   /* Convert labels */
1039:   DMGetNumLabels(dm, &numLabels);
1040:   for (l = 0; l < numLabels; ++l) {
1041:     const char *lname;
1042:     PetscBool  isDepth, isDim;

1044:     DMGetLabelName(dm, l, &lname);
1045:     PetscStrcmp(lname, "depth", &isDepth);
1046:     if (isDepth) continue;
1047:     PetscStrcmp(lname, "dim", &isDim);
1048:     if (isDim) continue;
1049:     DMCreateLabel(sdm, lname);
1050:     DMGetLabelIdIS(dm, lname, &idIS);
1051:     ISGetLocalSize(idIS, &numFS);
1052:     ISGetIndices(idIS, &ids);
1053:     for (fs = 0; fs < numFS; ++fs) {
1054:       IS             pointIS;
1055:       const PetscInt *points;
1056:       PetscInt       numPoints;

1058:       DMGetStratumIS(dm, lname, ids[fs], &pointIS);
1059:       ISGetLocalSize(pointIS, &numPoints);
1060:       ISGetIndices(pointIS, &points);
1061:       for (p = 0; p < numPoints; ++p) {
1062:         PetscInt newpoint = points[p];

1064:         DMSetLabelValue(sdm, lname, newpoint, ids[fs]);
1065:       }
1066:       ISRestoreIndices(pointIS, &points);
1067:       ISDestroy(&pointIS);
1068:     }
1069:     ISRestoreIndices(idIS, &ids);
1070:     ISDestroy(&idIS);
1071:   }
1072:   {
1073:     /* Convert pointSF */
1074:     const PetscSFNode *remotePoints;
1075:     PetscSFNode       *gremotePoints;
1076:     const PetscInt    *localPoints;
1077:     PetscInt          *glocalPoints,*newLocation,*newRemoteLocation;
1078:     PetscInt          numRoots, numLeaves;
1079:     PetscMPIInt       size;

1081:     MPI_Comm_size(PetscObjectComm((PetscObject)dm), &size);
1082:     DMGetPointSF(dm, &sfPoint);
1083:     DMGetPointSF(sdm, &gsfPoint);
1084:     DMPlexGetChart(dm,&pStart,&pEnd);
1085:     PetscSFGetGraph(sfPoint, &numRoots, &numLeaves, &localPoints, &remotePoints);
1086:     if (numRoots >= 0) {
1087:       PetscMalloc2(numRoots,&newLocation,pEnd-pStart,&newRemoteLocation);
1088:       for (l=0; l<numRoots; l++) newLocation[l] = l; /* + (l >= cEnd ? numGhostCells : 0); */
1089:       PetscSFBcastBegin(sfPoint, MPIU_INT, newLocation, newRemoteLocation);
1090:       PetscSFBcastEnd(sfPoint, MPIU_INT, newLocation, newRemoteLocation);
1091:       PetscMalloc1(numLeaves,    &glocalPoints);
1092:       PetscMalloc1(numLeaves, &gremotePoints);
1093:       for (l = 0; l < numLeaves; ++l) {
1094:         glocalPoints[l]        = localPoints[l]; /* localPoints[l] >= cEnd ? localPoints[l] + numGhostCells : localPoints[l]; */
1095:         gremotePoints[l].rank  = remotePoints[l].rank;
1096:         gremotePoints[l].index = newRemoteLocation[localPoints[l]];
1097:       }
1098:       PetscFree2(newLocation,newRemoteLocation);
1099:       PetscSFSetGraph(gsfPoint, numRoots+numGhostCells, numLeaves, glocalPoints, PETSC_OWN_POINTER, gremotePoints, PETSC_OWN_POINTER);
1100:     }
1101:     DMDestroy(dmSplit);
1102:     *dmSplit = sdm;
1103:   }
1104:   return(0);
1105: }

1107: PetscErrorCode CreatePartitionVec(DM dm, DM *dmCell, Vec *partition)
1108: {
1109:   PetscSF        sfPoint;
1110:   PetscSection   coordSection;
1111:   Vec            coordinates;
1112:   PetscSection   sectionCell;
1113:   PetscScalar    *part;
1114:   PetscInt       cStart, cEnd, c;
1115:   PetscMPIInt    rank;

1119:   DMGetCoordinateSection(dm, &coordSection);
1120:   DMGetCoordinatesLocal(dm, &coordinates);
1121:   DMClone(dm, dmCell);
1122:   DMGetPointSF(dm, &sfPoint);
1123:   DMSetPointSF(*dmCell, sfPoint);
1124:   DMSetCoordinateSection(*dmCell, PETSC_DETERMINE, coordSection);
1125:   DMSetCoordinatesLocal(*dmCell, coordinates);
1126:   MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);
1127:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionCell);
1128:   DMPlexGetHeightStratum(*dmCell, 0, &cStart, &cEnd);
1129:   PetscSectionSetChart(sectionCell, cStart, cEnd);
1130:   for (c = cStart; c < cEnd; ++c) {
1131:     PetscSectionSetDof(sectionCell, c, 1);
1132:   }
1133:   PetscSectionSetUp(sectionCell);
1134:   DMSetSection(*dmCell, sectionCell);
1135:   PetscSectionDestroy(&sectionCell);
1136:   DMCreateLocalVector(*dmCell, partition);
1137:   PetscObjectSetName((PetscObject)*partition, "partition");
1138:   VecGetArray(*partition, &part);
1139:   for (c = cStart; c < cEnd; ++c) {
1140:     PetscScalar *p;

1142:     DMPlexPointLocalRef(*dmCell, c, part, &p);
1143:     p[0] = rank;
1144:   }
1145:   VecRestoreArray(*partition, &part);
1146:   return(0);
1147: }

1149: PetscErrorCode CreateMassMatrix(DM dm, Vec *massMatrix, User user)
1150: {
1151:   DM                dmMass, dmFace, dmCell, dmCoord;
1152:   PetscSection      coordSection;
1153:   Vec               coordinates, facegeom, cellgeom;
1154:   PetscSection      sectionMass;
1155:   PetscScalar       *m;
1156:   const PetscScalar *fgeom, *cgeom, *coords;
1157:   PetscInt          vStart, vEnd, v;
1158:   PetscErrorCode    ierr;

1161:   DMGetCoordinateSection(dm, &coordSection);
1162:   DMGetCoordinatesLocal(dm, &coordinates);
1163:   DMClone(dm, &dmMass);
1164:   DMSetCoordinateSection(dmMass, PETSC_DETERMINE, coordSection);
1165:   DMSetCoordinatesLocal(dmMass, coordinates);
1166:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionMass);
1167:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
1168:   PetscSectionSetChart(sectionMass, vStart, vEnd);
1169:   for (v = vStart; v < vEnd; ++v) {
1170:     PetscInt numFaces;

1172:     DMPlexGetSupportSize(dmMass, v, &numFaces);
1173:     PetscSectionSetDof(sectionMass, v, numFaces*numFaces);
1174:   }
1175:   PetscSectionSetUp(sectionMass);
1176:   DMSetSection(dmMass, sectionMass);
1177:   PetscSectionDestroy(&sectionMass);
1178:   DMGetLocalVector(dmMass, massMatrix);
1179:   VecGetArray(*massMatrix, &m);
1180:   DMPlexTSGetGeometryFVM(dm, &facegeom, &cellgeom, NULL);
1181:   VecGetDM(facegeom, &dmFace);
1182:   VecGetArrayRead(facegeom, &fgeom);
1183:   VecGetDM(cellgeom, &dmCell);
1184:   VecGetArrayRead(cellgeom, &cgeom);
1185:   DMGetCoordinateDM(dm, &dmCoord);
1186:   VecGetArrayRead(coordinates, &coords);
1187:   for (v = vStart; v < vEnd; ++v) {
1188:     const PetscInt        *faces;
1189:     PetscFVFaceGeom       *fgA, *fgB, *cg;
1190:     PetscScalar           *vertex;
1191:     PetscInt               numFaces, sides[2], f, g;

1193:     DMPlexPointLocalRead(dmCoord, v, coords, &vertex);
1194:     DMPlexGetSupportSize(dmMass, v, &numFaces);
1195:     DMPlexGetSupport(dmMass, v, &faces);
1196:     for (f = 0; f < numFaces; ++f) {
1197:       sides[0] = faces[f];
1198:       DMPlexPointLocalRead(dmFace, faces[f], fgeom, &fgA);
1199:       for (g = 0; g < numFaces; ++g) {
1200:         const PetscInt *cells = NULL;
1201:         PetscReal      area   = 0.0;
1202:         PetscInt       numCells;

1204:         sides[1] = faces[g];
1205:         DMPlexPointLocalRead(dmFace, faces[g], fgeom, &fgB);
1206:         DMPlexGetJoin(dmMass, 2, sides, &numCells, &cells);
1207:         if (numCells != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Invalid join for faces");
1208:         DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cg);
1209:         area += PetscAbsScalar((vertex[0] - cg->centroid[0])*(fgA->centroid[1] - cg->centroid[1]) - (vertex[1] - cg->centroid[1])*(fgA->centroid[0] - cg->centroid[0]));
1210:         area += PetscAbsScalar((vertex[0] - cg->centroid[0])*(fgB->centroid[1] - cg->centroid[1]) - (vertex[1] - cg->centroid[1])*(fgB->centroid[0] - cg->centroid[0]));
1211:         m[f*numFaces+g] = Dot2Real(fgA->normal, fgB->normal)*area*0.5;
1212:         DMPlexRestoreJoin(dmMass, 2, sides, &numCells, &cells);
1213:       }
1214:     }
1215:   }
1216:   VecRestoreArrayRead(facegeom, &fgeom);
1217:   VecRestoreArrayRead(cellgeom, &cgeom);
1218:   VecRestoreArrayRead(coordinates, &coords);
1219:   VecRestoreArray(*massMatrix, &m);
1220:   DMDestroy(&dmMass);
1221:   return(0);
1222: }

1224: /* Behavior will be different for multi-physics or when using non-default boundary conditions */
1225: static PetscErrorCode ModelSolutionSetDefault(Model mod,SolutionFunction func,void *ctx)
1226: {
1228:   mod->solution    = func;
1229:   mod->solutionctx = ctx;
1230:   return(0);
1231: }

1233: static PetscErrorCode ModelFunctionalRegister(Model mod,const char *name,PetscInt *offset,FunctionalFunction func,void *ctx)
1234: {
1236:   FunctionalLink link,*ptr;
1237:   PetscInt       lastoffset = -1;

1240:   for (ptr=&mod->functionalRegistry; *ptr; ptr = &(*ptr)->next) lastoffset = (*ptr)->offset;
1241:   PetscNew(&link);
1242:   PetscStrallocpy(name,&link->name);
1243:   link->offset = lastoffset + 1;
1244:   link->func   = func;
1245:   link->ctx    = ctx;
1246:   link->next   = NULL;
1247:   *ptr         = link;
1248:   *offset      = link->offset;
1249:   return(0);
1250: }

1252: static PetscErrorCode ModelFunctionalSetFromOptions(Model mod,PetscOptionItems *PetscOptionsObject)
1253: {
1255:   PetscInt       i,j;
1256:   FunctionalLink link;
1257:   char           *names[256];

1260:   mod->numMonitored = ALEN(names);
1261:   PetscOptionsStringArray("-monitor","list of functionals to monitor","",names,&mod->numMonitored,NULL);
1262:   /* Create list of functionals that will be computed somehow */
1263:   PetscMalloc1(mod->numMonitored,&mod->functionalMonitored);
1264:   /* Create index of calls that we will have to make to compute these functionals (over-allocation in general). */
1265:   PetscMalloc1(mod->numMonitored,&mod->functionalCall);
1266:   mod->numCall = 0;
1267:   for (i=0; i<mod->numMonitored; i++) {
1268:     for (link=mod->functionalRegistry; link; link=link->next) {
1269:       PetscBool match;
1270:       PetscStrcasecmp(names[i],link->name,&match);
1271:       if (match) break;
1272:     }
1273:     if (!link) SETERRQ1(mod->comm,PETSC_ERR_USER,"No known functional '%s'",names[i]);
1274:     mod->functionalMonitored[i] = link;
1275:     for (j=0; j<i; j++) {
1276:       if (mod->functionalCall[j]->func == link->func && mod->functionalCall[j]->ctx == link->ctx) goto next_name;
1277:     }
1278:     mod->functionalCall[mod->numCall++] = link; /* Just points to the first link using the result. There may be more results. */
1279: next_name:
1280:     PetscFree(names[i]);
1281:   }

1283:   /* Find out the maximum index of any functional computed by a function we will be calling (even if we are not using it) */
1284:   mod->maxComputed = -1;
1285:   for (link=mod->functionalRegistry; link; link=link->next) {
1286:     for (i=0; i<mod->numCall; i++) {
1287:       FunctionalLink call = mod->functionalCall[i];
1288:       if (link->func == call->func && link->ctx == call->ctx) {
1289:         mod->maxComputed = PetscMax(mod->maxComputed,link->offset);
1290:       }
1291:     }
1292:   }
1293:   return(0);
1294: }

1296: static PetscErrorCode FunctionalLinkDestroy(FunctionalLink *link)
1297: {
1299:   FunctionalLink l,next;

1302:   if (!link) return(0);
1303:   l     = *link;
1304:   *link = NULL;
1305:   for (; l; l=next) {
1306:     next = l->next;
1307:     PetscFree(l->name);
1308:     PetscFree(l);
1309:   }
1310:   return(0);
1311: }

1313: /* put the solution callback into a functional callback */
1314: static PetscErrorCode SolutionFunctional(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *modctx)
1315: {
1316:   Model          mod;
1319:   mod  = (Model) modctx;
1320:   (*mod->solution)(mod, time, x, u, mod->solutionctx);
1321:   return(0);
1322: }

1324: PetscErrorCode SetInitialCondition(DM dm, Vec X, User user)
1325: {
1326:   PetscErrorCode     (*func[1]) (PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
1327:   void               *ctx[1];
1328:   Model              mod = user->model;
1329:   PetscErrorCode     ierr;

1332:   func[0] = SolutionFunctional;
1333:   ctx[0]  = (void *) mod;
1334:   DMProjectFunction(dm,0.0,func,ctx,INSERT_ALL_VALUES,X);
1335:   return(0);
1336: }

1338: static PetscErrorCode OutputVTK(DM dm, const char *filename, PetscViewer *viewer)
1339: {

1343:   PetscViewerCreate(PetscObjectComm((PetscObject)dm), viewer);
1344:   PetscViewerSetType(*viewer, PETSCVIEWERVTK);
1345:   PetscViewerFileSetName(*viewer, filename);
1346:   return(0);
1347: }

1349: static PetscErrorCode MonitorVTK(TS ts,PetscInt stepnum,PetscReal time,Vec X,void *ctx)
1350: {
1351:   User           user = (User)ctx;
1352:   DM             dm;
1353:   Vec            cellgeom;
1354:   PetscViewer    viewer;
1355:   char           filename[PETSC_MAX_PATH_LEN],*ftable = NULL;
1356:   PetscReal      xnorm;
1357:   PetscInt       cEndInterior;

1361:   PetscObjectSetName((PetscObject) X, "u");
1362:   VecGetDM(X,&dm);
1363:   DMPlexTSGetGeometryFVM(dm, NULL, &cellgeom, NULL);
1364:   VecNorm(X,NORM_INFINITY,&xnorm);

1366:   if (stepnum >= 0) {
1367:     stepnum += user->monitorStepOffset;
1368:   }
1369:   if (stepnum >= 0) {           /* No summary for final time */
1370:     Model             mod = user->model;
1371:     PetscInt          c,cStart,cEnd,fcount,i;
1372:     size_t            ftableused,ftablealloc;
1373:     const PetscScalar *cgeom,*x;
1374:     DM                dmCell;
1375:     DMLabel           vtkLabel;
1376:     PetscReal         *fmin,*fmax,*fintegral,*ftmp;
1377:     fcount = mod->maxComputed+1;
1378:     PetscMalloc4(fcount,&fmin,fcount,&fmax,fcount,&fintegral,fcount,&ftmp);
1379:     for (i=0; i<fcount; i++) {
1380:       fmin[i]      = PETSC_MAX_REAL;
1381:       fmax[i]      = PETSC_MIN_REAL;
1382:       fintegral[i] = 0;
1383:     }
1384:     VecGetDM(cellgeom,&dmCell);
1385:     DMPlexGetHybridBounds(dmCell, &cEndInterior, NULL, NULL, NULL);
1386:     DMPlexGetHeightStratum(dmCell,0,&cStart,&cEnd);
1387:     VecGetArrayRead(cellgeom,&cgeom);
1388:     VecGetArrayRead(X,&x);
1389:     DMGetLabel(dm,"vtk",&vtkLabel);
1390:     for (c = cStart; c < cEndInterior; ++c) {
1391:       PetscFVCellGeom       *cg;
1392:       const PetscScalar     *cx    = NULL;
1393:       PetscInt              vtkVal = 0;

1395:       /* not that these two routines as currently implemented work for any dm with a
1396:        * defaultSection/defaultGlobalSection */
1397:       DMPlexPointLocalRead(dmCell,c,cgeom,&cg);
1398:       DMPlexPointGlobalRead(dm,c,x,&cx);
1399:       if (vtkLabel) {DMLabelGetValue(vtkLabel,c,&vtkVal);}
1400:       if (!vtkVal || !cx) continue;        /* ghost, or not a global cell */
1401:       for (i=0; i<mod->numCall; i++) {
1402:         FunctionalLink flink = mod->functionalCall[i];
1403:         (*flink->func)(mod,time,cg->centroid,cx,ftmp,flink->ctx);
1404:       }
1405:       for (i=0; i<fcount; i++) {
1406:         fmin[i]       = PetscMin(fmin[i],ftmp[i]);
1407:         fmax[i]       = PetscMax(fmax[i],ftmp[i]);
1408:         fintegral[i] += cg->volume * ftmp[i];
1409:       }
1410:     }
1411:     VecRestoreArrayRead(cellgeom,&cgeom);
1412:     VecRestoreArrayRead(X,&x);
1413:     MPI_Allreduce(MPI_IN_PLACE,fmin,fcount,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)ts));
1414:     MPI_Allreduce(MPI_IN_PLACE,fmax,fcount,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
1415:     MPI_Allreduce(MPI_IN_PLACE,fintegral,fcount,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));

1417:     ftablealloc = fcount * 100;
1418:     ftableused  = 0;
1419:     PetscMalloc1(ftablealloc,&ftable);
1420:     for (i=0; i<mod->numMonitored; i++) {
1421:       size_t         countused;
1422:       char           buffer[256],*p;
1423:       FunctionalLink flink = mod->functionalMonitored[i];
1424:       PetscInt       id    = flink->offset;
1425:       if (i % 3) {
1426:         PetscMemcpy(buffer,"  ",2);
1427:         p    = buffer + 2;
1428:       } else if (i) {
1429:         char newline[] = "\n";
1430:         PetscMemcpy(buffer,newline,sizeof newline-1);
1431:         p    = buffer + sizeof newline - 1;
1432:       } else {
1433:         p = buffer;
1434:       }
1435:       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]);
1436:       countused--;
1437:       countused += p - buffer;
1438:       if (countused > ftablealloc-ftableused-1) { /* reallocate */
1439:         char *ftablenew;
1440:         ftablealloc = 2*ftablealloc + countused;
1441:         PetscMalloc(ftablealloc,&ftablenew);
1442:         PetscMemcpy(ftablenew,ftable,ftableused);
1443:         PetscFree(ftable);
1444:         ftable = ftablenew;
1445:       }
1446:       PetscMemcpy(ftable+ftableused,buffer,countused);
1447:       ftableused += countused;
1448:       ftable[ftableused] = 0;
1449:     }
1450:     PetscFree4(fmin,fmax,fintegral,ftmp);

1452:     PetscPrintf(PetscObjectComm((PetscObject)ts),"% 3D  time %8.4g  |x| %8.4g  %s\n",stepnum,(double)time,(double)xnorm,ftable ? ftable : "");
1453:     PetscFree(ftable);
1454:   }
1455:   if (user->vtkInterval < 1) return(0);
1456:   if ((stepnum == -1) ^ (stepnum % user->vtkInterval == 0)) {
1457:     if (stepnum == -1) {        /* Final time is not multiple of normal time interval, write it anyway */
1458:       TSGetStepNumber(ts,&stepnum);
1459:     }
1460:     PetscSNPrintf(filename,sizeof filename,"%s-%03D.vtu",user->outputBasename,stepnum);
1461:     OutputVTK(dm,filename,&viewer);
1462:     VecView(X,viewer);
1463:     PetscViewerDestroy(&viewer);
1464:   }
1465:   return(0);
1466: }

1468: static PetscErrorCode initializeTS(DM dm, User user, TS *ts)
1469: {

1473:   TSCreate(PetscObjectComm((PetscObject)dm), ts);
1474:   TSSetType(*ts, TSSSP);
1475:   TSSetDM(*ts, dm);
1476:   if (user->vtkmon) {
1477:     TSMonitorSet(*ts,MonitorVTK,user,NULL);
1478:   }
1479:   DMTSSetBoundaryLocal(dm, DMPlexTSComputeBoundary, user);
1480:   DMTSSetRHSFunctionLocal(dm, DMPlexTSComputeRHSFunctionFVM, user);
1481:   TSSetMaxTime(*ts,2.0);
1482:   TSSetExactFinalTime(*ts,TS_EXACTFINALTIME_STEPOVER);
1483:   return(0);
1484: }

1486: static PetscErrorCode adaptToleranceFVM(PetscFV fvm, TS ts, Vec sol, VecTagger refineTag, VecTagger coarsenTag, User user, TS *tsNew, Vec *solNew)
1487: {
1488:   DM                dm, gradDM, plex, cellDM, adaptedDM = NULL;
1489:   Vec               cellGeom, faceGeom;
1490:   PetscBool         isForest, computeGradient;
1491:   Vec               grad, locGrad, locX, errVec;
1492:   PetscInt          cStart, cEnd, cEndInterior, c, dim, nRefine, nCoarsen;
1493:   PetscReal         minMaxInd[2] = {PETSC_MAX_REAL, PETSC_MIN_REAL}, minMaxIndGlobal[2], minInd, maxInd, time;
1494:   PetscScalar       *errArray;
1495:   const PetscScalar *pointVals;
1496:   const PetscScalar *pointGrads;
1497:   const PetscScalar *pointGeom;
1498:   DMLabel           adaptLabel = NULL;
1499:   IS                refineIS, coarsenIS;
1500:   PetscErrorCode    ierr;

1503:   TSGetTime(ts,&time);
1504:   VecGetDM(sol, &dm);
1505:   DMGetDimension(dm,&dim);
1506:   PetscFVGetComputeGradients(fvm,&computeGradient);
1507:   PetscFVSetComputeGradients(fvm,PETSC_TRUE);
1508:   DMIsForest(dm, &isForest);
1509:   DMConvert(dm, DMPLEX, &plex);
1510:   DMPlexGetDataFVM(plex, fvm, &cellGeom, &faceGeom, &gradDM);
1511:   DMCreateLocalVector(plex,&locX);
1512:   DMPlexInsertBoundaryValues(plex, PETSC_TRUE, locX, 0.0, faceGeom, cellGeom, NULL);
1513:   DMGlobalToLocalBegin(plex, sol, INSERT_VALUES, locX);
1514:   DMGlobalToLocalEnd  (plex, sol, INSERT_VALUES, locX);
1515:   DMCreateGlobalVector(gradDM, &grad);
1516:   DMPlexReconstructGradientsFVM(plex, locX, grad);
1517:   DMCreateLocalVector(gradDM, &locGrad);
1518:   DMGlobalToLocalBegin(gradDM, grad, INSERT_VALUES, locGrad);
1519:   DMGlobalToLocalEnd(gradDM, grad, INSERT_VALUES, locGrad);
1520:   VecDestroy(&grad);
1521:   DMPlexGetHeightStratum(plex,0,&cStart,&cEnd);
1522:   DMPlexGetHybridBounds(plex,&cEndInterior,NULL,NULL,NULL);
1523:   cEnd = (cEndInterior < 0) ? cEnd : cEndInterior;
1524:   VecGetArrayRead(locGrad,&pointGrads);
1525:   VecGetArrayRead(cellGeom,&pointGeom);
1526:   VecGetArrayRead(locX,&pointVals);
1527:   VecGetDM(cellGeom,&cellDM);
1528:   DMLabelCreate(PETSC_COMM_SELF,"adapt",&adaptLabel);
1529:   VecCreateMPI(PetscObjectComm((PetscObject)plex),cEnd-cStart,PETSC_DETERMINE,&errVec);
1530:   VecSetUp(errVec);
1531:   VecGetArray(errVec,&errArray);
1532:   for (c = cStart; c < cEnd; c++) {
1533:     PetscReal             errInd = 0.;
1534:     PetscScalar           *pointGrad;
1535:     PetscScalar           *pointVal;
1536:     PetscFVCellGeom       *cg;

1538:     DMPlexPointLocalRead(gradDM,c,pointGrads,&pointGrad);
1539:     DMPlexPointLocalRead(cellDM,c,pointGeom,&cg);
1540:     DMPlexPointLocalRead(plex,c,pointVals,&pointVal);

1542:     (user->model->errorIndicator)(dim,cg->volume,user->model->physics->dof,pointVal,pointGrad,&errInd,user->model->errorCtx);
1543:     errArray[c-cStart] = errInd;
1544:     minMaxInd[0] = PetscMin(minMaxInd[0],errInd);
1545:     minMaxInd[1] = PetscMax(minMaxInd[1],errInd);
1546:   }
1547:   VecRestoreArray(errVec,&errArray);
1548:   VecRestoreArrayRead(locX,&pointVals);
1549:   VecRestoreArrayRead(cellGeom,&pointGeom);
1550:   VecRestoreArrayRead(locGrad,&pointGrads);
1551:   VecDestroy(&locGrad);
1552:   VecDestroy(&locX);
1553:   DMDestroy(&plex);

1555:   VecTaggerComputeIS(refineTag,errVec,&refineIS);
1556:   VecTaggerComputeIS(coarsenTag,errVec,&coarsenIS);
1557:   ISGetSize(refineIS,&nRefine);
1558:   ISGetSize(coarsenIS,&nCoarsen);
1559:   if (nRefine) {DMLabelSetStratumIS(adaptLabel,DM_ADAPT_REFINE,refineIS);}
1560:   if (nCoarsen) {DMLabelSetStratumIS(adaptLabel,DM_ADAPT_COARSEN,coarsenIS);}
1561:   ISDestroy(&coarsenIS);
1562:   ISDestroy(&refineIS);
1563:   VecDestroy(&errVec);

1565:   PetscFVSetComputeGradients(fvm,computeGradient);
1566:   minMaxInd[1] = -minMaxInd[1];
1567:   MPI_Allreduce(minMaxInd,minMaxIndGlobal,2,MPIU_REAL,MPI_MIN,PetscObjectComm((PetscObject)dm));
1568:   minInd = minMaxIndGlobal[0];
1569:   maxInd = -minMaxIndGlobal[1];
1570:   PetscInfo2(ts, "error indicator range (%E, %E)\n", minInd, maxInd);
1571:   if (nRefine || nCoarsen) { /* at least one cell is over the refinement threshold */
1572:     DMAdaptLabel(dm,adaptLabel,&adaptedDM);
1573:   }
1574:   DMLabelDestroy(&adaptLabel);
1575:   if (adaptedDM) {
1576:     PetscInfo2(ts, "Adapted mesh, marking %D cells for refinement, and %D cells for coarsening\n", nRefine, nCoarsen);
1577:     if (tsNew) {initializeTS(adaptedDM, user, tsNew);}
1578:     if (solNew) {
1579:       DMCreateGlobalVector(adaptedDM, solNew);
1580:       PetscObjectSetName((PetscObject) *solNew, "solution");
1581:       DMForestTransferVec(dm, sol, adaptedDM, *solNew, PETSC_TRUE, time);
1582:     }
1583:     if (isForest) {DMForestSetAdaptivityForest(adaptedDM,NULL);} /* clear internal references to the previous dm */
1584:     DMDestroy(&adaptedDM);
1585:   } else {
1586:     if (tsNew)  *tsNew  = NULL;
1587:     if (solNew) *solNew = NULL;
1588:   }
1589:   return(0);
1590: }

1592: int main(int argc, char **argv)
1593: {
1594:   MPI_Comm          comm;
1595:   PetscDS           prob;
1596:   PetscFV           fvm;
1597:   PetscLimiter      limiter = NULL, noneLimiter = NULL;
1598:   User              user;
1599:   Model             mod;
1600:   Physics           phys;
1601:   DM                dm;
1602:   PetscReal         ftime, cfl, dt, minRadius;
1603:   PetscInt          dim, nsteps;
1604:   TS                ts;
1605:   TSConvergedReason reason;
1606:   Vec               X;
1607:   PetscViewer       viewer;
1608:   PetscBool         simplex = PETSC_FALSE, vtkCellGeom, splitFaces, useAMR;
1609:   PetscInt          overlap, adaptInterval;
1610:   char              filename[PETSC_MAX_PATH_LEN] = "";
1611:   char              physname[256]  = "advect";
1612:   VecTagger         refineTag = NULL, coarsenTag = NULL;
1613:   PetscErrorCode    ierr;

1615:   PetscInitialize(&argc, &argv, (char*) 0, help);if (ierr) return ierr;
1616:   comm = PETSC_COMM_WORLD;

1618:   PetscNew(&user);
1619:   PetscNew(&user->model);
1620:   PetscNew(&user->model->physics);
1621:   mod           = user->model;
1622:   phys          = mod->physics;
1623:   mod->comm     = comm;
1624:   useAMR        = PETSC_FALSE;
1625:   adaptInterval = 1;

1627:   /* Register physical models to be available on the command line */
1628:   PetscFunctionListAdd(&PhysicsList,"advect"          ,PhysicsCreate_Advect);
1629:   PetscFunctionListAdd(&PhysicsList,"sw"              ,PhysicsCreate_SW);
1630:   PetscFunctionListAdd(&PhysicsList,"euler"           ,PhysicsCreate_Euler);

1632:   PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Mesh Options","");
1633:   {
1634:     cfl  = 0.9 * 4; /* default SSPRKS2 with s=5 stages is stable for CFL number s-1 */
1635:     PetscOptionsReal("-ufv_cfl","CFL number per step","",cfl,&cfl,NULL);
1636:     PetscOptionsString("-f","Exodus.II filename to read","",filename,filename,sizeof(filename),NULL);
1637:     PetscOptionsBool("-simplex","Flag to use a simplex mesh","",simplex,&simplex,NULL);
1638:     splitFaces = PETSC_FALSE;
1639:     PetscOptionsBool("-ufv_split_faces","Split faces between cell sets","",splitFaces,&splitFaces,NULL);
1640:     overlap = 1;
1641:     PetscOptionsInt("-ufv_mesh_overlap","Number of cells to overlap partitions","",overlap,&overlap,NULL);
1642:     user->vtkInterval = 1;
1643:     PetscOptionsInt("-ufv_vtk_interval","VTK output interval (0 to disable)","",user->vtkInterval,&user->vtkInterval,NULL);
1644:     user->vtkmon = PETSC_TRUE;
1645:     PetscOptionsBool("-ufv_vtk_monitor","Use VTKMonitor routine","",user->vtkmon,&user->vtkmon,NULL);
1646:     vtkCellGeom = PETSC_FALSE;
1647:     PetscStrcpy(user->outputBasename, "ex11");
1648:     PetscOptionsString("-ufv_vtk_basename","VTK output basename","",user->outputBasename,user->outputBasename,PETSC_MAX_PATH_LEN,NULL);
1649:     PetscOptionsBool("-ufv_vtk_cellgeom","Write cell geometry (for debugging)","",vtkCellGeom,&vtkCellGeom,NULL);
1650:     PetscOptionsBool("-ufv_use_amr","use local adaptive mesh refinement","",useAMR,&useAMR,NULL);
1651:     PetscOptionsInt("-ufv_adapt_interval","time steps between AMR","",adaptInterval,&adaptInterval,NULL);
1652:   }
1653:   PetscOptionsEnd();

1655:   if (useAMR) {
1656:     VecTaggerBox refineBox, coarsenBox;

1658:     refineBox.min  = refineBox.max  = PETSC_MAX_REAL;
1659:     coarsenBox.min = coarsenBox.max = PETSC_MIN_REAL;

1661:     VecTaggerCreate(comm,&refineTag);
1662:     PetscObjectSetOptionsPrefix((PetscObject)refineTag,"refine_");
1663:     VecTaggerSetType(refineTag,VECTAGGERABSOLUTE);
1664:     VecTaggerAbsoluteSetBox(refineTag,&refineBox);
1665:     VecTaggerSetFromOptions(refineTag);
1666:     VecTaggerSetUp(refineTag);
1667:     PetscObjectViewFromOptions((PetscObject)refineTag,NULL,"-tag_view");

1669:     VecTaggerCreate(comm,&coarsenTag);
1670:     PetscObjectSetOptionsPrefix((PetscObject)coarsenTag,"coarsen_");
1671:     VecTaggerSetType(coarsenTag,VECTAGGERABSOLUTE);
1672:     VecTaggerAbsoluteSetBox(coarsenTag,&coarsenBox);
1673:     VecTaggerSetFromOptions(coarsenTag);
1674:     VecTaggerSetUp(coarsenTag);
1675:     PetscObjectViewFromOptions((PetscObject)coarsenTag,NULL,"-tag_view");
1676:   }

1678:   PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Physics Options","");
1679:   {
1680:     PetscErrorCode (*physcreate)(Model,Physics,PetscOptionItems*);
1681:     PetscOptionsFList("-physics","Physics module to solve","",PhysicsList,physname,physname,sizeof physname,NULL);
1682:     PetscFunctionListFind(PhysicsList,physname,&physcreate);
1683:     PetscMemzero(phys,sizeof(struct _n_Physics));
1684:     (*physcreate)(mod,phys,PetscOptionsObject);
1685:     /* Count number of fields and dofs */
1686:     for (phys->nfields=0,phys->dof=0; phys->field_desc[phys->nfields].name; phys->nfields++) phys->dof += phys->field_desc[phys->nfields].dof;
1687:     if (phys->dof <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set dof",physname);
1688:     ModelFunctionalSetFromOptions(mod,PetscOptionsObject);
1689:   }
1690:   PetscOptionsEnd();

1692:   /* Create mesh */
1693:   {
1694:     size_t len,i;
1695:     for (i = 0; i < DIM; i++) { mod->bounds[2*i] = 0.; mod->bounds[2*i+1] = 1.;};
1696:     PetscStrlen(filename,&len);
1697:     dim = DIM;
1698:     if (!len) { /* a null name means just do a hex box */
1699:       PetscInt cells[3] = {1, 1, 1}; /* coarse mesh is one cell; refine from there */
1700:       PetscBool flg1, flg2, skew = PETSC_FALSE;
1701:       PetscInt nret1 = DIM;
1702:       PetscInt nret2 = 2*DIM;
1703:       PetscOptionsBegin(comm,NULL,"Rectangular mesh options","");
1704:       PetscOptionsIntArray("-grid_size","number of cells in each direction","",cells,&nret1,&flg1);
1705:       PetscOptionsRealArray("-grid_bounds","bounds of the mesh in each direction (i.e., x_min,x_max,y_min,y_max","",mod->bounds,&nret2,&flg2);
1706:       PetscOptionsBool("-grid_skew_60","Skew grid for 60 degree shock mesh","",skew,&skew,NULL);
1707:       PetscOptionsEnd();
1708:       if (flg1) {
1709:         dim = nret1;
1710:         if (dim != DIM) SETERRQ1(comm,PETSC_ERR_ARG_SIZ,"Dim wrong size %D in -grid_size",dim);
1711:       }
1712:       DMPlexCreateBoxMesh(comm, dim, simplex, cells, NULL, NULL, mod->bcs, PETSC_TRUE, &dm);
1713:       if (flg2) {
1714:         PetscInt dimEmbed, i;
1715:         PetscInt nCoords;
1716:         PetscScalar *coords;
1717:         Vec coordinates;

1719:         DMGetCoordinatesLocal(dm,&coordinates);
1720:         DMGetCoordinateDim(dm,&dimEmbed);
1721:         VecGetLocalSize(coordinates,&nCoords);
1722:         if (nCoords % dimEmbed) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Coordinate vector the wrong size");
1723:         VecGetArray(coordinates,&coords);
1724:         for (i = 0; i < nCoords; i += dimEmbed) {
1725:           PetscInt j;

1727:           PetscScalar *coord = &coords[i];
1728:           for (j = 0; j < dimEmbed; j++) {
1729:             coord[j] = mod->bounds[2 * j] + coord[j] * (mod->bounds[2 * j + 1] - mod->bounds[2 * j]);
1730:             if (dim==2 && cells[1]==1 && j==0 && skew) {
1731:               if (cells[0]==2 && i==8) {
1732:                 coord[j] = .57735026918963; /* hack to get 60 deg skewed mesh */
1733:               }
1734:               else if (cells[0]==3) {
1735:                 if(i==2 || i==10) coord[j] = mod->bounds[1]/4.;
1736:                 else if (i==4) coord[j] = mod->bounds[1]/2.;
1737:                 else if (i==12) coord[j] = 1.57735026918963*mod->bounds[1]/2.;
1738:               }
1739:             }
1740:           }
1741:         }
1742:         VecRestoreArray(coordinates,&coords);
1743:         DMSetCoordinatesLocal(dm,coordinates);
1744:       }
1745:     } else {
1746:       DMPlexCreateFromFile(comm, filename, PETSC_TRUE, &dm);
1747:     }
1748:   }
1749:   DMViewFromOptions(dm, NULL, "-orig_dm_view");
1750:   DMGetDimension(dm, &dim);

1752:   /* set up BCs, functions, tags */
1753:   DMCreateLabel(dm, "Face Sets");

1755:   mod->errorIndicator = ErrorIndicator_Simple;

1757:   {
1758:     DM dmDist;

1760:     DMSetBasicAdjacency(dm, PETSC_TRUE, PETSC_FALSE);
1761:     DMPlexDistribute(dm, overlap, NULL, &dmDist);
1762:     if (dmDist) {
1763:       DMDestroy(&dm);
1764:       dm   = dmDist;
1765:     }
1766:   }

1768:   DMSetFromOptions(dm);

1770:   {
1771:     DM gdm;

1773:     DMPlexConstructGhostCells(dm, NULL, NULL, &gdm);
1774:     DMDestroy(&dm);
1775:     dm   = gdm;
1776:     DMViewFromOptions(dm, NULL, "-dm_view");
1777:   }
1778:   if (splitFaces) {ConstructCellBoundary(dm, user);}
1779:   SplitFaces(&dm, "split faces", user);

1781:   PetscFVCreate(comm, &fvm);
1782:   PetscFVSetFromOptions(fvm);
1783:   PetscFVSetNumComponents(fvm, phys->dof);
1784:   PetscFVSetSpatialDimension(fvm, dim);
1785:   PetscObjectSetName((PetscObject) fvm,"");
1786:   {
1787:     PetscInt f, dof;
1788:     for (f=0,dof=0; f < phys->nfields; f++) {
1789:       PetscInt newDof = phys->field_desc[f].dof;

1791:       if (newDof == 1) {
1792:         PetscFVSetComponentName(fvm,dof,phys->field_desc[f].name);
1793:       }
1794:       else {
1795:         PetscInt j;

1797:         for (j = 0; j < newDof; j++) {
1798:           char     compName[256]  = "Unknown";

1800:           PetscSNPrintf(compName,sizeof(compName),"%s_%d",phys->field_desc[f].name,j);
1801:           PetscFVSetComponentName(fvm,dof+j,compName);
1802:         }
1803:       }
1804:       dof += newDof;
1805:     }
1806:   }
1807:   /* FV is now structured with one field having all physics as components */
1808:   DMAddField(dm, NULL, (PetscObject) fvm);
1809:   DMCreateDS(dm);
1810:   DMGetDS(dm, &prob);
1811:   PetscDSSetRiemannSolver(prob, 0, user->model->physics->riemann);
1812:   PetscDSSetContext(prob, 0, user->model->physics);
1813:   (*mod->setupbc)(prob,phys);
1814:   PetscDSSetFromOptions(prob);
1815:   {
1816:     char      convType[256];
1817:     PetscBool flg;

1819:     PetscOptionsBegin(comm, "", "Mesh conversion options", "DMPLEX");
1820:     PetscOptionsFList("-dm_type","Convert DMPlex to another format","ex12",DMList,DMPLEX,convType,256,&flg);
1821:     PetscOptionsEnd();
1822:     if (flg) {
1823:       DM dmConv;

1825:       DMConvert(dm,convType,&dmConv);
1826:       if (dmConv) {
1827:         DMViewFromOptions(dmConv, NULL, "-dm_conv_view");
1828:         DMDestroy(&dm);
1829:         dm   = dmConv;
1830:         DMSetFromOptions(dm);
1831:       }
1832:     }
1833:   }

1835:   initializeTS(dm, user, &ts);

1837:   DMCreateGlobalVector(dm, &X);
1838:   PetscObjectSetName((PetscObject) X, "solution");
1839:   SetInitialCondition(dm, X, user);
1840:   if (useAMR) {
1841:     PetscInt adaptIter;

1843:     /* use no limiting when reconstructing gradients for adaptivity */
1844:     PetscFVGetLimiter(fvm, &limiter);
1845:     PetscObjectReference((PetscObject) limiter);
1846:     PetscLimiterCreate(PetscObjectComm((PetscObject) fvm), &noneLimiter);
1847:     PetscLimiterSetType(noneLimiter, PETSCLIMITERNONE);

1849:     PetscFVSetLimiter(fvm, noneLimiter);
1850:     for (adaptIter = 0; ; ++adaptIter) {
1851:       PetscLogDouble bytes;
1852:       TS             tsNew = NULL;

1854:       PetscMemoryGetCurrentUsage(&bytes);
1855:       PetscInfo2(ts, "refinement loop %D: memory used %g\n", adaptIter, bytes);
1856:       DMViewFromOptions(dm, NULL, "-initial_dm_view");
1857:       VecViewFromOptions(X, NULL, "-initial_vec_view");
1858: #if 0
1859:       if (viewInitial) {
1860:         PetscViewer viewer;
1861:         char        buf[256];
1862:         PetscBool   isHDF5, isVTK;

1864:         PetscViewerCreate(comm,&viewer);
1865:         PetscViewerSetType(viewer,PETSCVIEWERVTK);
1866:         PetscViewerSetOptionsPrefix(viewer,"initial_");
1867:         PetscViewerSetFromOptions(viewer);
1868:         PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERHDF5,&isHDF5);
1869:         PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERVTK,&isVTK);
1870:         if (isHDF5) {
1871:           PetscSNPrintf(buf, 256, "ex11-initial-%d.h5", adaptIter);
1872:         } else if (isVTK) {
1873:           PetscSNPrintf(buf, 256, "ex11-initial-%d.vtu", adaptIter);
1874:           PetscViewerPushFormat(viewer,PETSC_VIEWER_VTK_VTU);
1875:         }
1876:         PetscViewerFileSetMode(viewer,FILE_MODE_WRITE);
1877:         PetscViewerFileSetName(viewer,buf);
1878:         if (isHDF5) {
1879:           DMView(dm,viewer);
1880:           PetscViewerFileSetMode(viewer,FILE_MODE_UPDATE);
1881:         }
1882:         VecView(X,viewer);
1883:         PetscViewerDestroy(&viewer);
1884:       }
1885: #endif

1887:       adaptToleranceFVM(fvm, ts, X, refineTag, coarsenTag, user, &tsNew, NULL);
1888:       if (!tsNew) {
1889:         break;
1890:       } else {
1891:         DMDestroy(&dm);
1892:         VecDestroy(&X);
1893:         TSDestroy(&ts);
1894:         ts   = tsNew;
1895:         TSGetDM(ts,&dm);
1896:         PetscObjectReference((PetscObject)dm);
1897:         DMCreateGlobalVector(dm,&X);
1898:         PetscObjectSetName((PetscObject) X, "solution");
1899:         SetInitialCondition(dm, X, user);
1900:       }
1901:     }
1902:     /* restore original limiter */
1903:     PetscFVSetLimiter(fvm, limiter);
1904:   }

1906:   if (vtkCellGeom) {
1907:     DM  dmCell;
1908:     Vec cellgeom, partition;

1910:     DMPlexTSGetGeometryFVM(dm, NULL, &cellgeom, NULL);
1911:     OutputVTK(dm, "ex11-cellgeom.vtk", &viewer);
1912:     VecView(cellgeom, viewer);
1913:     PetscViewerDestroy(&viewer);
1914:     CreatePartitionVec(dm, &dmCell, &partition);
1915:     OutputVTK(dmCell, "ex11-partition.vtk", &viewer);
1916:     VecView(partition, viewer);
1917:     PetscViewerDestroy(&viewer);
1918:     VecDestroy(&partition);
1919:     DMDestroy(&dmCell);
1920:   }

1922:   /* collect max maxspeed from all processes -- todo */
1923:   DMPlexTSGetGeometryFVM(dm, NULL, NULL, &minRadius);
1924:   MPI_Allreduce(&phys->maxspeed,&mod->maxspeed,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
1925:   if (mod->maxspeed <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set maxspeed",physname);
1926:   dt   = cfl * minRadius / mod->maxspeed;
1927:   TSSetTimeStep(ts,dt);
1928:   TSSetFromOptions(ts);
1929:   if (!useAMR) {
1930:     TSSolve(ts,X);
1931:     TSGetSolveTime(ts,&ftime);
1932:     TSGetStepNumber(ts,&nsteps);
1933:   } else {
1934:     PetscReal finalTime;
1935:     PetscInt  adaptIter;
1936:     TS        tsNew = NULL;
1937:     Vec       solNew = NULL;

1939:     TSGetMaxTime(ts,&finalTime);
1940:     TSSetMaxSteps(ts,adaptInterval);
1941:     TSSolve(ts,X);
1942:     TSGetSolveTime(ts,&ftime);
1943:     TSGetStepNumber(ts,&nsteps);
1944:     for (adaptIter = 0;ftime < finalTime;adaptIter++) {
1945:       PetscLogDouble bytes;

1947:       PetscMemoryGetCurrentUsage(&bytes);
1948:       PetscInfo2(ts, "AMR time step loop %D: memory used %g\n", adaptIter, bytes);
1949:       PetscFVSetLimiter(fvm,noneLimiter);
1950:       adaptToleranceFVM(fvm,ts,X,refineTag,coarsenTag,user,&tsNew,&solNew);
1951:       PetscFVSetLimiter(fvm,limiter);
1952:       if (tsNew) {
1953:         PetscInfo(ts, "AMR used\n");
1954:         DMDestroy(&dm);
1955:         VecDestroy(&X);
1956:         TSDestroy(&ts);
1957:         ts   = tsNew;
1958:         X    = solNew;
1959:         TSSetFromOptions(ts);
1960:         VecGetDM(X,&dm);
1961:         PetscObjectReference((PetscObject)dm);
1962:         DMPlexTSGetGeometryFVM(dm, NULL, NULL, &minRadius);
1963:         MPI_Allreduce(&phys->maxspeed,&mod->maxspeed,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
1964:         if (mod->maxspeed <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set maxspeed",physname);
1965:         dt   = cfl * minRadius / mod->maxspeed;
1966:         TSSetStepNumber(ts,nsteps);
1967:         TSSetTime(ts,ftime);
1968:         TSSetTimeStep(ts,dt);
1969:       } else {
1970:         PetscInfo(ts, "AMR not used\n");
1971:       }
1972:       user->monitorStepOffset = nsteps;
1973:       TSSetMaxSteps(ts,nsteps+adaptInterval);
1974:       TSSolve(ts,X);
1975:       TSGetSolveTime(ts,&ftime);
1976:       TSGetStepNumber(ts,&nsteps);
1977:     }
1978:   }
1979:   TSGetConvergedReason(ts,&reason);
1980:   PetscPrintf(PETSC_COMM_WORLD,"%s at time %g after %D steps\n",TSConvergedReasons[reason],(double)ftime,nsteps);
1981:   TSDestroy(&ts);

1983:   VecTaggerDestroy(&refineTag);
1984:   VecTaggerDestroy(&coarsenTag);
1985:   PetscFunctionListDestroy(&PhysicsList);
1986:   FunctionalLinkDestroy(&user->model->functionalRegistry);
1987:   PetscFree(user->model->functionalMonitored);
1988:   PetscFree(user->model->functionalCall);
1989:   PetscFree(user->model->physics->data);
1990:   PetscFree(user->model->physics);
1991:   PetscFree(user->model);
1992:   PetscFree(user);
1993:   VecDestroy(&X);
1994:   PetscLimiterDestroy(&limiter);
1995:   PetscLimiterDestroy(&noneLimiter);
1996:   PetscFVDestroy(&fvm);
1997:   DMDestroy(&dm);
1998:   PetscFinalize();
1999:   return ierr;
2000: }

2002: /* Godunov fluxs */
2003: PetscScalar cvmgp_(PetscScalar *a, PetscScalar *b, PetscScalar *test)
2004: {
2005:     /* System generated locals */
2006:     PetscScalar ret_val;

2008:     if (PetscRealPart(*test) > 0.) {
2009:         goto L10;
2010:     }
2011:     ret_val = *b;
2012:     return ret_val;
2013: L10:
2014:     ret_val = *a;
2015:     return ret_val;
2016: } /* cvmgp_ */

2018: PetscScalar cvmgm_(PetscScalar *a, PetscScalar *b, PetscScalar *test)
2019: {
2020:     /* System generated locals */
2021:     PetscScalar ret_val;

2023:     if (PetscRealPart(*test) < 0.) {
2024:         goto L10;
2025:     }
2026:     ret_val = *b;
2027:     return ret_val;
2028: L10:
2029:     ret_val = *a;
2030:     return ret_val;
2031: } /* cvmgm_ */

2033: int riem1mdt( PetscScalar *gaml, PetscScalar *gamr, PetscScalar *rl, PetscScalar *pl,
2034:               PetscScalar *uxl, PetscScalar *rr, PetscScalar *pr,
2035:               PetscScalar *uxr, PetscScalar *rstarl, PetscScalar *rstarr, PetscScalar *
2036:               pstar, PetscScalar *ustar)
2037: {
2038:     /* Initialized data */

2040:     static PetscScalar smallp = 1e-8;

2042:     /* System generated locals */
2043:     int i__1;
2044:     PetscScalar d__1, d__2;

2046:     /* Local variables */
2047:     static int i0;
2048:     static PetscScalar cl, cr, wl, zl, wr, zr, pst, durl, skpr1, skpr2;
2049:     static int iwave;
2050:     static PetscScalar gascl4, gascr4, cstarl, dpstar, cstarr;
2051:     /* static PetscScalar csqrl, csqrr, gascl1, gascl2, gascl3, gascr1, gascr2, gascr3; */
2052:     static int iterno;
2053:     static PetscScalar ustarl, ustarr, rarepr1, rarepr2;



2057:     /* gascl1 = *gaml - 1.; */
2058:     /* gascl2 = (*gaml + 1.) * .5; */
2059:     /* gascl3 = gascl2 / *gaml; */
2060:     gascl4 = 1. / (*gaml - 1.);

2062:     /* gascr1 = *gamr - 1.; */
2063:     /* gascr2 = (*gamr + 1.) * .5; */
2064:     /* gascr3 = gascr2 / *gamr; */
2065:     gascr4 = 1. / (*gamr - 1.);
2066:     iterno = 10;
2067: /*        find pstar: */
2068:     cl = PetscSqrtScalar(*gaml * *pl / *rl);
2069:     cr = PetscSqrtScalar(*gamr * *pr / *rr);
2070:     wl = *rl * cl;
2071:     wr = *rr * cr;
2072:     /* csqrl = wl * wl; */
2073:     /* csqrr = wr * wr; */
2074:     *pstar = (wl * *pr + wr * *pl) / (wl + wr);
2075:     *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
2076:     pst = *pl / *pr;
2077:     skpr1 = cr * (pst - 1.) * PetscSqrtScalar(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
2078:     d__1 = (*gamr - 1.) / (*gamr * 2.);
2079:     rarepr2 = gascr4 * 2. * cr * (1. - PetscPowScalar(pst, d__1));
2080:     pst = *pr / *pl;
2081:     skpr2 = cl * (pst - 1.) * PetscSqrtScalar(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
2082:     d__1 = (*gaml - 1.) / (*gaml * 2.);
2083:     rarepr1 = gascl4 * 2. * cl * (1. - PetscPowScalar(pst, d__1));
2084:     durl = *uxr - *uxl;
2085:     if (PetscRealPart(*pr) < PetscRealPart(*pl)) {
2086:         if (PetscRealPart(durl) >= PetscRealPart(rarepr1)) {
2087:             iwave = 100;
2088:         } else if (PetscRealPart(durl) <= PetscRealPart(-skpr1)) {
2089:             iwave = 300;
2090:         } else {
2091:             iwave = 400;
2092:         }
2093:     } else {
2094:         if (PetscRealPart(durl) >= PetscRealPart(rarepr2)) {
2095:             iwave = 100;
2096:         } else if (PetscRealPart(durl) <= PetscRealPart(-skpr2)) {
2097:             iwave = 300;
2098:         } else {
2099:             iwave = 200;
2100:         }
2101:     }
2102:     if (iwave == 100) {
2103: /*     1-wave: rarefaction wave, 3-wave: rarefaction wave */
2104: /*     case (100) */
2105:         i__1 = iterno;
2106:         for (i0 = 1; i0 <= i__1; ++i0) {
2107:             d__1 = *pstar / *pl;
2108:             d__2 = 1. / *gaml;
2109:             *rstarl = *rl * PetscPowScalar(d__1, d__2);
2110:             cstarl = PetscSqrtScalar(*gaml * *pstar / *rstarl);
2111:             ustarl = *uxl - gascl4 * 2. * (cstarl - cl);
2112:             zl = *rstarl * cstarl;
2113:             d__1 = *pstar / *pr;
2114:             d__2 = 1. / *gamr;
2115:             *rstarr = *rr * PetscPowScalar(d__1, d__2);
2116:             cstarr = PetscSqrtScalar(*gamr * *pstar / *rstarr);
2117:             ustarr = *uxr + gascr4 * 2. * (cstarr - cr);
2118:             zr = *rstarr * cstarr;
2119:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
2120:             *pstar -= dpstar;
2121:             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
2122:             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
2123: #if 0
2124:         break;
2125: #endif
2126:             }
2127:         }
2128: /*     1-wave: shock wave, 3-wave: rarefaction wave */
2129:     } else if (iwave == 200) {
2130: /*     case (200) */
2131:         i__1 = iterno;
2132:         for (i0 = 1; i0 <= i__1; ++i0) {
2133:             pst = *pstar / *pl;
2134:             ustarl = *uxl - (pst - 1.) * cl * PetscSqrtScalar(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
2135:             zl = *pl / cl * PetscSqrtScalar(*gaml * 2. * (*gaml - 1. + (*gaml + 1.) * pst)) * (*gaml - 1. + (*gaml + 1.) * pst) / (*gaml * 3. - 1. + (*gaml + 1.) * pst);
2136:             d__1 = *pstar / *pr;
2137:             d__2 = 1. / *gamr;
2138:             *rstarr = *rr * PetscPowScalar(d__1, d__2);
2139:             cstarr = PetscSqrtScalar(*gamr * *pstar / *rstarr);
2140:             zr = *rstarr * cstarr;
2141:             ustarr = *uxr + gascr4 * 2. * (cstarr - cr);
2142:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
2143:             *pstar -= dpstar;
2144:             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
2145:             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
2146: #if 0
2147:         break;
2148: #endif
2149:             }
2150:         }
2151: /*     1-wave: shock wave, 3-wave: shock */
2152:     } else if (iwave == 300) {
2153: /*     case (300) */
2154:         i__1 = iterno;
2155:         for (i0 = 1; i0 <= i__1; ++i0) {
2156:             pst = *pstar / *pl;
2157:             ustarl = *uxl - (pst - 1.) * cl * PetscSqrtScalar(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
2158:             zl = *pl / cl * PetscSqrtScalar(*gaml * 2. * (*gaml - 1. + (*gaml + 1.) * pst)) * (*gaml - 1. + (*gaml + 1.) * pst) / (*gaml * 3. - 1. + (*gaml + 1.) * pst);
2159:             pst = *pstar / *pr;
2160:             ustarr = *uxr + (pst - 1.) * cr * PetscSqrtScalar(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
2161:             zr = *pr / cr * PetscSqrtScalar(*gamr * 2. * (*gamr - 1. + (*gamr + 1.) * pst)) * (*gamr - 1. + (*gamr + 1.) * pst) / (*gamr * 3. - 1. + (*gamr + 1.) * pst);
2162:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
2163:             *pstar -= dpstar;
2164:             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
2165:             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
2166: #if 0
2167:         break;
2168: #endif
2169:             }
2170:         }
2171: /*     1-wave: rarefaction wave, 3-wave: shock */
2172:     } else if (iwave == 400) {
2173: /*     case (400) */
2174:         i__1 = iterno;
2175:         for (i0 = 1; i0 <= i__1; ++i0) {
2176:             d__1 = *pstar / *pl;
2177:             d__2 = 1. / *gaml;
2178:             *rstarl = *rl * PetscPowScalar(d__1, d__2);
2179:             cstarl = PetscSqrtScalar(*gaml * *pstar / *rstarl);
2180:             ustarl = *uxl - gascl4 * 2. * (cstarl - cl);
2181:             zl = *rstarl * cstarl;
2182:             pst = *pstar / *pr;
2183:             ustarr = *uxr + (pst - 1.) * cr * PetscSqrtScalar(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
2184:             zr = *pr / cr * PetscSqrtScalar(*gamr * 2. * (*gamr - 1. + (*gamr + 1.) * pst)) * (*gamr - 1. + (*gamr + 1.) * pst) / (*gamr * 3. - 1. + (*gamr + 1.) * pst);
2185:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
2186:             *pstar -= dpstar;
2187:             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
2188:             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
2189: #if 0
2190:               break;
2191: #endif
2192:             }
2193:         }
2194:     }

2196:     *ustar = (zl * ustarr + zr * ustarl) / (zl + zr);
2197:     if (PetscRealPart(*pstar) > PetscRealPart(*pl)) {
2198:         pst = *pstar / *pl;
2199:         *rstarl = ((*gaml + 1.) * pst + *gaml - 1.) / ((*gaml - 1.) * pst + *
2200:                 gaml + 1.) * *rl;
2201:     }
2202:     if (PetscRealPart(*pstar) > PetscRealPart(*pr)) {
2203:         pst = *pstar / *pr;
2204:         *rstarr = ((*gamr + 1.) * pst + *gamr - 1.) / ((*gamr - 1.) * pst + *
2205:                 gamr + 1.) * *rr;
2206:     }
2207:     return iwave;
2208: }

2210: PetscScalar sign(PetscScalar x)
2211: {
2212:     if(PetscRealPart(x) > 0) return 1.0;
2213:     if(PetscRealPart(x) < 0) return -1.0;
2214:     return 0.0;
2215: }
2216: /*        Riemann Solver */
2217: /* -------------------------------------------------------------------- */
2218: int riemannsolver(PetscScalar *xcen, PetscScalar *xp,
2219:                    PetscScalar *dtt, PetscScalar *rl, PetscScalar *uxl, PetscScalar *pl,
2220:                    PetscScalar *utl, PetscScalar *ubl, PetscScalar *gaml, PetscScalar *rho1l,
2221:                    PetscScalar *rr, PetscScalar *uxr, PetscScalar *pr, PetscScalar *utr,
2222:                    PetscScalar *ubr, PetscScalar *gamr, PetscScalar *rho1r, PetscScalar *rx,
2223:                    PetscScalar *uxm, PetscScalar *px, PetscScalar *utx, PetscScalar *ubx,
2224:                    PetscScalar *gam, PetscScalar *rho1)
2225: {
2226:     /* System generated locals */
2227:     PetscScalar d__1, d__2;

2229:     /* Local variables */
2230:     static PetscScalar s, c0, p0, r0, u0, w0, x0, x2, ri, cx, sgn0, wsp0, gasc1, gasc2, gasc3, gasc4;
2231:     static PetscScalar cstar, pstar, rstar, ustar, xstar, wspst, ushock, streng, rstarl, rstarr, rstars;
2232:     int iwave;

2234:     if (*rl == *rr && *pr == *pl && *uxl == *uxr && *gaml == *gamr) {
2235:         *rx = *rl;
2236:         *px = *pl;
2237:         *uxm = *uxl;
2238:         *gam = *gaml;
2239:         x2 = *xcen + *uxm * *dtt;

2241:         if (PetscRealPart(*xp) >= PetscRealPart(x2)) {
2242:             *utx = *utr;
2243:             *ubx = *ubr;
2244:             *rho1 = *rho1r;
2245:         } else {
2246:             *utx = *utl;
2247:             *ubx = *ubl;
2248:             *rho1 = *rho1l;
2249:         }
2250:         return 0;
2251:     }
2252:     iwave = riem1mdt(gaml, gamr, rl, pl, uxl, rr, pr, uxr, &rstarl, &rstarr, &pstar, &ustar);

2254:     x2 = *xcen + ustar * *dtt;
2255:     d__1 = *xp - x2;
2256:     sgn0 = sign(d__1);
2257: /*            x is in 3-wave if sgn0 = 1 */
2258: /*            x is in 1-wave if sgn0 = -1 */
2259:     r0 = cvmgm_(rl, rr, &sgn0);
2260:     p0 = cvmgm_(pl, pr, &sgn0);
2261:     u0 = cvmgm_(uxl, uxr, &sgn0);
2262:     *gam = cvmgm_(gaml, gamr, &sgn0);
2263:     gasc1 = *gam - 1.;
2264:     gasc2 = (*gam + 1.) * .5;
2265:     gasc3 = gasc2 / *gam;
2266:     gasc4 = 1. / (*gam - 1.);
2267:     c0 = PetscSqrtScalar(*gam * p0 / r0);
2268:     streng = pstar - p0;
2269:     w0 = *gam * r0 * p0 * (gasc3 * streng / p0 + 1.);
2270:     rstars = r0 / (1. - r0 * streng / w0);
2271:     d__1 = p0 / pstar;
2272:     d__2 = -1. / *gam;
2273:     rstarr = r0 * PetscPowScalar(d__1, d__2);
2274:     rstar = cvmgm_(&rstarr, &rstars, &streng);
2275:     w0 = PetscSqrtScalar(w0);
2276:     cstar = PetscSqrtScalar(*gam * pstar / rstar);
2277:     wsp0 = u0 + sgn0 * c0;
2278:     wspst = ustar + sgn0 * cstar;
2279:     ushock = ustar + sgn0 * w0 / rstar;
2280:     wspst = cvmgp_(&ushock, &wspst, &streng);
2281:     wsp0 = cvmgp_(&ushock, &wsp0, &streng);
2282:     x0 = *xcen + wsp0 * *dtt;
2283:     xstar = *xcen + wspst * *dtt;
2284: /*           using gas formula to evaluate rarefaction wave */
2285: /*            ri : reiman invariant */
2286:     ri = u0 - sgn0 * 2. * gasc4 * c0;
2287:     cx = sgn0 * .5 * gasc1 / gasc2 * ((*xp - *xcen) / *dtt - ri);
2288:     *uxm = ri + sgn0 * 2. * gasc4 * cx;
2289:     s = p0 / PetscPowScalar(r0, *gam);
2290:     d__1 = cx * cx / (*gam * s);
2291:     *rx = PetscPowScalar(d__1, gasc4);
2292:     *px = cx * cx * *rx / *gam;
2293:     d__1 = sgn0 * (x0 - *xp);
2294:     *rx = cvmgp_(rx, &r0, &d__1);
2295:     d__1 = sgn0 * (x0 - *xp);
2296:     *px = cvmgp_(px, &p0, &d__1);
2297:     d__1 = sgn0 * (x0 - *xp);
2298:     *uxm = cvmgp_(uxm, &u0, &d__1);
2299:     d__1 = sgn0 * (xstar - *xp);
2300:     *rx = cvmgm_(rx, &rstar, &d__1);
2301:     d__1 = sgn0 * (xstar - *xp);
2302:     *px = cvmgm_(px, &pstar, &d__1);
2303:     d__1 = sgn0 * (xstar - *xp);
2304:     *uxm = cvmgm_(uxm, &ustar, &d__1);
2305:     if (PetscRealPart(*xp) >= PetscRealPart(x2)) {
2306:         *utx = *utr;
2307:         *ubx = *ubr;
2308:         *rho1 = *rho1r;
2309:     } else {
2310:         *utx = *utl;
2311:         *ubx = *ubl;
2312:         *rho1 = *rho1l;
2313:     }
2314:     return iwave;
2315: }
2316: int godunovflux( const PetscScalar *ul, const PetscScalar *ur,
2317:                  PetscScalar *flux, const PetscReal *nn, const int *ndim,
2318:                  const PetscReal *gamma)
2319: {
2320:     /* System generated locals */
2321:   int i__1,iwave;
2322:     PetscScalar d__1, d__2, d__3;

2324:     /* Local variables */
2325:     static int k;
2326:     static PetscScalar bn[3], fn, ft, tg[3], pl, rl, pm, pr, rr, xp, ubl, ubm,
2327:             ubr, dtt, unm, tmp, utl, utm, uxl, utr, uxr, gaml, gamm, gamr,
2328:             xcen, rhom, rho1l, rho1m, rho1r;
2329:     /* Parameter adjustments */
2330:     --nn;
2331:     --flux;
2332:     --ur;
2333:     --ul;

2335:     /* Function Body */
2336:     xcen = 0.;
2337:     xp = 0.;
2338:     i__1 = *ndim;
2339:     for (k = 1; k <= i__1; ++k) {
2340:         tg[k - 1] = 0.;
2341:         bn[k - 1] = 0.;
2342:     }
2343:     dtt = 1.;
2344:     if (*ndim == 3) {
2345:         if (nn[1] == 0. && nn[2] == 0.) {
2346:             tg[0] = 1.;
2347:         } else {
2348:             tg[0] = -nn[2];
2349:             tg[1] = nn[1];
2350:         }
2351: /*           tmp=dsqrt(tg(1)**2+tg(2)**2) */
2352: /*           tg=tg/tmp */
2353:         bn[0] = -nn[3] * tg[1];
2354:         bn[1] = nn[3] * tg[0];
2355:         bn[2] = nn[1] * tg[1] - nn[2] * tg[0];
2356: /* Computing 2nd power */
2357:         d__1 = bn[0];
2358: /* Computing 2nd power */
2359:         d__2 = bn[1];
2360: /* Computing 2nd power */
2361:         d__3 = bn[2];
2362:         tmp = PetscSqrtScalar(d__1 * d__1 + d__2 * d__2 + d__3 * d__3);
2363:         i__1 = *ndim;
2364:         for (k = 1; k <= i__1; ++k) {
2365:             bn[k - 1] /= tmp;
2366:         }
2367:     } else if (*ndim == 2) {
2368:         tg[0] = -nn[2];
2369:         tg[1] = nn[1];
2370: /*           tmp=dsqrt(tg(1)**2+tg(2)**2) */
2371: /*           tg=tg/tmp */
2372:         bn[0] = 0.;
2373:         bn[1] = 0.;
2374:         bn[2] = 1.;
2375:     }
2376:     rl = ul[1];
2377:     rr = ur[1];
2378:     uxl = 0.;
2379:     uxr = 0.;
2380:     utl = 0.;
2381:     utr = 0.;
2382:     ubl = 0.;
2383:     ubr = 0.;
2384:     i__1 = *ndim;
2385:     for (k = 1; k <= i__1; ++k) {
2386:         uxl += ul[k + 1] * nn[k];
2387:         uxr += ur[k + 1] * nn[k];
2388:         utl += ul[k + 1] * tg[k - 1];
2389:         utr += ur[k + 1] * tg[k - 1];
2390:         ubl += ul[k + 1] * bn[k - 1];
2391:         ubr += ur[k + 1] * bn[k - 1];
2392:     }
2393:     uxl /= rl;
2394:     uxr /= rr;
2395:     utl /= rl;
2396:     utr /= rr;
2397:     ubl /= rl;
2398:     ubr /= rr;

2400:     gaml = *gamma;
2401:     gamr = *gamma;
2402: /* Computing 2nd power */
2403:     d__1 = uxl;
2404: /* Computing 2nd power */
2405:     d__2 = utl;
2406: /* Computing 2nd power */
2407:     d__3 = ubl;
2408:     pl = (*gamma - 1.) * (ul[*ndim + 2] - rl * .5 * (d__1 * d__1 + d__2 * d__2 + d__3 * d__3));
2409: /* Computing 2nd power */
2410:     d__1 = uxr;
2411: /* Computing 2nd power */
2412:     d__2 = utr;
2413: /* Computing 2nd power */
2414:     d__3 = ubr;
2415:     pr = (*gamma - 1.) * (ur[*ndim + 2] - rr * .5 * (d__1 * d__1 + d__2 * d__2 + d__3 * d__3));
2416:     rho1l = rl;
2417:     rho1r = rr;

2419:     iwave = riemannsolver(&xcen, &xp, &dtt, &rl, &uxl, &pl, &utl, &ubl, &gaml, &
2420:                           rho1l, &rr, &uxr, &pr, &utr, &ubr, &gamr, &rho1r, &rhom, &unm, &
2421:                           pm, &utm, &ubm, &gamm, &rho1m);

2423:     flux[1] = rhom * unm;
2424:     fn = rhom * unm * unm + pm;
2425:     ft = rhom * unm * utm;
2426: /*           flux(2)=fn*nn(1)+ft*nn(2) */
2427: /*           flux(3)=fn*tg(1)+ft*tg(2) */
2428:     flux[2] = fn * nn[1] + ft * tg[0];
2429:     flux[3] = fn * nn[2] + ft * tg[1];
2430: /*           flux(2)=rhom*unm*(unm)+pm */
2431: /*           flux(3)=rhom*(unm)*utm */
2432:     if (*ndim == 3) {
2433:         flux[4] = rhom * unm * ubm;
2434:     }
2435:     flux[*ndim + 2] = (rhom * .5 * (unm * unm + utm * utm + ubm * ubm) + gamm / (gamm - 1.) * pm) * unm;
2436:     return iwave;
2437: } /* godunovflux_ */

2439: /* Subroutine to set up the initial conditions for the */
2440: /* Shock Interface interaction or linear wave (Ravi Samtaney,Mark Adams). */
2441: /* ----------------------------------------------------------------------- */
2442: int projecteqstate(PetscReal wc[], const PetscReal ueq[], PetscReal lv[][3])
2443: {
2444:   int j,k;
2445: /*      Wc=matmul(lv,Ueq) 3 vars */
2446:   for (k = 0; k < 3; ++k) {
2447:     wc[k] = 0.;
2448:     for (j = 0; j < 3; ++j) {
2449:       wc[k] += lv[k][j]*ueq[j];
2450:     }
2451:   }
2452:   return 0;
2453: }
2454: /* ----------------------------------------------------------------------- */
2455: int projecttoprim(PetscReal v[], const PetscReal wc[], PetscReal rv[][3])
2456: {
2457:   int k,j;
2458:   /*      V=matmul(rv,WC) 3 vars */
2459:   for (k = 0; k < 3; ++k) {
2460:     v[k] = 0.;
2461:     for (j = 0; j < 3; ++j) {
2462:       v[k] += rv[k][j]*wc[j];
2463:     }
2464:   }
2465:   return 0;
2466: }
2467: /* ---------------------------------------------------------------------- */
2468: int eigenvectors(PetscReal rv[][3], PetscReal lv[][3], const PetscReal ueq[], PetscReal gamma)
2469: {
2470:   int j,k;
2471:   PetscReal rho,csnd,p0;
2472:   /* PetscScalar u; */

2474:   for (k = 0; k < 3; ++k) for (j = 0; j < 3; ++j) { lv[k][j] = 0.; rv[k][j] = 0.; }
2475:   rho = ueq[0];
2476:   /* u = ueq[1]; */
2477:   p0 = ueq[2];
2478:   csnd = PetscSqrtReal(gamma * p0 / rho);
2479:   lv[0][1] = rho * .5;
2480:   lv[0][2] = -.5 / csnd;
2481:   lv[1][0] = csnd;
2482:   lv[1][2] = -1. / csnd;
2483:   lv[2][1] = rho * .5;
2484:   lv[2][2] = .5 / csnd;
2485:   rv[0][0] = -1. / csnd;
2486:   rv[1][0] = 1. / rho;
2487:   rv[2][0] = -csnd;
2488:   rv[0][1] = 1. / csnd;
2489:   rv[0][2] = 1. / csnd;
2490:   rv[1][2] = 1. / rho;
2491:   rv[2][2] = csnd;
2492:   return 0;
2493: }

2495: int initLinearWave(EulerNode *ux, const PetscReal gamma, const PetscReal coord[], const PetscReal Lx)
2496: {
2497:   PetscReal p0,u0,wcp[3],wc[3];
2498:   PetscReal lv[3][3];
2499:   PetscReal vp[3];
2500:   PetscReal rv[3][3];
2501:   PetscReal eps, ueq[3], rho0, twopi;

2503:   /* Function Body */
2504:   twopi = 2.*PETSC_PI;
2505:   eps = 1e-4; /* perturbation */
2506:   rho0 = 1e3;   /* density of water */
2507:   p0 = 101325.; /* init pressure of 1 atm (?) */
2508:   u0 = 0.;
2509:   ueq[0] = rho0;
2510:   ueq[1] = u0;
2511:   ueq[2] = p0;
2512:   /* Project initial state to characteristic variables */
2513:   eigenvectors(rv, lv, ueq, gamma);
2514:   projecteqstate(wc, ueq, lv);
2515:   wcp[0] = wc[0];
2516:   wcp[1] = wc[1];
2517:   wcp[2] = wc[2] + eps * PetscCosReal(coord[0] * 2. * twopi / Lx);
2518:   projecttoprim(vp, wcp, rv);
2519:   ux->r = vp[0]; /* density */
2520:   ux->ru[0] = vp[0] * vp[1]; /* x momentum */
2521:   ux->ru[1] = 0.;
2522: #if defined DIM > 2
2523:   if (dim>2) ux->ru[2] = 0.;
2524: #endif
2525:   /* E = rho * e + rho * v^2/2 = p/(gam-1) + rho*v^2/2 */
2526:   ux->E = vp[2]/(gamma - 1.) + 0.5*vp[0]*vp[1]*vp[1];
2527:   return 0;
2528: }

2530: /*TEST

2532:   # 2D Advection 0-10
2533:   test:
2534:     suffix: 0
2535:     requires: exodusii
2536:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo

2538:   test:
2539:     suffix: 1
2540:     requires: exodusii
2541:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo

2543:   test:
2544:     suffix: 2
2545:     requires: exodusii
2546:     nsize: 2
2547:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo

2549:   test:
2550:     suffix: 3
2551:     requires: exodusii
2552:     nsize: 2
2553:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo

2555:   test:
2556:     suffix: 4
2557:     requires: exodusii
2558:     nsize: 8
2559:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad.exo

2561:   test:
2562:     suffix: 5
2563:     requires: exodusii
2564:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo -ts_type rosw -ts_adapt_reject_safety 1

2566:   test:
2567:     suffix: 6
2568:     requires: exodusii
2569:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/squaremotor-30.exo -ufv_split_faces

2571:   test:
2572:     suffix: 7
2573:     requires: exodusii
2574:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 1

2576:   test:
2577:     suffix: 8
2578:     requires: exodusii
2579:     nsize: 2
2580:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 1

2582:   test:
2583:     suffix: 9
2584:     requires: exodusii
2585:     nsize: 8
2586:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 1

2588:   test:
2589:     suffix: 10
2590:     requires: exodusii
2591:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad.exo

2593:   # 2D Shallow water
2594:   test:
2595:     suffix: sw_0
2596:     requires: exodusii
2597:     args: -ufv_vtk_interval 0 -f ${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

2599:   # 2D Advection: p4est
2600:   test:
2601:     suffix: p4est_advec_2d
2602:     requires: p4est
2603:     args: -ufv_vtk_interval 0 -f -dm_type p4est -dm_forest_minimum_refinement 1 -dm_forest_initial_refinement 2 -dm_p4est_refine_pattern hash -dm_forest_maximum_refinement 5

2605:   # Advection in a box
2606:   test:
2607:     suffix: adv_2d_quad_0
2608:     args: -ufv_vtk_interval 0 -dm_refine 3 -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3

2610:   test:
2611:     suffix: adv_2d_quad_1
2612:     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
2613:     timeoutfactor: 3

2615:   test:
2616:     suffix: adv_2d_quad_p4est_0
2617:     requires: p4est
2618:     args: -ufv_vtk_interval 0 -dm_refine 5 -dm_type p4est -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3

2620:   test:
2621:     suffix: adv_2d_quad_p4est_1
2622:     requires: p4est
2623:     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
2624:     timeoutfactor: 3

2626:   test:
2627:     suffix: adv_2d_quad_p4est_adapt_0
2628:     requires: p4est !__float128 #broken for quad precision
2629:     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
2630:     timeoutfactor: 3

2632:   test:
2633:     suffix: adv_2d_tri_0
2634:     requires: triangle
2635:     TODO: how did this ever get in master when there is no support for this
2636:     args: -ufv_vtk_interval 0 -simplex -dm_refine 3 -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3

2638:   test:
2639:     suffix: adv_2d_tri_1
2640:     requires: triangle
2641:     TODO: how did this ever get in master when there is no support for this
2642:     args: -ufv_vtk_interval 0 -simplex -dm_refine 5 -dm_plex_separate_marker -grid_bounds -0.5,0.5,-0.5,0.5 -bc_inflow 1,2,4 -bc_outflow 3 -advect_sol_type bump -advect_bump_center 0.25,0 -advect_bump_radius 0.1

2644:   test:
2645:     suffix: adv_0
2646:     requires: exodusii
2647:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/blockcylinder-50.exo -bc_inflow 100,101,200 -bc_outflow 201

2649:   test:
2650:     suffix: shock_0
2651:     requires: p4est !single !complex
2652:     args: -ufv_vtk_interval 0 -monitor density,energy -f -grid_size 2,1 -grid_bounds -1,1.,0.,1 -bc_wall 1,2,3,4 -dm_type p4est -dm_forest_partition_overlap 1 -dm_forest_maximum_refinement 6 -dm_forest_minimum_refinement 2 -dm_forest_initial_refinement 2 -ufv_use_amr -refine_vec_tagger_box 0.5,inf -coarsen_vec_tagger_box 0,1.e-2 -refine_tag_view -coarsen_tag_view -physics euler -eu_type iv_shock -ufv_cfl 10 -eu_alpha 60. -grid_skew_60 -eu_gamma 1.4 -eu_amach 2.02 -eu_rho2 3. -petscfv_type leastsquares -petsclimiter_type minmod -petscfv_compute_gradients 0 -ts_max_time 0.5 -ts_ssp_type rks2 -ts_ssp_nstages 10 -ufv_vtk_basename ${wPETSC_DIR}/ex11
2653:     timeoutfactor: 3

2655:   # Test GLVis visualization of PetscFV fields
2656:   test:
2657:     suffix: glvis_adv_2d_tet
2658:     args: -ufv_vtk_interval 0 -ts_monitor_solution glvis: -ts_max_steps 0 -ufv_vtk_monitor 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/square_periodic.msh

2660:   test:
2661:     suffix: glvis_adv_2d_quad
2662:     args: -ufv_vtk_interval 0 -ts_monitor_solution glvis: -ts_max_steps 0 -ufv_vtk_monitor 0 -dm_refine 5 -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3

2664:   test:
2665:     suffix: tut_1
2666:     requires: exodusii
2667:     nsize: 1
2668:     args: -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo

2670:   test:
2671:     suffix: tut_2
2672:     requires: exodusii
2673:     nsize: 1
2674:     args: -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo -ts_type rosw

2676:   test:
2677:     suffix: tut_3
2678:     requires: exodusii
2679:     nsize: 4
2680:     args: -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/annulus-20.exo -monitor Error -advect_sol_type bump -petscfv_type leastsquares -petsclimiter_type sin

2682:   test:
2683:     suffix: tut_4
2684:     requires: exodusii
2685:     nsize: 4
2686:     args: -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/annulus-20.exo -physics sw -monitor Height,Energy -petscfv_type leastsquares -petsclimiter_type minmod

2688: TEST*/