Actual source code: ex11.c

petsc-3.7.3 2016-07-24
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  1: static char help[] = "Second Order TVD Finite Volume Example.\n";

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

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

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

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

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

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

 45: static PetscFunctionList PhysicsList;

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

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

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

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

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

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

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

104: struct _n_User {
105:   PetscInt numSplitFaces;
106:   PetscInt vtkInterval;   /* For monitor */
107:   Model    model;
108: };

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

115:   for (i=0; i<DIM; i++) prod += x[i]*y[i];
116:   return prod;
117: }
118: PETSC_STATIC_INLINE PetscReal NormDIM(const PetscScalar *x) { return PetscSqrtReal(PetscAbsScalar(DotDIM(x,x))); }

120: PETSC_STATIC_INLINE PetscScalar Dot2(const PetscScalar *x,const PetscScalar *y) { return x[0]*y[0] + x[1]*y[1];}
121: PETSC_STATIC_INLINE PetscReal Norm2(const PetscScalar *x) { return PetscSqrtReal(PetscAbsScalar(Dot2(x,x)));}
122: PETSC_STATIC_INLINE void Normalize2(PetscScalar *x) { PetscReal a = 1./Norm2(x); x[0] *= a; x[1] *= a; }
123: PETSC_STATIC_INLINE void Waxpy2(PetscScalar a,const PetscScalar *x,const PetscScalar *y,PetscScalar *w) { w[0] = a*x[0] + y[0]; w[1] = a*x[1] + y[1]; }
124: PETSC_STATIC_INLINE void Scale2(PetscScalar a,const PetscScalar *x,PetscScalar *y) { y[0] = a*x[0]; y[1] = a*x[1]; }

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

132: typedef struct {
133:   PetscReal wind[DIM];
134: } Physics_Advect_Tilted;
135: typedef struct {
136:   PetscReal         center[DIM];
137:   PetscReal         radius;
138:   AdvectSolBumpType type;
139: } Physics_Advect_Bump;

141: typedef struct {
142:   PetscReal     inflowState;
143:   AdvectSolType soltype;
144:   union {
145:     Physics_Advect_Tilted tilted;
146:     Physics_Advect_Bump   bump;
147:   } sol;
148:   struct {
149:     PetscInt Error;
150:   } functional;
151: } Physics_Advect;

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

157: static PetscErrorCode PhysicsBoundary_Advect_Inflow(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
158: {
159:   Physics        phys    = (Physics)ctx;
160:   Physics_Advect *advect = (Physics_Advect*)phys->data;

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

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

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

183:   switch (advect->soltype) {
184:   case ADVECT_SOL_TILTED: {
185:     Physics_Advect_Tilted *tilted = &advect->sol.tilted;
186:     wind[0] = tilted->wind[0];
187:     wind[1] = tilted->wind[1];
188:   } break;
189:   case ADVECT_SOL_BUMP:
190:     wind[0] = -qp[1];
191:     wind[1] = qp[0];
192:     break;
193:     /* default: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for solution type %s",AdvectSolBumpTypes[advect->soltype]); */
194:   }
195:   wn      = Dot2(wind, n);
196:   flux[0] = (wn > 0 ? xL[0] : xR[0]) * wn;
197: }

201: static PetscErrorCode PhysicsSolution_Advect(Model mod,PetscReal time,const PetscReal *x,PetscScalar *u,void *ctx)
202: {
203:   Physics        phys    = (Physics)ctx;
204:   Physics_Advect *advect = (Physics_Advect*)phys->data;

207:   switch (advect->soltype) {
208:   case ADVECT_SOL_TILTED: {
209:     PetscReal             x0[DIM];
210:     Physics_Advect_Tilted *tilted = &advect->sol.tilted;
211:     Waxpy2(-time,tilted->wind,x,x0);
212:     if (x0[1] > 0) u[0] = 1.*x[0] + 3.*x[1];
213:     else u[0] = advect->inflowState;
214:   } break;
215:   case ADVECT_SOL_BUMP: {
216:     Physics_Advect_Bump *bump = &advect->sol.bump;
217:     PetscReal           x0[DIM],v[DIM],r,cost,sint;
218:     cost  = PetscCosReal(time);
219:     sint  = PetscSinReal(time);
220:     x0[0] = cost*x[0] + sint*x[1];
221:     x0[1] = -sint*x[0] + cost*x[1];
222:     Waxpy2(-1,bump->center,x0,v);
223:     r = Norm2(v);
224:     switch (bump->type) {
225:     case ADVECT_SOL_BUMP_CONE:
226:       u[0] = PetscMax(1 - r/bump->radius,0);
227:       break;
228:     case ADVECT_SOL_BUMP_COS:
229:       u[0] = 0.5 + 0.5*PetscCosReal(PetscMin(r/bump->radius,1)*PETSC_PI);
230:       break;
231:     }
232:   } break;
233:   default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unknown solution type");
234:   }
235:   return(0);
236: }

240: static PetscErrorCode PhysicsFunctional_Advect(Model mod,PetscReal time,const PetscScalar *x,const PetscScalar *y,PetscReal *f,void *ctx)
241: {
242:   Physics        phys    = (Physics)ctx;
243:   Physics_Advect *advect = (Physics_Advect*)phys->data;
244:   PetscScalar    yexact[1];

248:   PhysicsSolution_Advect(mod,time,x,yexact,phys);
249:   f[advect->functional.Error] = PetscAbsScalar(y[0]-yexact[0]);
250:   return(0);
251: }

255: static PetscErrorCode SetUpBC_Advect(DM dm, Physics phys)
256: {
258:   const PetscInt inflowids[] = {100,200,300},outflowids[] = {101};
260:   /* Register "canned" boundary conditions and defaults for where to apply. */
261:   DMAddBoundary(dm, PETSC_TRUE, "inflow",  "Face Sets", 0, 0, NULL, (void (*)()) PhysicsBoundary_Advect_Inflow,  ALEN(inflowids),  inflowids,  phys);
262:   DMAddBoundary(dm, PETSC_FALSE, "outflow", "Face Sets", 0, 0, NULL, (void (*)()) PhysicsBoundary_Advect_Outflow, ALEN(outflowids), outflowids, phys);
263:   return(0);
264: }

268: static PetscErrorCode PhysicsCreate_Advect(Model mod,Physics phys,PetscOptionItems *PetscOptionsObject)
269: {
270:   Physics_Advect *advect;

274:   phys->field_desc = PhysicsFields_Advect;
275:   phys->riemann    = (PetscRiemannFunc)PhysicsRiemann_Advect;
276:   PetscNew(&advect);
277:   phys->data       = advect;
278:   mod->setupbc = SetUpBC_Advect;

280:   PetscOptionsHead(PetscOptionsObject,"Advect options");
281:   {
282:     PetscInt two = 2,dof = 1;
283:     advect->soltype = ADVECT_SOL_TILTED;
284:     PetscOptionsEnum("-advect_sol_type","solution type","",AdvectSolTypes,(PetscEnum)advect->soltype,(PetscEnum*)&advect->soltype,NULL);
285:     switch (advect->soltype) {
286:     case ADVECT_SOL_TILTED: {
287:       Physics_Advect_Tilted *tilted = &advect->sol.tilted;
288:       two = 2;
289:       tilted->wind[0] = 0.0;
290:       tilted->wind[1] = 1.0;
291:       PetscOptionsRealArray("-advect_tilted_wind","background wind vx,vy","",tilted->wind,&two,NULL);
292:       advect->inflowState = -2.0;
293:       PetscOptionsRealArray("-advect_tilted_inflow","Inflow state","",&advect->inflowState,&dof,NULL);
294:       phys->maxspeed = Norm2(tilted->wind);
295:     } break;
296:     case ADVECT_SOL_BUMP: {
297:       Physics_Advect_Bump *bump = &advect->sol.bump;
298:       two = 2;
299:       bump->center[0] = 2.;
300:       bump->center[1] = 0.;
301:       PetscOptionsRealArray("-advect_bump_center","location of center of bump x,y","",bump->center,&two,NULL);
302:       bump->radius = 0.9;
303:       PetscOptionsReal("-advect_bump_radius","radius of bump","",bump->radius,&bump->radius,NULL);
304:       bump->type = ADVECT_SOL_BUMP_CONE;
305:       PetscOptionsEnum("-advect_bump_type","type of bump","",AdvectSolBumpTypes,(PetscEnum)bump->type,(PetscEnum*)&bump->type,NULL);
306:       phys->maxspeed = 3.;       /* radius of mesh, kludge */
307:     } break;
308:     }
309:   }
310:   PetscOptionsTail();
311:   /* Initial/transient solution with default boundary conditions */
312:   ModelSolutionSetDefault(mod,PhysicsSolution_Advect,phys);
313:   /* Register "canned" functionals */
314:   ModelFunctionalRegister(mod,"Error",&advect->functional.Error,PhysicsFunctional_Advect,phys);
315:   mod->bcs[0] = mod->bcs[1] = mod->bcs[2] = DM_BOUNDARY_GHOSTED;
316:   return(0);
317: }

319: /******************* Shallow Water ********************/
320: typedef struct {
321:   PetscReal gravity;
322:   PetscReal boundaryHeight;
323:   struct {
324:     PetscInt Height;
325:     PetscInt Speed;
326:     PetscInt Energy;
327:   } functional;
328: } Physics_SW;
329: typedef struct {
330:   PetscScalar vals[0];
331:   PetscScalar h;
332:   PetscScalar uh[DIM];
333: } SWNode;

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

339: /*
340:  * h_t + div(uh) = 0
341:  * (uh)_t + div (u\otimes uh + g h^2 / 2 I) = 0
342:  *
343:  * */
344: static PetscErrorCode SWFlux(Physics phys,const PetscReal *n,const SWNode *x,SWNode *f)
345: {
346:   Physics_SW  *sw = (Physics_SW*)phys->data;
347:   PetscScalar uhn,u[DIM];
348:   PetscInt    i;

351:   Scale2(1./x->h,x->uh,u);
352:   uhn  = Dot2(x->uh,n);
353:   f->h = uhn;
354:   for (i=0; i<DIM; i++) f->uh[i] = u[i] * uhn + sw->gravity * PetscSqr(x->h) * n[i];
355:   return(0);
356: }

360: static PetscErrorCode PhysicsBoundary_SW_Wall(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
361: {
363:   xG[0] = xI[0];
364:   xG[1] = -xI[1];
365:   xG[2] = -xI[2];
366:   return(0);
367: }

371: static void PhysicsRiemann_SW(PetscInt dim, PetscInt Nf, const PetscReal *qp, const PetscReal *n, const PetscScalar *xL, const PetscScalar *xR, PetscScalar *flux, Physics phys)
372: {
373:   Physics_SW   *sw = (Physics_SW*)phys->data;
374:   PetscReal    cL,cR,speed,nn[DIM];
375:   const SWNode *uL = (const SWNode*)xL,*uR = (const SWNode*)xR;
376:   SWNode       fL,fR;
377:   PetscInt     i;

379:   if (uL->h < 0 || uR->h < 0) {for (i=0; i<1+dim; i++) flux[i] = NAN; return;} /* SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Reconstructed thickness is negative"); */
380:   nn[0] = n[0];
381:   nn[1] = n[1];
382:   Normalize2(nn);
383:   SWFlux(phys,nn,uL,&fL);
384:   SWFlux(phys,nn,uR,&fR);
385:   cL    = PetscSqrtReal(sw->gravity*PetscRealPart(uL->h));
386:   cR    = PetscSqrtReal(sw->gravity*PetscRealPart(uR->h)); /* gravity wave speed */
387:   speed = PetscMax(PetscAbsScalar(Dot2(uL->uh,nn)/uL->h) + cL,PetscAbsScalar(Dot2(uR->uh,nn)/uR->h) + cR);
388:   for (i=0; i<1+dim; i++) flux[i] = (0.5*(fL.vals[i] + fR.vals[i]) + 0.5*speed*(xL[i] - xR[i])) * Norm2(n);
389: }

393: static PetscErrorCode PhysicsSolution_SW(Model mod,PetscReal time,const PetscReal *x,PetscScalar *u,void *ctx)
394: {
395:   PetscReal dx[2],r,sigma;

398:   if (time != 0.0) SETERRQ1(mod->comm,PETSC_ERR_SUP,"No solution known for time %g",(double)time);
399:   dx[0] = x[0] - 1.5;
400:   dx[1] = x[1] - 1.0;
401:   r     = Norm2(dx);
402:   sigma = 0.5;
403:   u[0]  = 1 + 2*PetscExpScalar(-PetscSqr(r)/(2*PetscSqr(sigma)));
404:   u[1]  = 0.0;
405:   u[2]  = 0.0;
406:   return(0);
407: }

411: static PetscErrorCode PhysicsFunctional_SW(Model mod,PetscReal time,const PetscReal *coord,const PetscScalar *xx,PetscReal *f,void *ctx)
412: {
413:   Physics      phys = (Physics)ctx;
414:   Physics_SW   *sw  = (Physics_SW*)phys->data;
415:   const SWNode *x   = (const SWNode*)xx;
416:   PetscScalar  u[2];
417:   PetscReal    h;

420:   h = PetscRealPart(x->h);
421:   Scale2(1./x->h,x->uh,u);
422:   f[sw->functional.Height] = h;
423:   f[sw->functional.Speed]  = Norm2(u) + PetscSqrtReal(sw->gravity*h);
424:   f[sw->functional.Energy] = 0.5*(Dot2(x->uh,u) + sw->gravity*PetscSqr(h));
425:   return(0);
426: }

430: static PetscErrorCode SetUpBC_SW(DM dm,Physics phys)
431: {
433:   const PetscInt wallids[] = {100,101,200,300};
435:   DMAddBoundary(dm, PETSC_FALSE, "wall", "Face Sets", 0, 0, NULL, (void (*)()) PhysicsBoundary_SW_Wall, ALEN(wallids), wallids, phys);
436:   return(0);
437: }

441: static PetscErrorCode PhysicsCreate_SW(Model mod,Physics phys,PetscOptionItems *PetscOptionsObject)
442: {
443:   Physics_SW     *sw;

447:   phys->field_desc = PhysicsFields_SW;
448:   phys->riemann = (PetscRiemannFunc) PhysicsRiemann_SW;
449:   PetscNew(&sw);
450:   phys->data    = sw;
451:   mod->setupbc  = SetUpBC_SW;

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

461:   ModelSolutionSetDefault(mod,PhysicsSolution_SW,phys);
462:   ModelFunctionalRegister(mod,"Height",&sw->functional.Height,PhysicsFunctional_SW,phys);
463:   ModelFunctionalRegister(mod,"Speed",&sw->functional.Speed,PhysicsFunctional_SW,phys);
464:   ModelFunctionalRegister(mod,"Energy",&sw->functional.Energy,PhysicsFunctional_SW,phys);

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

468:   return(0);
469: }

471: /******************* Euler Density Shock (EULER_IV_SHOCK,EULER_SS_SHOCK) ********************/
472: /* An initial‐value and self‐similar solutions of the compressible Euler equations */
473: /* Ravi Samtaney and D. I. Pullin */
474: /* Phys. Fluids 8, 2650 (1996); http://dx.doi.org/10.1063/1.869050 */
475: typedef enum {EULER_PAR_GAMMA,EULER_PAR_RHOR,EULER_PAR_AMACH,EULER_PAR_ITANA,EULER_PAR_SIZE} EulerParamIdx;
476: typedef enum {EULER_IV_SHOCK,EULER_SS_SHOCK,EULER_SHOCK_TUBE,EULER_LINEAR_WAVE} EulerType;
477: typedef struct {
478:   PetscScalar vals[0];
479:   PetscScalar r;
480:   PetscScalar ru[DIM];
481:   PetscScalar E;
482: } EulerNode;
483: typedef PetscErrorCode (*EquationOfState)(const PetscReal*, const EulerNode*, PetscScalar*);
484: typedef struct {
485:   EulerType       type;
486:   PetscReal       pars[EULER_PAR_SIZE];
487:   EquationOfState sound;
488:   struct {
489:     PetscInt Density;
490:     PetscInt Momentum;
491:     PetscInt Energy;
492:     PetscInt Pressure;
493:     PetscInt Speed;
494:   } monitor;
495: } Physics_Euler;

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

499: /* initial condition */
500: int initLinearWave(EulerNode *ux, const PetscScalar gamma, const PetscReal coord[], const PetscReal Lx);
503: static PetscErrorCode PhysicsSolution_Euler(Model mod, PetscReal time, const PetscReal *x, PetscScalar *u, void *ctx)
504: {
505:   PetscInt i;
506:   Physics         phys = (Physics)ctx;
507:   Physics_Euler   *eu  = (Physics_Euler*)phys->data;
508:   EulerNode       *uu  = (EulerNode*)u;
509:   PetscScalar p0,gamma,c;
511:   if (time != 0.0) SETERRQ1(mod->comm,PETSC_ERR_SUP,"No solution known for time %g",(double)time);

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

517:   if (eu->type==EULER_IV_SHOCK || eu->type==EULER_SS_SHOCK) {
518:     /******************* Euler Density Shock ********************/
519:     /* On initial‐value and self‐similar solutions of the compressible Euler equations */
520:     /* Ravi Samtaney and D. I. Pullin */
521:     /* Phys. Fluids 8, 2650 (1996); http://dx.doi.org/10.1063/1.869050 */
522:     /* initial conditions 1: left of shock, 0: left of discontinuity 2: right of discontinuity,  */
523:     p0 = 1.;
524:     if (x[0] < 0.0 + x[1]*eu->pars[EULER_PAR_ITANA]) {
525:       if (x[0] < mod->bounds[0]*0.5) { /* left of shock (1) */
526:         PetscScalar amach,rho,press,gas1,p1;
527:         amach = eu->pars[EULER_PAR_AMACH];
528:         rho = 1.;
529:         press = p0;
530:         p1 = press*(1.0+2.0*gamma/(gamma+1.0)*(amach*amach-1.0));
531:         gas1 = (gamma-1.0)/(gamma+1.0);
532:         uu->r = rho*(p1/press+gas1)/(gas1*p1/press+1.0);
533:         uu->ru[0]   = ((uu->r - rho)*sqrt(gamma*press/rho)*amach);
534:         uu->E = p1/(gamma-1.0) + .5/uu->r*uu->ru[0]*uu->ru[0];
535:       }
536:       else { /* left of discontinuity (0) */
537:         uu->r = 1.; /* rho = 1 */
538:         uu->E = p0/(gamma-1.0);
539:       }
540:     }
541:     else { /* right of discontinuity (2) */
542:       uu->r = eu->pars[EULER_PAR_RHOR];
543:       uu->E = p0/(gamma-1.0);
544:     }
545:   }
546:   else if (eu->type==EULER_SHOCK_TUBE) {
547:     /* 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. */
548:     if (x[0] < 0.0 ) {
549:       uu->r = 8.;
550:       uu->E = 10./(gamma-1.);
551:     }
552:     else {
553:       uu->r = 1.;
554:       uu->E = 1./(gamma-1.);
555:     }
556:   }
557:   else if (eu->type==EULER_LINEAR_WAVE) {
558:     initLinearWave( uu, gamma, x, mod->bounds[1] - mod->bounds[0]);
559:   }
560:   else SETERRQ1(mod->comm,PETSC_ERR_SUP,"Unknown type %d",eu->type);

562:   // set phys->maxspeed: (mod->maxspeed = phys->maxspeed) in main;
563:   eu->sound(&gamma,uu,&c);
564:   c = PetscAbsScalar(uu->ru[0]/uu->r) + c;
565:   if (c > phys->maxspeed) phys->maxspeed = c;

567:   return(0);
568: }

572: static PetscErrorCode Pressure_PG(const PetscReal gamma,const EulerNode *x,PetscScalar *p)
573: {
574:   PetscScalar ru2;
576:   ru2  = DotDIM(x->ru,x->ru);
577:   (*p)=(x->E - 0.5*ru2/x->r)*(gamma - 1.0); /* (E - rho V^2/2)(gamma-1) = e rho (gamma-1) */
578:   return(0);
579: }

583: static PetscErrorCode SpeedOfSound_PG(const PetscReal *gamma, const EulerNode *x, PetscScalar *c)
584: {
585:   PetscScalar p;

588:   Pressure_PG(*gamma,x,&p);
589:   if (p<0.) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"negative pressure time %g -- NEED TO FIX!!!!!!",p);
590:   /* pars[EULER_PAR_GAMMA] = heat capacity ratio */
591:   (*c)=PetscSqrtScalar(*gamma * p / x->r);
592:   return(0);
593: }

597: /*
598:  * x = (rho,rho*(u_1),...,rho*e)^T
599:  * x_t+div(f_1(x))+...+div(f_DIM(x)) = 0
600:  *
601:  * f_i(x) = u_i*x+(0,0,...,p,...,p*u_i)^T
602:  *
603:  */
604: static PetscErrorCode EulerFlux(Physics phys,const PetscReal *n,const EulerNode *x,EulerNode *f)
605: {
606:   Physics_Euler *eu = (Physics_Euler*)phys->data;
607:   PetscScalar   nu,p;
608:   PetscInt      i;

611:   Pressure_PG(eu->pars[EULER_PAR_GAMMA],x,&p);
612:   nu = DotDIM(x->ru,n);
613:   f->r = nu;   /* A rho u */
614:   nu /= x->r;  /* A u */
615:   for (i=0; i<DIM; i++) f->ru[i] = nu * x->ru[i] + n[i]*p;  /* r u^2 + p */
616:   f->E = nu * (x->E + p); /* u(e+p) */
617:   return(0);
618: }

620: /* PetscReal* => EulerNode* conversion */
623: static PetscErrorCode PhysicsBoundary_Euler_Wall(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *a_xI, PetscScalar *a_xG, void *ctx)
624: {
625:   PetscInt    i;
626:   const EulerNode *xI = (const EulerNode*)a_xI;
627:   EulerNode       *xG = (EulerNode*)a_xG;
628:   Physics         phys = (Physics)ctx;
629:   Physics_Euler   *eu  = (Physics_Euler*)phys->data;
631:   xG->r = xI->r;           /* ghost cell density - same */
632:   xG->E = xI->E;           /* ghost cell energy - same */
633:   if (n[1] != 0.) {        /* top and bottom */
634:     xG->ru[0] =  xI->ru[0]; /* copy tang to wall */
635:     xG->ru[1] = -xI->ru[1]; /* reflect perp to t/b wall */
636:   }
637:   else { /* sides */
638:     for (i=0; i<DIM; i++) xG->ru[i] = xI->ru[i]; /* copy */
639:   }
640:   if (eu->type == EULER_LINEAR_WAVE) { // debug
641:     // PetscPrintf(PETSC_COMM_WORLD,"%s coord=%g,%g\n",__FUNCT__,c[0],c[1]);
642:   }
643:   return(0);
644: }
645: int godunovflux( const PetscScalar *ul, const PetscScalar *ur, PetscScalar *flux, const PetscReal *nn, const int *ndim, const PetscReal *gamma);
646: /* PetscReal* => EulerNode* conversion */
649: static void PhysicsRiemann_Euler_Godunov( PetscInt dim, PetscInt Nf, const PetscReal *qp, const PetscReal *n,
650:                                           const PetscScalar *xL, const PetscScalar *xR, PetscScalar *flux, Physics phys)
651: {
652:   Physics_Euler   *eu = (Physics_Euler*)phys->data;
653:   PetscReal       cL,cR,speed,velL,velR,nn[DIM],s2;
654:   PetscInt        i;
655:   PetscErrorCode  ierr;

658:   for (i=0,s2=0.; i<DIM; i++) {
659:     nn[i] = n[i];
660:     s2 += nn[i]*nn[i];
661:   }
662:   s2 = PetscSqrtReal(s2); /* |n|_2 = sum(n^2)^1/2 */
663:   for (i=0.; i<DIM; i++) nn[i] /= s2;
664:   if (0) { /* Rusanov */
665:     const EulerNode *uL = (const EulerNode*)xL,*uR = (const EulerNode*)xR;
666:     EulerNode       fL,fR;
667:     EulerFlux(phys,nn,uL,&fL);
668:     EulerFlux(phys,nn,uR,&fR);
669:     eu->sound(&eu->pars[EULER_PAR_GAMMA],uL,&cL);if (ierr) exit(13);
670:     eu->sound(&eu->pars[EULER_PAR_GAMMA],uR,&cR);if (ierr) exit(14);
671:     velL = DotDIM(uL->ru,nn)/uL->r;
672:     velR = DotDIM(uR->ru,nn)/uR->r;
673:     speed = PetscMax(PetscAbsScalar(velR) + cR,PetscAbsScalar(velL) + cL);
674:     for (i=0; i<2+dim; i++) flux[i] = 0.5*((fL.vals[i]+fR.vals[i]) + speed*(xL[i] - xR[i]))*s2;
675:   }
676:   else {
677:     int dim = DIM;
678:     /* int iwave =  */
679:     godunovflux(xL, xR, flux, nn, &dim, &eu->pars[EULER_PAR_GAMMA]);
680:     for (i=0; i<2+dim; i++) flux[i] *= s2;
681:   }
682:   PetscFunctionReturnVoid();
683: }

687: static PetscErrorCode PhysicsFunctional_Euler(Model mod,PetscReal time,const PetscReal *coord,const PetscScalar *xx,PetscReal *f,void *ctx)
688: {
689:   Physics         phys = (Physics)ctx;
690:   Physics_Euler   *eu  = (Physics_Euler*)phys->data;
691:   const EulerNode *x   = (const EulerNode*)xx;
692:   PetscScalar     p;

695:   f[eu->monitor.Density]  = x->r;
696:   f[eu->monitor.Momentum] = NormDIM(x->ru);
697:   f[eu->monitor.Energy]   = x->E;
698:   f[eu->monitor.Speed]    = NormDIM(x->ru)/x->r;
699:   Pressure_PG(eu->pars[EULER_PAR_GAMMA], x, &p);
700:   f[eu->monitor.Pressure] = p;
701:   return(0);
702: }

706: static PetscErrorCode SetUpBC_Euler(DM dm,Physics phys)
707: {
708:   PetscErrorCode  ierr;
709:   Physics_Euler   *eu = phys->data;
710:   if (eu->type == EULER_LINEAR_WAVE) {
711:     const PetscInt wallids[] = {100,101};
712:     DMAddBoundary(dm, PETSC_FALSE, "wall", "Face Sets", 0, 0, NULL, (void (*)()) PhysicsBoundary_Euler_Wall, ALEN(wallids), wallids, phys);
713:   }
714:   else {
715:     const PetscInt wallids[] = {100,101,200,300};
716:     DMAddBoundary(dm, PETSC_FALSE, "wall", "Face Sets", 0, 0, NULL, (void (*)()) PhysicsBoundary_Euler_Wall, ALEN(wallids), wallids, phys);
717:   }
718:   return(0);
719: }

723: static PetscErrorCode PhysicsCreate_Euler(Model mod,Physics phys,PetscOptionItems *PetscOptionsObject)
724: {
725:   Physics_Euler   *eu;
726:   PetscErrorCode  ierr;

729:   phys->field_desc = PhysicsFields_Euler;
730:   phys->riemann = (PetscRiemannFunc) PhysicsRiemann_Euler_Godunov;
731:   PetscNew(&eu);
732:   phys->data    = eu;
733:   mod->setupbc = SetUpBC_Euler;
734:   PetscOptionsHead(PetscOptionsObject,"Euler options");
735:   {
736:     PetscReal alpha;
737:     char type[64] = "linear_wave";
738:     PetscBool  is;
739:     mod->bcs[0] = mod->bcs[1] = mod->bcs[2] = DM_BOUNDARY_GHOSTED;
740:     eu->pars[EULER_PAR_GAMMA] = 1.4;
741:     eu->pars[EULER_PAR_AMACH] = 2.02;
742:     eu->pars[EULER_PAR_RHOR] = 3.0;
743:     eu->pars[EULER_PAR_ITANA] = 0.57735026918963; /* angle of Euler self similar (SS) shock */
744:     PetscOptionsReal("-eu_gamma","Heat capacity ratio","",eu->pars[EULER_PAR_GAMMA],&eu->pars[EULER_PAR_GAMMA],NULL);
745:     PetscOptionsReal("-eu_amach","Shock speed (Mach)","",eu->pars[EULER_PAR_AMACH],&eu->pars[EULER_PAR_AMACH],NULL);
746:     PetscOptionsReal("-eu_rho2","Density right of discontinuity","",eu->pars[EULER_PAR_RHOR],&eu->pars[EULER_PAR_RHOR],NULL);
747:     alpha = 60.;
748:     PetscOptionsReal("-eu_alpha","Angle of discontinuity","",alpha,&alpha,NULL);
749:     if (alpha<=0. || alpha>90.) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Alpha bust be > 0 and <= 90 (%g)",alpha);
750:     eu->pars[EULER_PAR_ITANA] = 1./tan ( alpha * M_PI / 180.0 );
751:     PetscOptionsString("-eu_type","Type of Euler test","",type,type,sizeof(type),NULL);
752:     PetscStrcmp(type,"linear_wave", &is);
753:     if (is) {
754:       eu->type = EULER_LINEAR_WAVE;
755:       mod->bcs[0] = mod->bcs[1] = mod->bcs[2] = DM_BOUNDARY_PERIODIC;
756:       mod->bcs[1] = DM_BOUNDARY_GHOSTED; /* debug */
757:       PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",__FUNCT__,"linear_wave");
758:     }
759:     else {
760:       if (DIM != 2) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"DIM must be 2 unless linear wave test %s",type);
761:       PetscStrcmp(type,"iv_shock", &is);
762:       if (is) {
763:         eu->type = EULER_IV_SHOCK;
764:         PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",__FUNCT__,"iv_shock");
765:       }
766:       else {
767:         PetscStrcmp(type,"ss_shock", &is);
768:         if (is) {
769:           eu->type = EULER_SS_SHOCK;
770:           PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",__FUNCT__,"ss_shock");
771:         }
772:         else {
773:           PetscStrcmp(type,"shock_tube", &is);
774:           if (is) eu->type = EULER_SHOCK_TUBE;
775:           else SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Unknown Euler type %s",type);
776:           PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",__FUNCT__,"shock_tube");
777:         }
778:       }
779:     }
780:   }
781:   PetscOptionsTail();
782:   eu->sound = SpeedOfSound_PG;
783:   phys->maxspeed = 0.; /* will get set in solution */
784:   ModelSolutionSetDefault(mod,PhysicsSolution_Euler,phys);
785:   ModelFunctionalRegister(mod,"Speed",&eu->monitor.Speed,PhysicsFunctional_Euler,phys);
786:   ModelFunctionalRegister(mod,"Energy",&eu->monitor.Energy,PhysicsFunctional_Euler,phys);
787:   ModelFunctionalRegister(mod,"Density",&eu->monitor.Density,PhysicsFunctional_Euler,phys);
788:   ModelFunctionalRegister(mod,"Momentum",&eu->monitor.Momentum,PhysicsFunctional_Euler,phys);
789:   ModelFunctionalRegister(mod,"Pressure",&eu->monitor.Pressure,PhysicsFunctional_Euler,phys);

791:   return(0);
792: }

796: PetscErrorCode ConstructCellBoundary(DM dm, User user)
797: {
798:   const char     *name   = "Cell Sets";
799:   const char     *bdname = "split faces";
800:   IS             regionIS, innerIS;
801:   const PetscInt *regions, *cells;
802:   PetscInt       numRegions, innerRegion, numCells, c;
803:   PetscInt       cStart, cEnd, cEndInterior, fStart, fEnd;
804:   PetscBool      hasLabel;

808:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
809:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
810:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);

812:   DMHasLabel(dm, name, &hasLabel);
813:   if (!hasLabel) return(0);
814:   DMGetLabelSize(dm, name, &numRegions);
815:   if (numRegions != 2) return(0);
816:   /* Get the inner id */
817:   DMGetLabelIdIS(dm, name, &regionIS);
818:   ISGetIndices(regionIS, &regions);
819:   innerRegion = regions[0];
820:   ISRestoreIndices(regionIS, &regions);
821:   ISDestroy(&regionIS);
822:   /* Find the faces between cells in different regions, could call DMPlexCreateNeighborCSR() */
823:   DMGetStratumIS(dm, name, innerRegion, &innerIS);
824:   ISGetLocalSize(innerIS, &numCells);
825:   ISGetIndices(innerIS, &cells);
826:   DMCreateLabel(dm, bdname);
827:   for (c = 0; c < numCells; ++c) {
828:     const PetscInt cell = cells[c];
829:     const PetscInt *faces;
830:     PetscInt       numFaces, f;

832:     if ((cell < cStart) || (cell >= cEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Got invalid point %d which is not a cell", cell);
833:     DMPlexGetConeSize(dm, cell, &numFaces);
834:     DMPlexGetCone(dm, cell, &faces);
835:     for (f = 0; f < numFaces; ++f) {
836:       const PetscInt face = faces[f];
837:       const PetscInt *neighbors;
838:       PetscInt       nC, regionA, regionB;

840:       if ((face < fStart) || (face >= fEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Got invalid point %d which is not a face", face);
841:       DMPlexGetSupportSize(dm, face, &nC);
842:       if (nC != 2) continue;
843:       DMPlexGetSupport(dm, face, &neighbors);
844:       if ((neighbors[0] >= cEndInterior) || (neighbors[1] >= cEndInterior)) continue;
845:       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]);
846:       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]);
847:       DMGetLabelValue(dm, name, neighbors[0], &regionA);
848:       DMGetLabelValue(dm, name, neighbors[1], &regionB);
849:       if (regionA < 0) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Invalid label %s: Cell %d has no value", name, neighbors[0]);
850:       if (regionB < 0) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Invalid label %s: Cell %d has no value", name, neighbors[1]);
851:       if (regionA != regionB) {
852:         DMSetLabelValue(dm, bdname, faces[f], 1);
853:       }
854:     }
855:   }
856:   ISRestoreIndices(innerIS, &cells);
857:   ISDestroy(&innerIS);
858:   {
859:     DMLabel label;

861:     DMGetLabel(dm, bdname, &label);
862:     DMLabelView(label, PETSC_VIEWER_STDOUT_WORLD);
863:   }
864:   return(0);
865: }

869: /* Right now, I have just added duplicate faces, which see both cells. We can
870: - Add duplicate vertices and decouple the face cones
871: - Disconnect faces from cells across the rotation gap
872: */
873: PetscErrorCode SplitFaces(DM *dmSplit, const char labelName[], User user)
874: {
875:   DM             dm = *dmSplit, sdm;
876:   PetscSF        sfPoint, gsfPoint;
877:   PetscSection   coordSection, newCoordSection;
878:   Vec            coordinates;
879:   IS             idIS;
880:   const PetscInt *ids;
881:   PetscInt       *newpoints;
882:   PetscInt       dim, depth, maxConeSize, maxSupportSize, numLabels, numGhostCells;
883:   PetscInt       numFS, fs, pStart, pEnd, p, cEnd, cEndInterior, vStart, vEnd, v, fStart, fEnd, newf, d, l;
884:   PetscBool      hasLabel;

888:   DMHasLabel(dm, labelName, &hasLabel);
889:   if (!hasLabel) return(0);
890:   DMCreate(PetscObjectComm((PetscObject)dm), &sdm);
891:   DMSetType(sdm, DMPLEX);
892:   DMGetDimension(dm, &dim);
893:   DMSetDimension(sdm, dim);

895:   DMGetLabelIdIS(dm, labelName, &idIS);
896:   ISGetLocalSize(idIS, &numFS);
897:   ISGetIndices(idIS, &ids);

899:   user->numSplitFaces = 0;
900:   for (fs = 0; fs < numFS; ++fs) {
901:     PetscInt numBdFaces;

903:     DMGetStratumSize(dm, labelName, ids[fs], &numBdFaces);
904:     user->numSplitFaces += numBdFaces;
905:   }
906:   DMPlexGetChart(dm, &pStart, &pEnd);
907:   pEnd += user->numSplitFaces;
908:   DMPlexSetChart(sdm, pStart, pEnd);
909:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
910:   DMPlexSetHybridBounds(sdm, cEndInterior, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_DETERMINE);
911:   DMPlexGetHeightStratum(dm, 0, NULL, &cEnd);
912:   numGhostCells = cEnd - cEndInterior;
913:   /* Set cone and support sizes */
914:   DMPlexGetDepth(dm, &depth);
915:   for (d = 0; d <= depth; ++d) {
916:     DMPlexGetDepthStratum(dm, d, &pStart, &pEnd);
917:     for (p = pStart; p < pEnd; ++p) {
918:       PetscInt newp = p;
919:       PetscInt size;

921:       DMPlexGetConeSize(dm, p, &size);
922:       DMPlexSetConeSize(sdm, newp, size);
923:       DMPlexGetSupportSize(dm, p, &size);
924:       DMPlexSetSupportSize(sdm, newp, size);
925:     }
926:   }
927:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
928:   for (fs = 0, newf = fEnd; fs < numFS; ++fs) {
929:     IS             faceIS;
930:     const PetscInt *faces;
931:     PetscInt       numFaces, f;

933:     DMGetStratumIS(dm, labelName, ids[fs], &faceIS);
934:     ISGetLocalSize(faceIS, &numFaces);
935:     ISGetIndices(faceIS, &faces);
936:     for (f = 0; f < numFaces; ++f, ++newf) {
937:       PetscInt size;

939:       /* Right now I think that both faces should see both cells */
940:       DMPlexGetConeSize(dm, faces[f], &size);
941:       DMPlexSetConeSize(sdm, newf, size);
942:       DMPlexGetSupportSize(dm, faces[f], &size);
943:       DMPlexSetSupportSize(sdm, newf, size);
944:     }
945:     ISRestoreIndices(faceIS, &faces);
946:     ISDestroy(&faceIS);
947:   }
948:   DMSetUp(sdm);
949:   /* Set cones and supports */
950:   DMPlexGetMaxSizes(dm, &maxConeSize, &maxSupportSize);
951:   PetscMalloc(PetscMax(maxConeSize, maxSupportSize) * sizeof(PetscInt), &newpoints);
952:   DMPlexGetChart(dm, &pStart, &pEnd);
953:   for (p = pStart; p < pEnd; ++p) {
954:     const PetscInt *points, *orientations;
955:     PetscInt       size, i, newp = p;

957:     DMPlexGetConeSize(dm, p, &size);
958:     DMPlexGetCone(dm, p, &points);
959:     DMPlexGetConeOrientation(dm, p, &orientations);
960:     for (i = 0; i < size; ++i) newpoints[i] = points[i];
961:     DMPlexSetCone(sdm, newp, newpoints);
962:     DMPlexSetConeOrientation(sdm, newp, orientations);
963:     DMPlexGetSupportSize(dm, p, &size);
964:     DMPlexGetSupport(dm, p, &points);
965:     for (i = 0; i < size; ++i) newpoints[i] = points[i];
966:     DMPlexSetSupport(sdm, newp, newpoints);
967:   }
968:   PetscFree(newpoints);
969:   for (fs = 0, newf = fEnd; fs < numFS; ++fs) {
970:     IS             faceIS;
971:     const PetscInt *faces;
972:     PetscInt       numFaces, f;

974:     DMGetStratumIS(dm, labelName, ids[fs], &faceIS);
975:     ISGetLocalSize(faceIS, &numFaces);
976:     ISGetIndices(faceIS, &faces);
977:     for (f = 0; f < numFaces; ++f, ++newf) {
978:       const PetscInt *points;

980:       DMPlexGetCone(dm, faces[f], &points);
981:       DMPlexSetCone(sdm, newf, points);
982:       DMPlexGetSupport(dm, faces[f], &points);
983:       DMPlexSetSupport(sdm, newf, points);
984:     }
985:     ISRestoreIndices(faceIS, &faces);
986:     ISDestroy(&faceIS);
987:   }
988:   ISRestoreIndices(idIS, &ids);
989:   ISDestroy(&idIS);
990:   DMPlexStratify(sdm);
991:   /* Convert coordinates */
992:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
993:   DMGetCoordinateSection(dm, &coordSection);
994:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &newCoordSection);
995:   PetscSectionSetNumFields(newCoordSection, 1);
996:   PetscSectionSetFieldComponents(newCoordSection, 0, dim);
997:   PetscSectionSetChart(newCoordSection, vStart, vEnd);
998:   for (v = vStart; v < vEnd; ++v) {
999:     PetscSectionSetDof(newCoordSection, v, dim);
1000:     PetscSectionSetFieldDof(newCoordSection, v, 0, dim);
1001:   }
1002:   PetscSectionSetUp(newCoordSection);
1003:   DMSetCoordinateSection(sdm, PETSC_DETERMINE, newCoordSection);
1004:   PetscSectionDestroy(&newCoordSection); /* relinquish our reference */
1005:   DMGetCoordinatesLocal(dm, &coordinates);
1006:   DMSetCoordinatesLocal(sdm, coordinates);
1007:   /* Convert labels */
1008:   DMGetNumLabels(dm, &numLabels);
1009:   for (l = 0; l < numLabels; ++l) {
1010:     const char *lname;
1011:     PetscBool  isDepth;

1013:     DMGetLabelName(dm, l, &lname);
1014:     PetscStrcmp(lname, "depth", &isDepth);
1015:     if (isDepth) continue;
1016:     DMCreateLabel(sdm, lname);
1017:     DMGetLabelIdIS(dm, lname, &idIS);
1018:     ISGetLocalSize(idIS, &numFS);
1019:     ISGetIndices(idIS, &ids);
1020:     for (fs = 0; fs < numFS; ++fs) {
1021:       IS             pointIS;
1022:       const PetscInt *points;
1023:       PetscInt       numPoints;

1025:       DMGetStratumIS(dm, lname, ids[fs], &pointIS);
1026:       ISGetLocalSize(pointIS, &numPoints);
1027:       ISGetIndices(pointIS, &points);
1028:       for (p = 0; p < numPoints; ++p) {
1029:         PetscInt newpoint = points[p];

1031:         DMSetLabelValue(sdm, lname, newpoint, ids[fs]);
1032:       }
1033:       ISRestoreIndices(pointIS, &points);
1034:       ISDestroy(&pointIS);
1035:     }
1036:     ISRestoreIndices(idIS, &ids);
1037:     ISDestroy(&idIS);
1038:   }
1039:   /* Convert pointSF */
1040:   const PetscSFNode *remotePoints;
1041:   PetscSFNode       *gremotePoints;
1042:   const PetscInt    *localPoints;
1043:   PetscInt          *glocalPoints,*newLocation,*newRemoteLocation;
1044:   PetscInt          numRoots, numLeaves;
1045:   PetscMPIInt       numProcs;

1047:   MPI_Comm_size(PetscObjectComm((PetscObject)dm), &numProcs);
1048:   DMGetPointSF(dm, &sfPoint);
1049:   DMGetPointSF(sdm, &gsfPoint);
1050:   DMPlexGetChart(dm,&pStart,&pEnd);
1051:   PetscSFGetGraph(sfPoint, &numRoots, &numLeaves, &localPoints, &remotePoints);
1052:   if (numRoots >= 0) {
1053:     PetscMalloc2(numRoots,&newLocation,pEnd-pStart,&newRemoteLocation);
1054:     for (l=0; l<numRoots; l++) newLocation[l] = l; /* + (l >= cEnd ? numGhostCells : 0); */
1055:     PetscSFBcastBegin(sfPoint, MPIU_INT, newLocation, newRemoteLocation);
1056:     PetscSFBcastEnd(sfPoint, MPIU_INT, newLocation, newRemoteLocation);
1057:     PetscMalloc1(numLeaves,    &glocalPoints);
1058:     PetscMalloc1(numLeaves, &gremotePoints);
1059:     for (l = 0; l < numLeaves; ++l) {
1060:       glocalPoints[l]        = localPoints[l]; /* localPoints[l] >= cEnd ? localPoints[l] + numGhostCells : localPoints[l]; */
1061:       gremotePoints[l].rank  = remotePoints[l].rank;
1062:       gremotePoints[l].index = newRemoteLocation[localPoints[l]];
1063:     }
1064:     PetscFree2(newLocation,newRemoteLocation);
1065:     PetscSFSetGraph(gsfPoint, numRoots+numGhostCells, numLeaves, glocalPoints, PETSC_OWN_POINTER, gremotePoints, PETSC_OWN_POINTER);
1066:   }
1067:   DMDestroy(dmSplit);
1068:   *dmSplit = sdm;
1069:   return(0);
1070: }

1074: PetscErrorCode CreatePartitionVec(DM dm, DM *dmCell, Vec *partition)
1075: {
1076:   PetscSF        sfPoint;
1077:   PetscSection   coordSection;
1078:   Vec            coordinates;
1079:   PetscSection   sectionCell;
1080:   PetscScalar    *part;
1081:   PetscInt       cStart, cEnd, c;
1082:   PetscMPIInt    rank;

1086:   DMGetCoordinateSection(dm, &coordSection);
1087:   DMGetCoordinatesLocal(dm, &coordinates);
1088:   DMClone(dm, dmCell);
1089:   DMGetPointSF(dm, &sfPoint);
1090:   DMSetPointSF(*dmCell, sfPoint);
1091:   DMSetCoordinateSection(*dmCell, PETSC_DETERMINE, coordSection);
1092:   DMSetCoordinatesLocal(*dmCell, coordinates);
1093:   MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);
1094:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionCell);
1095:   DMPlexGetHeightStratum(*dmCell, 0, &cStart, &cEnd);
1096:   PetscSectionSetChart(sectionCell, cStart, cEnd);
1097:   for (c = cStart; c < cEnd; ++c) {
1098:     PetscSectionSetDof(sectionCell, c, 1);
1099:   }
1100:   PetscSectionSetUp(sectionCell);
1101:   DMSetDefaultSection(*dmCell, sectionCell);
1102:   PetscSectionDestroy(&sectionCell);
1103:   DMCreateLocalVector(*dmCell, partition);
1104:   PetscObjectSetName((PetscObject)*partition, "partition");
1105:   VecGetArray(*partition, &part);
1106:   for (c = cStart; c < cEnd; ++c) {
1107:     PetscScalar *p;

1109:     DMPlexPointLocalRef(*dmCell, c, part, &p);
1110:     p[0] = rank;
1111:   }
1112:   VecRestoreArray(*partition, &part);
1113:   return(0);
1114: }

1118: PetscErrorCode CreateMassMatrix(DM dm, Vec *massMatrix, User user)
1119: {
1120:   DM                dmMass, dmFace, dmCell, dmCoord;
1121:   PetscSection      coordSection;
1122:   Vec               coordinates, facegeom, cellgeom;
1123:   PetscSection      sectionMass;
1124:   PetscScalar       *m;
1125:   const PetscScalar *fgeom, *cgeom, *coords;
1126:   PetscInt          vStart, vEnd, v;
1127:   PetscErrorCode    ierr;

1130:   DMGetCoordinateSection(dm, &coordSection);
1131:   DMGetCoordinatesLocal(dm, &coordinates);
1132:   DMClone(dm, &dmMass);
1133:   DMSetCoordinateSection(dmMass, PETSC_DETERMINE, coordSection);
1134:   DMSetCoordinatesLocal(dmMass, coordinates);
1135:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionMass);
1136:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
1137:   PetscSectionSetChart(sectionMass, vStart, vEnd);
1138:   for (v = vStart; v < vEnd; ++v) {
1139:     PetscInt numFaces;

1141:     DMPlexGetSupportSize(dmMass, v, &numFaces);
1142:     PetscSectionSetDof(sectionMass, v, numFaces*numFaces);
1143:   }
1144:   PetscSectionSetUp(sectionMass);
1145:   DMSetDefaultSection(dmMass, sectionMass);
1146:   PetscSectionDestroy(&sectionMass);
1147:   DMGetLocalVector(dmMass, massMatrix);
1148:   VecGetArray(*massMatrix, &m);
1149:   DMPlexTSGetGeometryFVM(dm, &facegeom, &cellgeom, NULL);
1150:   VecGetDM(facegeom, &dmFace);
1151:   VecGetArrayRead(facegeom, &fgeom);
1152:   VecGetDM(cellgeom, &dmCell);
1153:   VecGetArrayRead(cellgeom, &cgeom);
1154:   DMGetCoordinateDM(dm, &dmCoord);
1155:   VecGetArrayRead(coordinates, &coords);
1156:   for (v = vStart; v < vEnd; ++v) {
1157:     const PetscInt        *faces;
1158:     const PetscFVFaceGeom *fgA, *fgB, *cg;
1159:     const PetscScalar     *vertex;
1160:     PetscInt               numFaces, sides[2], f, g;

1162:     DMPlexPointLocalRead(dmCoord, v, coords, &vertex);
1163:     DMPlexGetSupportSize(dmMass, v, &numFaces);
1164:     DMPlexGetSupport(dmMass, v, &faces);
1165:     for (f = 0; f < numFaces; ++f) {
1166:       sides[0] = faces[f];
1167:       DMPlexPointLocalRead(dmFace, faces[f], fgeom, &fgA);
1168:       for (g = 0; g < numFaces; ++g) {
1169:         const PetscInt *cells = NULL;;
1170:         PetscReal      area   = 0.0;
1171:         PetscInt       numCells;

1173:         sides[1] = faces[g];
1174:         DMPlexPointLocalRead(dmFace, faces[g], fgeom, &fgB);
1175:         DMPlexGetJoin(dmMass, 2, sides, &numCells, &cells);
1176:         if (numCells != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Invalid join for faces");
1177:         DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cg);
1178:         area += PetscAbsScalar((vertex[0] - cg->centroid[0])*(fgA->centroid[1] - cg->centroid[1]) - (vertex[1] - cg->centroid[1])*(fgA->centroid[0] - cg->centroid[0]));
1179:         area += PetscAbsScalar((vertex[0] - cg->centroid[0])*(fgB->centroid[1] - cg->centroid[1]) - (vertex[1] - cg->centroid[1])*(fgB->centroid[0] - cg->centroid[0]));
1180:         m[f*numFaces+g] = Dot2(fgA->normal, fgB->normal)*area*0.5;
1181:         DMPlexRestoreJoin(dmMass, 2, sides, &numCells, &cells);
1182:       }
1183:     }
1184:   }
1185:   VecRestoreArrayRead(facegeom, &fgeom);
1186:   VecRestoreArrayRead(cellgeom, &cgeom);
1187:   VecRestoreArrayRead(coordinates, &coords);
1188:   VecRestoreArray(*massMatrix, &m);
1189:   DMDestroy(&dmMass);
1190:   return(0);
1191: }

1195: /* Behavior will be different for multi-physics or when using non-default boundary conditions */
1196: static PetscErrorCode ModelSolutionSetDefault(Model mod,SolutionFunction func,void *ctx)
1197: {
1199:   mod->solution    = func;
1200:   mod->solutionctx = ctx;
1201:   return(0);
1202: }

1206: static PetscErrorCode ModelFunctionalRegister(Model mod,const char *name,PetscInt *offset,FunctionalFunction func,void *ctx)
1207: {
1209:   FunctionalLink link,*ptr;
1210:   PetscInt       lastoffset = -1;

1213:   for (ptr=&mod->functionalRegistry; *ptr; ptr = &(*ptr)->next) lastoffset = (*ptr)->offset;
1214:   PetscNew(&link);
1215:   PetscStrallocpy(name,&link->name);
1216:   link->offset = lastoffset + 1;
1217:   link->func   = func;
1218:   link->ctx    = ctx;
1219:   link->next   = NULL;
1220:   *ptr         = link;
1221:   *offset      = link->offset;
1222:   return(0);
1223: }

1227: static PetscErrorCode ModelFunctionalSetFromOptions(Model mod,PetscOptionItems *PetscOptionsObject)
1228: {
1230:   PetscInt       i,j;
1231:   FunctionalLink link;
1232:   char           *names[256];

1235:   mod->numMonitored = ALEN(names);
1236:   PetscOptionsStringArray("-monitor","list of functionals to monitor","",names,&mod->numMonitored,NULL);
1237:   /* Create list of functionals that will be computed somehow */
1238:   PetscMalloc1(mod->numMonitored,&mod->functionalMonitored);
1239:   /* Create index of calls that we will have to make to compute these functionals (over-allocation in general). */
1240:   PetscMalloc1(mod->numMonitored,&mod->functionalCall);
1241:   mod->numCall = 0;
1242:   for (i=0; i<mod->numMonitored; i++) {
1243:     for (link=mod->functionalRegistry; link; link=link->next) {
1244:       PetscBool match;
1245:       PetscStrcasecmp(names[i],link->name,&match);
1246:       if (match) break;
1247:     }
1248:     if (!link) SETERRQ1(mod->comm,PETSC_ERR_USER,"No known functional '%s'",names[i]);
1249:     mod->functionalMonitored[i] = link;
1250:     for (j=0; j<i; j++) {
1251:       if (mod->functionalCall[j]->func == link->func && mod->functionalCall[j]->ctx == link->ctx) goto next_name;
1252:     }
1253:     mod->functionalCall[mod->numCall++] = link; /* Just points to the first link using the result. There may be more results. */
1254: next_name:
1255:     PetscFree(names[i]);
1256:   }

1258:   /* Find out the maximum index of any functional computed by a function we will be calling (even if we are not using it) */
1259:   mod->maxComputed = -1;
1260:   for (link=mod->functionalRegistry; link; link=link->next) {
1261:     for (i=0; i<mod->numCall; i++) {
1262:       FunctionalLink call = mod->functionalCall[i];
1263:       if (link->func == call->func && link->ctx == call->ctx) {
1264:         mod->maxComputed = PetscMax(mod->maxComputed,link->offset);
1265:       }
1266:     }
1267:   }
1268:   return(0);
1269: }

1273: static PetscErrorCode FunctionalLinkDestroy(FunctionalLink *link)
1274: {
1276:   FunctionalLink l,next;

1279:   if (!link) return(0);
1280:   l     = *link;
1281:   *link = NULL;
1282:   for (; l; l=next) {
1283:     next = l->next;
1284:     PetscFree(l->name);
1285:     PetscFree(l);
1286:   }
1287:   return(0);
1288: }

1292: /* put the solution callback into a functional callback */
1293: static PetscErrorCode SolutionFunctional(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *modctx)
1294: {
1295:   Model          mod;
1298:   mod  = (Model) modctx;
1299:   (*mod->solution)(mod, time, x, u, mod->solutionctx);
1300:   return(0);
1301: }

1305: PetscErrorCode SetInitialCondition(DM dm, Vec X, User user)
1306: {
1307:   PetscErrorCode     (*func[1]) (PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
1308:   void               *ctx[1];
1309:   Model              mod = user->model;
1310:   PetscErrorCode     ierr;

1313:   func[0] = SolutionFunctional;
1314:   ctx[0]  = (void *) mod;
1315:   DMProjectFunction(dm,0.0,func,ctx,INSERT_ALL_VALUES,X);
1316:   return(0);
1317: }

1321: static PetscErrorCode OutputVTK(DM dm, const char *filename, PetscViewer *viewer)
1322: {

1326:   PetscViewerCreate(PetscObjectComm((PetscObject)dm), viewer);
1327:   PetscViewerSetType(*viewer, PETSCVIEWERVTK);
1328:   PetscViewerFileSetName(*viewer, filename);
1329:   return(0);
1330: }

1334: static PetscErrorCode MonitorVTK(TS ts,PetscInt stepnum,PetscReal time,Vec X,void *ctx)
1335: {
1336:   User           user = (User)ctx;
1337:   DM             dm;
1338:   Vec            cellgeom;
1339:   PetscViewer    viewer;
1340:   char           filename[PETSC_MAX_PATH_LEN],*ftable = NULL;
1341:   PetscReal      xnorm;
1342:   PetscInt       cEndInterior;

1346:   PetscObjectSetName((PetscObject) X, "u");
1347:   VecGetDM(X,&dm);
1348:   DMPlexTSGetGeometryFVM(dm, NULL, &cellgeom, NULL);
1349:   VecNorm(X,NORM_INFINITY,&xnorm);

1351:   if (stepnum >= 0) {           /* No summary for final time */
1352:     Model             mod = user->model;
1353:     PetscInt          c,cStart,cEnd,fcount,i;
1354:     size_t            ftableused,ftablealloc;
1355:     const PetscScalar *cgeom,*x;
1356:     DM                dmCell;
1357:     PetscReal         *fmin,*fmax,*fintegral,*ftmp;
1358:     fcount = mod->maxComputed+1;
1359:     PetscMalloc4(fcount,&fmin,fcount,&fmax,fcount,&fintegral,fcount,&ftmp);
1360:     for (i=0; i<fcount; i++) {
1361:       fmin[i]      = PETSC_MAX_REAL;
1362:       fmax[i]      = PETSC_MIN_REAL;
1363:       fintegral[i] = 0;
1364:     }
1365:     VecGetDM(cellgeom,&dmCell);
1366:     DMPlexGetHybridBounds(dmCell, &cEndInterior, NULL, NULL, NULL);
1367:     DMPlexGetHeightStratum(dmCell,0,&cStart,&cEnd);
1368:     VecGetArrayRead(cellgeom,&cgeom);
1369:     VecGetArrayRead(X,&x);
1370:     for (c = cStart; c < cEndInterior; ++c) {
1371:       const PetscFVCellGeom *cg;
1372:       const PetscScalar     *cx;
1373:       /* not that these two routines as currently implemented work for any dm with a
1374:        * defaultSection/defaultGlobalSection */
1375:       DMPlexPointLocalRead(dmCell,c,cgeom,&cg);
1376:       DMPlexPointGlobalRead(dm,c,x,&cx);
1377:       if (!cx) continue;        /* not a global cell */
1378:       for (i=0; i<mod->numCall; i++) {
1379:         FunctionalLink flink = mod->functionalCall[i];
1380:         (*flink->func)(mod,time,cg->centroid,cx,ftmp,flink->ctx);
1381:       }
1382:       for (i=0; i<fcount; i++) {
1383:         fmin[i]       = PetscMin(fmin[i],ftmp[i]);
1384:         fmax[i]       = PetscMax(fmax[i],ftmp[i]);
1385:         fintegral[i] += cg->volume * ftmp[i];
1386:       }
1387:     }
1388:     VecRestoreArrayRead(cellgeom,&cgeom);
1389:     VecRestoreArrayRead(X,&x);
1390:     MPI_Allreduce(MPI_IN_PLACE,fmin,fcount,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)ts));
1391:     MPI_Allreduce(MPI_IN_PLACE,fmax,fcount,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
1392:     MPI_Allreduce(MPI_IN_PLACE,fintegral,fcount,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));

1394:     ftablealloc = fcount * 100;
1395:     ftableused  = 0;
1396:     PetscMalloc1(ftablealloc,&ftable);
1397:     for (i=0; i<mod->numMonitored; i++) {
1398:       size_t         countused;
1399:       char           buffer[256],*p;
1400:       FunctionalLink flink = mod->functionalMonitored[i];
1401:       PetscInt       id    = flink->offset;
1402:       if (i % 3) {
1403:         PetscMemcpy(buffer,"  ",2);
1404:         p    = buffer + 2;
1405:       } else if (i) {
1406:         char newline[] = "\n";
1407:         PetscMemcpy(buffer,newline,sizeof newline-1);
1408:         p    = buffer + sizeof newline - 1;
1409:       } else {
1410:         p = buffer;
1411:       }
1412:       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]);
1413:       countused += p - buffer;
1414:       if (countused > ftablealloc-ftableused-1) { /* reallocate */
1415:         char *ftablenew;
1416:         ftablealloc = 2*ftablealloc + countused;
1417:         PetscMalloc(ftablealloc,&ftablenew);
1418:         PetscMemcpy(ftablenew,ftable,ftableused);
1419:         PetscFree(ftable);
1420:         ftable = ftablenew;
1421:       }
1422:       PetscMemcpy(ftable+ftableused,buffer,countused);
1423:       ftableused += countused;
1424:       ftable[ftableused] = 0;
1425:     }
1426:     PetscFree4(fmin,fmax,fintegral,ftmp);

1428:     PetscPrintf(PetscObjectComm((PetscObject)ts),"% 3D  time %8.4g  |x| %8.4g  %s\n",stepnum,(double)time,(double)xnorm,ftable ? ftable : "");
1429:     PetscFree(ftable);
1430:   }
1431:   if (user->vtkInterval < 1) return(0);
1432:   if ((stepnum == -1) ^ (stepnum % user->vtkInterval == 0)) {
1433:     if (stepnum == -1) {        /* Final time is not multiple of normal time interval, write it anyway */
1434:       TSGetTimeStepNumber(ts,&stepnum);
1435:     }
1436:     PetscSNPrintf(filename,sizeof filename,"ex11-%03D.vtu",stepnum);
1437:     OutputVTK(dm,filename,&viewer);
1438:     VecView(X,viewer);
1439:     PetscViewerDestroy(&viewer);
1440:   }
1441:   return(0);
1442: }

1446: int main(int argc, char **argv)
1447: {
1448:   MPI_Comm          comm;
1449:   PetscDS           prob;
1450:   PetscFV           fvm;
1451:   User              user;
1452:   Model             mod;
1453:   Physics           phys;
1454:   DM                dm;
1455:   PetscReal         ftime, cfl, dt, minRadius;
1456:   PetscInt          dim, nsteps;
1457:   TS                ts;
1458:   TSConvergedReason reason;
1459:   Vec               X;
1460:   PetscViewer       viewer;
1461:   PetscBool         vtkCellGeom, splitFaces;
1462:   PetscInt          overlap;
1463:   char              filename[PETSC_MAX_PATH_LEN] = "sevenside.exo";
1464:   char              physname[256]  = "advect";
1465:   PetscErrorCode    ierr;

1467:   PetscInitialize(&argc, &argv, (char*) 0, help);
1468:   comm = PETSC_COMM_WORLD;

1470:   PetscNew(&user);
1471:   PetscNew(&user->model);
1472:   PetscNew(&user->model->physics);
1473:   mod  = user->model;
1474:   phys = mod->physics;
1475:   mod->comm = comm;

1477:   /* Register physical models to be available on the command line */
1478:   PetscFunctionListAdd(&PhysicsList,"advect"          ,PhysicsCreate_Advect);
1479:   PetscFunctionListAdd(&PhysicsList,"sw"              ,PhysicsCreate_SW);
1480:   PetscFunctionListAdd(&PhysicsList,"euler"           ,PhysicsCreate_Euler);

1482:   PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Mesh Options","");
1483:   {
1484:     cfl  = 0.9 * 4; /* default SSPRKS2 with s=5 stages is stable for CFL number s-1 */
1485:     PetscOptionsReal("-ufv_cfl","CFL number per step","",cfl,&cfl,NULL);
1486:     PetscOptionsString("-f","Exodus.II filename to read","",filename,filename,sizeof(filename),NULL);
1487:     splitFaces = PETSC_FALSE;
1488:     PetscOptionsBool("-ufv_split_faces","Split faces between cell sets","",splitFaces,&splitFaces,NULL);
1489:     overlap = 1;
1490:     PetscOptionsInt("-ufv_mesh_overlap","Number of cells to overlap partitions","",overlap,&overlap,NULL);
1491:     user->vtkInterval = 1;
1492:     PetscOptionsInt("-ufv_vtk_interval","VTK output interval (0 to disable)","",user->vtkInterval,&user->vtkInterval,NULL);
1493:     vtkCellGeom = PETSC_FALSE;
1494:     PetscOptionsBool("-ufv_vtk_cellgeom","Write cell geometry (for debugging)","",vtkCellGeom,&vtkCellGeom,NULL);
1495:   }
1496:   PetscOptionsEnd();

1498:   PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Physics Options","");
1499:   {
1500:     PetscErrorCode (*physcreate)(Model,Physics,PetscOptionItems*);
1501:     PetscOptionsFList("-physics","Physics module to solve","",PhysicsList,physname,physname,sizeof physname,NULL);
1502:     PetscFunctionListFind(PhysicsList,physname,&physcreate);
1503:     PetscMemzero(phys,sizeof(struct _n_Physics));
1504:     (*physcreate)(mod,phys,PetscOptionsObject);
1505:     /* Count number of fields and dofs */
1506:     for (phys->nfields=0,phys->dof=0; phys->field_desc[phys->nfields].name; phys->nfields++) phys->dof += phys->field_desc[phys->nfields].dof;
1507:     if (phys->dof <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set dof",physname);
1508:     ModelFunctionalSetFromOptions(mod,PetscOptionsObject);
1509:   }
1510:   PetscOptionsEnd();

1512:   {
1513:     size_t len,i;
1514:     for (i = 0; i < DIM; i++) { mod->bounds[2*i] = 0.; mod->bounds[2*i+1] = 1.;};
1515:     PetscStrlen(filename,&len);
1516:     dim = DIM;
1517:     if (!len) { /* a null name means just do a hex box */
1518:       PetscInt cells[3] = {1, 1, 1}; /* coarse mesh is one cell; refine from there */
1519:       PetscBool flg1, flg2;
1520:       PetscInt nret1 = DIM;
1521:       PetscInt nret2 = 2*DIM;
1522:       PetscOptionsBegin(comm,NULL,"Rectangular mesh options","");
1523:       PetscOptionsIntArray("-grid_size","number of cells in each direction","",cells,&nret1,&flg1);
1524:       PetscOptionsRealArray("-grid_bounds","bounds of the mesh in each direction (e.g., x_min,x_max,y_min,y_max","",mod->bounds,&nret2,&flg2);
1525:       PetscOptionsEnd();
1526:       if (flg1) {
1527:         dim = nret1;
1528:         if (dim != DIM) SETERRQ1(comm,PETSC_ERR_ARG_SIZ,"Dim wrong size %D in -grid_size",dim);
1529:       }
1530:       DMPlexCreateHexBoxMesh(comm, dim, cells, mod->bcs[0], mod->bcs[1], mod->bcs[2], &dm);
1531:       if (flg2) {
1532:         PetscInt dimEmbed, i;
1533:         PetscInt nCoords;
1534:         PetscScalar *coords;
1535:         Vec coordinates;

1537:         DMGetCoordinatesLocal(dm,&coordinates);
1538:         DMGetCoordinateDim(dm,&dimEmbed);
1539:         VecGetLocalSize(coordinates,&nCoords);
1540:         if (nCoords % dimEmbed) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Coordinate vector the wrong size");
1541:         VecGetArray(coordinates,&coords);
1542:         for (i = 0; i < nCoords; i += dimEmbed) {
1543:           PetscInt j;

1545:           PetscScalar *coord = &coords[i];
1546:           for (j = 0; j < dimEmbed; j++) {
1547:             coord[j] = mod->bounds[2 * j] + coord[j] * (mod->bounds[2 * j + 1] - mod->bounds[2 * j]);
1548:             if (dim==2 && cells[1]==1 && j==0 && 0) {
1549:               if (cells[0]==2 && coord[j]==mod->bounds[3] && i==8) {
1550:                 coord[j] *= (1.57735026918963); /* hack to get 60 deg skewed mesh */
1551:               }
1552:               else if (cells[0]==3) {
1553:                 if(i==2 || i==10) coord[j] = mod->bounds[1]/4.;
1554:                 else if (i==4) coord[j] = mod->bounds[1]/2.;
1555:                 else if (i==12) coord[j] = 1.57735026918963*mod->bounds[1]/2.;
1556:               }
1557:             }
1558:           }
1559:         }
1560:         VecRestoreArray(coordinates,&coords);
1561:         DMSetCoordinatesLocal(dm,coordinates);
1562:       }
1563:     }
1564:     else {
1565:       DMPlexCreateFromFile(comm, filename, PETSC_TRUE, &dm);
1566:     }
1567:   }
1568:   DMViewFromOptions(dm, NULL, "-dm_view");
1569:   DMGetDimension(dm, &dim);

1571:   /* set up BCs, functions, tags */
1572:   DMCreateLabel(dm, "Face Sets");
1573:   (*mod->setupbc)(dm,phys);

1575:   {
1576:     DM dmDist;

1578:     DMPlexSetAdjacencyUseCone(dm, PETSC_TRUE);
1579:     DMPlexSetAdjacencyUseClosure(dm, PETSC_FALSE);
1580:     DMPlexDistribute(dm, overlap, NULL, &dmDist);
1581:     if (dmDist) {
1582:       DMDestroy(&dm);
1583:       dm   = dmDist;
1584:     }
1585:   }

1587:   DMSetFromOptions(dm);

1589:   {
1590:     DM gdm;

1592:     DMPlexConstructGhostCells(dm, NULL, NULL, &gdm);
1593:     DMDestroy(&dm);
1594:     dm   = gdm;
1595:     DMViewFromOptions(dm, NULL, "-dm_view");
1596:   }
1597:   if (splitFaces) {ConstructCellBoundary(dm, user);}
1598:   SplitFaces(&dm, "split faces", user);

1600:   {
1601:     char      convType[256];
1602:     PetscBool flg;

1604:     PetscOptionsBegin(comm, "", "Mesh conversion options", "DMPLEX");
1605:     PetscOptionsFList("-dm_plex_convert_type","Convert DMPlex to another format","ex12",DMList,DMPLEX,convType,256,&flg);
1606:     PetscOptionsEnd();
1607:     if (flg) {
1608:       DM dmConv;

1610:       DMConvert(dm,convType,&dmConv);
1611:       if (dmConv) {
1612:         DMViewFromOptions(dmConv, NULL, "-dm_conv_view");
1613:         DMDestroy(&dm);
1614:         dm   = dmConv;
1615:         DMSetFromOptions(dm);
1616:       }
1617:     }
1618:   }

1620:   PetscFVCreate(comm, &fvm);
1621:   PetscFVSetFromOptions(fvm);
1622:   PetscFVSetNumComponents(fvm, phys->dof);
1623:   PetscFVSetSpatialDimension(fvm, dim);
1624:   PetscObjectSetName((PetscObject) fvm,"");
1625:   {
1626:     PetscInt f, dof;
1627:     for (f=0,dof=0; f < phys->nfields; f++) {
1628:       PetscInt newDof = phys->field_desc[f].dof;

1630:       if (newDof == 1) {
1631:         PetscFVSetComponentName(fvm,dof,phys->field_desc[f].name);
1632:       }
1633:       else {
1634:         PetscInt j;

1636:         for (j = 0; j < newDof; j++) {
1637:           char     compName[256]  = "Unknown";

1639:           PetscSNPrintf(compName,sizeof(compName),"%s_%d",phys->field_desc[f].name,j);
1640:           PetscFVSetComponentName(fvm,dof+j,compName);
1641:         }
1642:       }
1643:       dof += newDof;
1644:     }
1645:   }
1646:   DMGetDS(dm, &prob);
1647:   /* FV is now structured with one field having all physics as components */
1648:   PetscDSAddDiscretization(prob, (PetscObject) fvm);
1649:   PetscDSSetRiemannSolver(prob, 0, user->model->physics->riemann);
1650:   PetscDSSetContext(prob, 0, user->model->physics);

1652:   TSCreate(comm, &ts);
1653:   TSSetType(ts, TSSSP);
1654:   TSSetDM(ts, dm);
1655:   TSMonitorSet(ts,MonitorVTK,user,NULL);
1656:   DMTSSetBoundaryLocal(dm, DMPlexTSComputeBoundary, user);
1657:   DMTSSetRHSFunctionLocal(dm, DMPlexTSComputeRHSFunctionFVM, user);

1659:   DMCreateGlobalVector(dm, &X);
1660:   PetscObjectSetName((PetscObject) X, "solution");
1661:   SetInitialCondition(dm, X, user);
1662:   if (vtkCellGeom) {
1663:     DM  dmCell;
1664:     Vec cellgeom, partition;

1666:     DMPlexTSGetGeometryFVM(dm, NULL, &cellgeom, NULL);
1667:     OutputVTK(dm, "ex11-cellgeom.vtk", &viewer);
1668:     VecView(cellgeom, viewer);
1669:     PetscViewerDestroy(&viewer);
1670:     CreatePartitionVec(dm, &dmCell, &partition);
1671:     OutputVTK(dmCell, "ex11-partition.vtk", &viewer);
1672:     VecView(partition, viewer);
1673:     PetscViewerDestroy(&viewer);
1674:     VecDestroy(&partition);
1675:     DMDestroy(&dmCell);
1676:   }

1678:   DMPlexTSGetGeometryFVM(dm, NULL, NULL, &minRadius);
1679:   TSSetDuration(ts,1000,2.0);
1680:   /* collect max maxspeed from all processes -- todo */
1681:   mod->maxspeed = phys->maxspeed;
1682:   if (mod->maxspeed <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set maxspeed",physname);
1683:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
1684:   dt   = cfl * minRadius / user->model->maxspeed;
1685:   TSSetInitialTimeStep(ts,0.0,dt);
1686:   TSSetFromOptions(ts);
1687:   TSSolve(ts,X);
1688:   TSGetSolveTime(ts,&ftime);
1689:   TSGetTimeStepNumber(ts,&nsteps);
1690:   TSGetConvergedReason(ts,&reason);
1691:   PetscPrintf(PETSC_COMM_WORLD,"%s at time %g after %D steps\n",TSConvergedReasons[reason],(double)ftime,nsteps);
1692:   TSDestroy(&ts);

1694:   PetscFunctionListDestroy(&PhysicsList);
1695:   FunctionalLinkDestroy(&user->model->functionalRegistry);
1696:   PetscFree(user->model->functionalMonitored);
1697:   PetscFree(user->model->functionalCall);
1698:   PetscFree(user->model->physics->data);
1699:   PetscFree(user->model->physics);
1700:   PetscFree(user->model);
1701:   PetscFree(user);
1702:   VecDestroy(&X);
1703:   PetscFVDestroy(&fvm);
1704:   DMDestroy(&dm);
1705:   PetscFinalize();
1706:   return(0);
1707: }

1709: /* Godunov fluxs */
1710: PetscScalar cvmgp_(PetscScalar *a, PetscScalar *b, PetscScalar *test)
1711: {
1712:     /* System generated locals */
1713:     PetscScalar ret_val;

1715:     if (*test > 0.) {
1716:         goto L10;
1717:     }
1718:     ret_val = *b;
1719:     return ret_val;
1720: L10:
1721:     ret_val = *a;
1722:     return ret_val;
1723: } /* cvmgp_ */

1725: PetscScalar cvmgm_(PetscScalar *a, PetscScalar *b, PetscScalar *test)
1726: {
1727:     /* System generated locals */
1728:     PetscScalar ret_val;

1730:     if (*test < 0.) {
1731:         goto L10;
1732:     }
1733:     ret_val = *b;
1734:     return ret_val;
1735: L10:
1736:     ret_val = *a;
1737:     return ret_val;
1738: } /* cvmgm_ */

1742: int riem1mdt( PetscScalar *gaml, PetscScalar *gamr, PetscScalar *rl, PetscScalar *pl,
1743:               PetscScalar *uxl, PetscScalar *rr, PetscScalar *pr,
1744:               PetscScalar *uxr, PetscScalar *rstarl, PetscScalar *rstarr, PetscScalar *
1745:               pstar, PetscScalar *ustar)
1746: {
1747:     /* Initialized data */

1749:     static PetscScalar smallp = 1e-8;

1751:     /* System generated locals */
1752:     int i__1;
1753:     PetscScalar d__1, d__2;

1755:     /* Local variables */
1756:     static int i0;
1757:     static PetscScalar cl, cr, wl, zl, wr, zr, pst, durl, skpr1, skpr2;
1758:     static int iwave;
1759:     static PetscScalar csqrl, csqrr, gascl1, gascl2, gascl3, gascl4, gascr1, gascr2, gascr3, gascr4, cstarl, dpstar, cstarr;
1760:     static int iterno;
1761:     static PetscScalar ustarl, ustarr, rarepr1, rarepr2;



1765:     gascl1 = *gaml - 1.;
1766:     gascl2 = (*gaml + 1.) * .5;
1767:     gascl3 = gascl2 / *gaml;
1768:     gascl4 = 1.f / (*gaml - 1.);

1770:     gascr1 = *gamr - 1.;
1771:     gascr2 = (*gamr + 1.) * .5;
1772:     gascr3 = gascr2 / *gamr;
1773:     gascr4 = 1. / (*gamr - 1.);
1774:     iterno = 10;
1775: /*        find pstar: */
1776:     cl = sqrt(*gaml * *pl / *rl);
1777:     cr = sqrt(*gamr * *pr / *rr);
1778:     wl = *rl * cl;
1779:     wr = *rr * cr;
1780:     csqrl = wl * wl;
1781:     csqrr = wr * wr;
1782:     *pstar = (wl * *pr + wr * *pl) / (wl + wr);
1783:     *pstar = PetscMax(*pstar,smallp);
1784:     pst = *pl / *pr;
1785:     skpr1 = cr * (pst - 1.) * sqrt(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
1786:     d__1 = (*gamr - 1.) / (*gamr * 2.);
1787:     rarepr2 = gascr4 * 2. * cr * (1. - PetscPowScalar(pst, d__1));
1788:     pst = *pr / *pl;
1789:     skpr2 = cl * (pst - 1.) * sqrt(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
1790:     d__1 = (*gaml - 1.) / (*gaml * 2.);
1791:     rarepr1 = gascl4 * 2. * cl * (1. - PetscPowScalar(pst, d__1));
1792:     durl = *uxr - *uxl;
1793:     if (*pr < *pl) {
1794:         if (durl >= rarepr1) {
1795:             iwave = 100;
1796:         } else if (durl <= -skpr1) {
1797:             iwave = 300;
1798:         } else {
1799:             iwave = 400;
1800:         }
1801:     } else {
1802:         if (durl >= rarepr2) {
1803:             iwave = 100;
1804:         } else if (durl <= -skpr2) {
1805:             iwave = 300;
1806:         } else {
1807:             iwave = 200;
1808:         }
1809:     }
1810:     if (iwave == 100) {
1811: /*     1-wave: rarefaction wave, 3-wave: rarefaction wave */
1812: /*     case (100) */
1813:         i__1 = iterno;
1814:         for (i0 = 1; i0 <= i__1; ++i0) {
1815:             d__1 = *pstar / *pl;
1816:             d__2 = 1. / *gaml;
1817:             *rstarl = *rl * PetscPowScalar(d__1, d__2);
1818:             cstarl = sqrt(*gaml * *pstar / *rstarl);
1819:             ustarl = *uxl - gascl4 * 2. * (cstarl - cl);
1820:             zl = *rstarl * cstarl;
1821:             d__1 = *pstar / *pr;
1822:             d__2 = 1. / *gamr;
1823:             *rstarr = *rr * PetscPowScalar(d__1, d__2);
1824:             cstarr = sqrt(*gamr * *pstar / *rstarr);
1825:             ustarr = *uxr + gascr4 * 2. * (cstarr - cr);
1826:             zr = *rstarr * cstarr;
1827:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
1828:             *pstar -= dpstar;
1829:             *pstar = PetscMax(*pstar,smallp);
1830:             if (PetscAbsScalar(dpstar) / *pstar <= 1e-8) {
1831:               //break;
1832:             }
1833:         }
1834: /*     1-wave: shock wave, 3-wave: rarefaction wave */
1835:     } else if (iwave == 200) {
1836: /*     case (200) */
1837:         i__1 = iterno;
1838:         for (i0 = 1; i0 <= i__1; ++i0) {
1839:             pst = *pstar / *pl;
1840:             ustarl = *uxl - (pst - 1.) * cl * sqrt(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
1841:             zl = *pl / cl * sqrt(*gaml * 2. * (*gaml - 1. + (*gaml + 1.) * pst)) * (*gaml - 1. + (*gaml + 1.) * pst) / (*gaml * 3. - 1. + (*gaml + 1.) * pst);
1842:             d__1 = *pstar / *pr;
1843:             d__2 = 1. / *gamr;
1844:             *rstarr = *rr * PetscPowScalar(d__1, d__2);
1845:             cstarr = sqrt(*gamr * *pstar / *rstarr);
1846:             zr = *rstarr * cstarr;
1847:             ustarr = *uxr + gascr4 * 2. * (cstarr - cr);
1848:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
1849:             *pstar -= dpstar;
1850:             *pstar = PetscMax(*pstar,smallp);
1851:             if (PetscAbsScalar(dpstar) / *pstar <= 1e-8) {
1852:               //break;
1853:             }
1854:         }
1855: /*     1-wave: shock wave, 3-wave: shock */
1856:     } else if (iwave == 300) {
1857: /*     case (300) */
1858:         i__1 = iterno;
1859:         for (i0 = 1; i0 <= i__1; ++i0) {
1860:             pst = *pstar / *pl;
1861:             ustarl = *uxl - (pst - 1.) * cl * sqrt(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
1862:             zl = *pl / cl * sqrt(*gaml * 2. * (*gaml - 1. + (*gaml + 1.) * pst)) * (*gaml - 1. + (*gaml + 1.) * pst) / (*gaml * 3. - 1. + (*gaml + 1.) * pst);
1863:             pst = *pstar / *pr;
1864:             ustarr = *uxr + (pst - 1.) * cr * sqrt(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
1865:             zr = *pr / cr * sqrt(*gamr * 2. * (*gamr - 1. + (*gamr + 1.) * pst)) * (*gamr - 1. + (*gamr + 1.) * pst) / (*gamr * 3. - 1. + (*gamr + 1.) * pst);
1866:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
1867:             *pstar -= dpstar;
1868:             *pstar = PetscMax(*pstar,smallp);
1869:             if (PetscAbsScalar(dpstar) / *pstar <= 1e-8) {
1870:               //break;
1871:             }
1872:         }
1873: /*     1-wave: rarefaction wave, 3-wave: shock */
1874:     } else if (iwave == 400) {
1875: /*     case (400) */
1876:         i__1 = iterno;
1877:         for (i0 = 1; i0 <= i__1; ++i0) {
1878:             d__1 = *pstar / *pl;
1879:             d__2 = 1. / *gaml;
1880:             *rstarl = *rl * PetscPowScalar(d__1, d__2);
1881:             cstarl = sqrt(*gaml * *pstar / *rstarl);
1882:             ustarl = *uxl - gascl4 * 2. * (cstarl - cl);
1883:             zl = *rstarl * cstarl;
1884:             pst = *pstar / *pr;
1885:             ustarr = *uxr + (pst - 1.) * cr * sqrt(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
1886:             zr = *pr / cr * sqrt(*gamr * 2. * (*gamr - 1. + (*gamr + 1.) * pst)) * (*gamr - 1. + (*gamr + 1.) * pst) / (*gamr * 3. - 1. + (*gamr + 1.) * pst);
1887:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
1888:             *pstar -= dpstar;
1889:             *pstar = PetscMax(*pstar,smallp);
1890:             if (PetscAbsScalar(dpstar) / *pstar <= 1e-8) {
1891:               //break;
1892:             }
1893:         }
1894:     }

1896:     *ustar = (zl * ustarr + zr * ustarl) / (zl + zr);
1897:     if (*pstar > *pl) {
1898:         pst = *pstar / *pl;
1899:         *rstarl = ((*gaml + 1.) * pst + *gaml - 1.) / ((*gaml - 1.) * pst + *
1900:                 gaml + 1.) * *rl;
1901:     }
1902:     if (*pstar > *pr) {
1903:         pst = *pstar / *pr;
1904:         *rstarr = ((*gamr + 1.) * pst + *gamr - 1.) / ((*gamr - 1.) * pst + *
1905:                 gamr + 1.) * *rr;
1906:     }
1907:     return iwave;
1908: }

1910: PetscScalar sign(PetscScalar x)
1911: {
1912:     if(x > 0) return 1.0;
1913:     if(x < 0) return -1.0;
1914:     return 0.0;
1915: }
1916: /*        Riemann Solver */
1919: /* -------------------------------------------------------------------- */
1920: int riemannsolver(PetscScalar *xcen, PetscScalar *xp,
1921:                    PetscScalar *dtt, PetscScalar *rl, PetscScalar *uxl, PetscScalar *pl,
1922:                    PetscScalar *utl, PetscScalar *ubl, PetscScalar *gaml, PetscScalar *rho1l,
1923:                    PetscScalar *rr, PetscScalar *uxr, PetscScalar *pr, PetscScalar *utr,
1924:                    PetscScalar *ubr, PetscScalar *gamr, PetscScalar *rho1r, PetscScalar *rx,
1925:                    PetscScalar *uxm, PetscScalar *px, PetscScalar *utx, PetscScalar *ubx,
1926:                    PetscScalar *gam, PetscScalar *rho1)
1927: {
1928:     /* System generated locals */
1929:     PetscScalar d__1, d__2;

1931:     /* Local variables */
1932:     static PetscScalar s, c0, p0, r0, u0, w0, x0, x2, ri, cx, sgn0, wsp0, gasc1, gasc2, gasc3, gasc4;
1933:     static PetscScalar cstar, pstar, rstar, ustar, xstar, wspst, ushock, streng, rstarl, rstarr, rstars;

1935:     if (*rl == *rr && *pr == *pl && *uxl == *uxr && *gaml == *gamr) {
1936:         *rx = *rl;
1937:         *px = *pl;
1938:         *uxm = *uxl;
1939:         *gam = *gaml;
1940:         x2 = *xcen + *uxm * *dtt;

1942:         if (*xp >= x2) {
1943:             *utx = *utr;
1944:             *ubx = *ubr;
1945:             *rho1 = *rho1r;
1946:         } else {
1947:             *utx = *utl;
1948:             *ubx = *ubl;
1949:             *rho1 = *rho1l;
1950:         }
1951:         return 0;
1952:     }
1953:     int iwave = riem1mdt(gaml, gamr, rl, pl, uxl, rr, pr, uxr, &rstarl, &rstarr, &pstar, &ustar);

1955:     x2 = *xcen + ustar * *dtt;
1956:     d__1 = *xp - x2;
1957:     sgn0 = sign(d__1);
1958: /*            x is in 3-wave if sgn0 = 1 */
1959: /*            x is in 1-wave if sgn0 = -1 */
1960:     r0 = cvmgm_(rl, rr, &sgn0);
1961:     p0 = cvmgm_(pl, pr, &sgn0);
1962:     u0 = cvmgm_(uxl, uxr, &sgn0);
1963:     *gam = cvmgm_(gaml, gamr, &sgn0);
1964:     gasc1 = *gam - 1.;
1965:     gasc2 = (*gam + 1.) * .5;
1966:     gasc3 = gasc2 / *gam;
1967:     gasc4 = 1. / (*gam - 1.);
1968:     c0 = sqrt(*gam * p0 / r0);
1969:     streng = pstar - p0;
1970:     w0 = *gam * r0 * p0 * (gasc3 * streng / p0 + 1.);
1971:     rstars = r0 / (1. - r0 * streng / w0);
1972:     d__1 = p0 / pstar;
1973:     d__2 = -1. / *gam;
1974:     rstarr = r0 * PetscPowScalar(d__1, d__2);
1975:     rstar = cvmgm_(&rstarr, &rstars, &streng);
1976:     w0 = sqrt(w0);
1977:     cstar = sqrt(*gam * pstar / rstar);
1978:     wsp0 = u0 + sgn0 * c0;
1979:     wspst = ustar + sgn0 * cstar;
1980:     ushock = ustar + sgn0 * w0 / rstar;
1981:     wspst = cvmgp_(&ushock, &wspst, &streng);
1982:     wsp0 = cvmgp_(&ushock, &wsp0, &streng);
1983:     x0 = *xcen + wsp0 * *dtt;
1984:     xstar = *xcen + wspst * *dtt;
1985: /*           using gas formula to evaluate rarefaction wave */
1986: /*            ri : reiman invariant */
1987:     ri = u0 - sgn0 * 2. * gasc4 * c0;
1988:     cx = sgn0 * .5 * gasc1 / gasc2 * ((*xp - *xcen) / *dtt - ri);
1989:     *uxm = ri + sgn0 * 2. * gasc4 * cx;
1990:     s = p0 / PetscPowScalar(r0, *gam);
1991:     d__1 = cx * cx / (*gam * s);
1992:     *rx = PetscPowScalar(d__1, gasc4);
1993:     *px = cx * cx * *rx / *gam;
1994:     d__1 = sgn0 * (x0 - *xp);
1995:     *rx = cvmgp_(rx, &r0, &d__1);
1996:     d__1 = sgn0 * (x0 - *xp);
1997:     *px = cvmgp_(px, &p0, &d__1);
1998:     d__1 = sgn0 * (x0 - *xp);
1999:     *uxm = cvmgp_(uxm, &u0, &d__1);
2000:     d__1 = sgn0 * (xstar - *xp);
2001:     *rx = cvmgm_(rx, &rstar, &d__1);
2002:     d__1 = sgn0 * (xstar - *xp);
2003:     *px = cvmgm_(px, &pstar, &d__1);
2004:     d__1 = sgn0 * (xstar - *xp);
2005:     *uxm = cvmgm_(uxm, &ustar, &d__1);
2006:     if (*xp >= x2) {
2007:         *utx = *utr;
2008:         *ubx = *ubr;
2009:         *rho1 = *rho1r;
2010:     } else {
2011:         *utx = *utl;
2012:         *ubx = *ubl;
2013:         *rho1 = *rho1l;
2014:     }
2015:     return iwave;
2016: }
2019: int godunovflux( const PetscScalar *ul, const PetscScalar *ur,
2020:                  PetscScalar *flux, const PetscScalar *nn, const int *ndim,
2021:                  const PetscScalar *gamma)
2022: {
2023:     /* System generated locals */
2024:   int i__1,iwave;
2025:     PetscScalar d__1, d__2, d__3;

2027:     /* Local variables */
2028:     static int k;
2029:     static PetscScalar bn[3], fn, ft, tg[3], pl, rl, pm, pr, rr, xp, ubl, ubm,
2030:             ubr, dtt, unm, tmp, utl, utm, uxl, utr, uxr, gaml, gamm, gamr,
2031:             xcen, rhom, rho1l, rho1m, rho1r;
2032:     /* Parameter adjustments */
2033:     --nn;
2034:     --flux;
2035:     --ur;
2036:     --ul;

2038:     /* Function Body */
2039:     xcen = 0.;
2040:     xp = 0.;
2041:     i__1 = *ndim;
2042:     for (k = 1; k <= i__1; ++k) {
2043:         tg[k - 1] = 0.;
2044:         bn[k - 1] = 0.;
2045:     }
2046:     dtt = 1.;
2047:     if (*ndim == 3) {
2048:         if (nn[1] == 0. && nn[2] == 0.) {
2049:             tg[0] = 1.;
2050:         } else {
2051:             tg[0] = -nn[2];
2052:             tg[1] = nn[1];
2053:         }
2054: /*           tmp=dsqrt(tg(1)**2+tg(2)**2) */
2055: /*           tg=tg/tmp */
2056:         bn[0] = -nn[3] * tg[1];
2057:         bn[1] = nn[3] * tg[0];
2058:         bn[2] = nn[1] * tg[1] - nn[2] * tg[0];
2059: /* Computing 2nd power */
2060:         d__1 = bn[0];
2061: /* Computing 2nd power */
2062:         d__2 = bn[1];
2063: /* Computing 2nd power */
2064:         d__3 = bn[2];
2065:         tmp = sqrt(d__1 * d__1 + d__2 * d__2 + d__3 * d__3);
2066:         i__1 = *ndim;
2067:         for (k = 1; k <= i__1; ++k) {
2068:             bn[k - 1] /= tmp;
2069:         }
2070:     } else if (*ndim == 2) {
2071:         tg[0] = -nn[2];
2072:         tg[1] = nn[1];
2073: /*           tmp=dsqrt(tg(1)**2+tg(2)**2) */
2074: /*           tg=tg/tmp */
2075:         bn[0] = 0.;
2076:         bn[1] = 0.;
2077:         bn[2] = 1.;
2078:     }
2079:     rl = ul[1];
2080:     rr = ur[1];
2081:     uxl = 0.;
2082:     uxr = 0.;
2083:     utl = 0.;
2084:     utr = 0.;
2085:     ubl = 0.;
2086:     ubr = 0.;
2087:     i__1 = *ndim;
2088:     for (k = 1; k <= i__1; ++k) {
2089:         uxl += ul[k + 1] * nn[k];
2090:         uxr += ur[k + 1] * nn[k];
2091:         utl += ul[k + 1] * tg[k - 1];
2092:         utr += ur[k + 1] * tg[k - 1];
2093:         ubl += ul[k + 1] * bn[k - 1];
2094:         ubr += ur[k + 1] * bn[k - 1];
2095:     }
2096:     uxl /= rl;
2097:     uxr /= rr;
2098:     utl /= rl;
2099:     utr /= rr;
2100:     ubl /= rl;
2101:     ubr /= rr;

2103:     gaml = *gamma;
2104:     gamr = *gamma;
2105: /* Computing 2nd power */
2106:     d__1 = uxl;
2107: /* Computing 2nd power */
2108:     d__2 = utl;
2109: /* Computing 2nd power */
2110:     d__3 = ubl;
2111:     pl = (*gamma - 1.) * (ul[*ndim + 2] - rl * .5 * (d__1 * d__1 + d__2 * d__2 + d__3 * d__3));
2112: /* Computing 2nd power */
2113:     d__1 = uxr;
2114: /* Computing 2nd power */
2115:     d__2 = utr;
2116: /* Computing 2nd power */
2117:     d__3 = ubr;
2118:     pr = (*gamma - 1.) * (ur[*ndim + 2] - rr * .5 * (d__1 * d__1 + d__2 * d__2 + d__3 * d__3));
2119:     rho1l = rl;
2120:     rho1r = rr;

2122:     iwave = riemannsolver(&xcen, &xp, &dtt, &rl, &uxl, &pl, &utl, &ubl, &gaml, &
2123:                           rho1l, &rr, &uxr, &pr, &utr, &ubr, &gamr, &rho1r, &rhom, &unm, &
2124:                           pm, &utm, &ubm, &gamm, &rho1m);

2126:     flux[1] = rhom * unm;
2127:     fn = rhom * unm * unm + pm;
2128:     ft = rhom * unm * utm;
2129: /*           flux(2)=fn*nn(1)+ft*nn(2) */
2130: /*           flux(3)=fn*tg(1)+ft*tg(2) */
2131:     flux[2] = fn * nn[1] + ft * tg[0];
2132:     flux[3] = fn * nn[2] + ft * tg[1];
2133: /*           flux(2)=rhom*unm*(unm)+pm */
2134: /*           flux(3)=rhom*(unm)*utm */
2135:     if (*ndim == 3) {
2136:         flux[4] = rhom * unm * ubm;
2137:     }
2138:     flux[*ndim + 2] = (rhom * .5 * (unm * unm + utm * utm + ubm * ubm) + gamm / (gamm - 1.) * pm) * unm;
2139:     return iwave;
2140: } /* godunovflux_ */

2142: /* Subroutine to set up the initial conditions for the */
2143: /* Shock Interface interaction or linear wave (Ravi Samtaney,Mark Adams). */
2144: /* ----------------------------------------------------------------------- */
2145: int projecteqstate(PetscScalar wc[], const PetscScalar ueq[], const PetscScalar lv[][3])
2146: {
2147:   int j,k;
2148: /*      Wc=matmul(lv,Ueq) 3 vars */
2149:   for (k = 0; k < 3; ++k) {
2150:     wc[k] = 0.;
2151:     for (j = 0; j < 3; ++j) {
2152:       wc[k] += lv[k][j]*ueq[j];
2153:     }
2154:   }
2155:   return 0;
2156: }
2157: /* ----------------------------------------------------------------------- */
2158: int projecttoprim(PetscScalar v[], const PetscScalar wc[], PetscScalar rv[][3])
2159: {
2160:   int k,j;
2161:   /*      V=matmul(rv,WC) 3 vars */
2162:   for (k = 0; k < 3; ++k) {
2163:     v[k] = 0.;
2164:     for (j = 0; j < 3; ++j) {
2165:       v[k] += rv[k][j]*wc[j];
2166:     }
2167:   }
2168:   return 0;
2169: }
2170: /* ---------------------------------------------------------------------- */
2171: int eigenvectors(PetscScalar rv[][3], PetscScalar lv[][3], const PetscScalar ueq[], PetscScalar gamma)
2172: {
2173:   int j,k;
2174:   PetscScalar rho,csnd,p0,u;

2176:   for (k = 0; k < 3; ++k) for (j = 0; j < 3; ++j) { lv[k][j] = 0.; rv[k][j] = 0.; }
2177:   rho = ueq[0];
2178:   u = ueq[1];
2179:   p0 = ueq[2];
2180:   csnd = PetscSqrtScalar(gamma * p0 / rho);
2181:   lv[0][1] = rho * .5;
2182:   lv[0][2] = -.5 / csnd;
2183:   lv[1][0] = csnd;
2184:   lv[1][2] = -1. / csnd;
2185:   lv[2][1] = rho * .5;
2186:   lv[2][2] = .5 / csnd;
2187:   rv[0][0] = -1. / csnd;
2188:   rv[1][0] = 1. / rho;
2189:   rv[2][0] = -csnd;
2190:   rv[0][1] = 1. / csnd;
2191:   rv[0][2] = 1. / csnd;
2192:   rv[1][2] = 1. / rho;
2193:   rv[2][2] = csnd;
2194:   return 0;
2195: }
2198: int initLinearWave(EulerNode *ux, const PetscScalar gamma, const PetscReal coord[], const PetscReal Lx)
2199: {
2200:   PetscScalar p0,u0,wcp[3],wc[3];
2201:   PetscScalar lv[3][3];
2202:   PetscScalar vp[3];
2203:   PetscScalar rv[3][3];
2204:   PetscScalar eps, ueq[3], rho0, twopi;

2206:   /* Function Body */
2207:   twopi = 2.*M_PI;
2208:   eps = 1e-4; /* perturbation */
2209:   rho0 = 1e3;   /* density of water */
2210:   p0 = 101325.; /* init pressure of 1 atm (?) */
2211:   u0 = 0.;
2212:   ueq[0] = rho0;
2213:   ueq[1] = u0;
2214:   ueq[2] = p0;
2215:   /* Project initial state to characteristic variables */
2216:   eigenvectors(rv, lv, ueq, gamma);
2217:   projecteqstate(wc, ueq, lv);
2218:   wcp[0] = wc[0];
2219:   wcp[1] = wc[1];
2220:   wcp[2] = wc[2] + eps * cos(coord[0] * 2. * twopi / Lx);
2221:   projecttoprim(vp, wcp, rv);
2222:   ux->r = vp[0]; /* density */
2223:   ux->ru[0] = vp[0] * vp[1]; /* x momentum */
2224:   ux->ru[1] = 0.;
2225: #if defined DIM > 2
2226:   if (dim>2) ux->ru[2] = 0.;
2227: #endif
2228:   /* E = rho * e + rho * v^2/2 = p/(gam-1) + rho*v^2/2 */
2229:   ux->E = vp[2]/(gamma - 1.) + 0.5*vp[0]*vp[1]*vp[1];
2230:   return 0;
2231: }