xref: /petsc/src/ts/tutorials/ex11.c (revision bef158480efac06de457f7a665168877ab3c2fd7)
1 static char help[] = "Second Order TVD Finite Volume Example.\n";
2 /*F
3 
4 We use a second order TVD finite volume method to evolve a system of PDEs. Our simple upwinded residual evaluation loops
5 over all mesh faces and uses a Riemann solver to produce the flux given the face geometry and cell values,
6 \begin{equation}
7   f_i = \mathrm{riemann}(\mathrm{phys}, p_\mathrm{centroid}, \hat n, x^L, x^R)
8 \end{equation}
9 and then update the cell values given the cell volume.
10 \begin{eqnarray}
11     f^L_i &-=& \frac{f_i}{vol^L} \\
12     f^R_i &+=& \frac{f_i}{vol^R}
13 \end{eqnarray}
14 
15 As an example, we can consider the shallow water wave equation,
16 \begin{eqnarray}
17      h_t + \nabla\cdot \left( uh                              \right) &=& 0 \\
18   (uh)_t + \nabla\cdot \left( u\otimes uh + \frac{g h^2}{2} I \right) &=& 0
19 \end{eqnarray}
20 where $h$ is wave height, $u$ is wave velocity, and $g$ is the acceleration due to gravity.
21 
22 A representative Riemann solver for the shallow water equations is given in the PhysicsRiemann_SW() function,
23 \begin{eqnarray}
24   f^{L,R}_h    &=& uh^{L,R} \cdot \hat n \\
25   f^{L,R}_{uh} &=& \frac{f^{L,R}_h}{h^{L,R}} uh^{L,R} + g (h^{L,R})^2 \hat n \\
26   c^{L,R}      &=& \sqrt{g h^{L,R}} \\
27   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) \\
28   f_i          &=& \frac{A_\mathrm{face}}{2} \left( f^L_i + f^R_i + s \left( x^L_i - x^R_i \right) \right)
29 \end{eqnarray}
30 where $c$ is the local gravity wave speed and $f_i$ is a Rusanov flux.
31 
32 The more sophisticated residual evaluation in RHSFunctionLocal_LS() uses a least-squares fit to a quadratic polynomial
33 over a neighborhood of the given element.
34 
35 The mesh is read in from an ExodusII file, usually generated by Cubit.
36 F*/
37 #include <petscdmplex.h>
38 #include <petscdmforest.h>
39 #include <petscds.h>
40 #include <petscts.h>
41 #include <petscsf.h> /* For SplitFaces() */
42 
43 #define DIM 2                   /* Geometric dimension */
44 #define ALEN(a) (sizeof(a)/sizeof((a)[0]))
45 
46 static PetscFunctionList PhysicsList, PhysicsRiemannList_SW;
47 
48 /* Represents continuum physical equations. */
49 typedef struct _n_Physics *Physics;
50 
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;
54 
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*);
64 
65 struct FieldDescription {
66   const char *name;
67   PetscInt dof;
68 };
69 
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 };
78 
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 };
87 
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 };
106 
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 };
115 
116 PETSC_STATIC_INLINE PetscReal DotDIMReal(const PetscReal *x,const PetscReal *y)
117 {
118   PetscInt  i;
119   PetscReal prod=0.0;
120 
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))); }
125 
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]; }
131 
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};
137 
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;
146 
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;
159 
160 static const struct FieldDescription PhysicsFields_Advect[] = {{"U",1},{NULL,0}};
161 
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;
166 
167   PetscFunctionBeginUser;
168   xG[0] = advect->inflowState;
169   PetscFunctionReturn(0);
170 }
171 
172 static PetscErrorCode PhysicsBoundary_Advect_Outflow(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
173 {
174   PetscFunctionBeginUser;
175   xG[0] = xI[0];
176   PetscFunctionReturn(0);
177 }
178 
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;
183 
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;
198 
199       rad2 = 0.;
200       for (i = 0; i < dim; i++) {
201         comp2[i] = qp[i] * qp[i];
202         rad2    += comp2[i];
203       }
204 
205       wind[0] = -qp[1];
206       wind[1] = qp[0];
207       if (rad2 > 1.) {
208         PetscInt  maxI = 0;
209         PetscReal maxComp2 = comp2[0];
210 
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 }
231 
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;
236 
237   PetscFunctionBeginUser;
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   PetscFunctionReturn(0);
268 }
269 
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];
275   PetscErrorCode ierr;
276 
277   PetscFunctionBeginUser;
278   ierr = PhysicsSolution_Advect(mod,time,x,yexact,phys);CHKERRQ(ierr);
279   f[advect->functional.Solution] = PetscRealPart(y[0]);
280   f[advect->functional.Error] = PetscAbsScalar(y[0]-yexact[0]);
281   PetscFunctionReturn(0);
282 }
283 
284 static PetscErrorCode SetUpBC_Advect(PetscDS prob, Physics phys)
285 {
286   PetscErrorCode ierr;
287   const PetscInt inflowids[] = {100,200,300},outflowids[] = {101};
288 
289   PetscFunctionBeginUser;
290   /* Register "canned" boundary conditions and defaults for where to apply. */
291   ierr = PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "inflow",  "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_Advect_Inflow, NULL,  ALEN(inflowids),  inflowids,  phys);CHKERRQ(ierr);
292   ierr = PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "outflow", "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_Advect_Outflow, NULL, ALEN(outflowids), outflowids, phys);CHKERRQ(ierr);
293   PetscFunctionReturn(0);
294 }
295 
296 static PetscErrorCode PhysicsCreate_Advect(Model mod,Physics phys,PetscOptionItems *PetscOptionsObject)
297 {
298   Physics_Advect *advect;
299   PetscErrorCode ierr;
300 
301   PetscFunctionBeginUser;
302   phys->field_desc = PhysicsFields_Advect;
303   phys->riemann    = (PetscRiemannFunc)PhysicsRiemann_Advect;
304   ierr = PetscNew(&advect);CHKERRQ(ierr);
305   phys->data       = advect;
306   mod->setupbc = SetUpBC_Advect;
307 
308   ierr = PetscOptionsHead(PetscOptionsObject,"Advect options");CHKERRQ(ierr);
309   {
310     PetscInt two = 2,dof = 1;
311     advect->soltype = ADVECT_SOL_TILTED;
312     ierr = PetscOptionsEnum("-advect_sol_type","solution type","",AdvectSolTypes,(PetscEnum)advect->soltype,(PetscEnum*)&advect->soltype,NULL);CHKERRQ(ierr);
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       ierr = PetscOptionsRealArray("-advect_tilted_wind","background wind vx,vy","",tilted->wind,&two,NULL);CHKERRQ(ierr);
320       advect->inflowState = -2.0;
321       ierr = PetscOptionsRealArray("-advect_tilted_inflow","Inflow state","",&advect->inflowState,&dof,NULL);CHKERRQ(ierr);
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       ierr = PetscOptionsRealArray("-advect_bump_center","location of center of bump x,y","",bump->center,&two,NULL);CHKERRQ(ierr);
331       bump->radius = 0.9;
332       ierr = PetscOptionsReal("-advect_bump_radius","radius of bump","",bump->radius,&bump->radius,NULL);CHKERRQ(ierr);
333       bump->type = ADVECT_SOL_BUMP_CONE;
334       ierr = PetscOptionsEnum("-advect_bump_type","type of bump","",AdvectSolBumpTypes,(PetscEnum)bump->type,(PetscEnum*)&bump->type,NULL);CHKERRQ(ierr);
335       phys->maxspeed = 3.;       /* radius of mesh, kludge */
336     } break;
337     }
338   }
339   ierr = PetscOptionsTail();CHKERRQ(ierr);
340   /* Initial/transient solution with default boundary conditions */
341   ierr = ModelSolutionSetDefault(mod,PhysicsSolution_Advect,phys);CHKERRQ(ierr);
342   /* Register "canned" functionals */
343   ierr = ModelFunctionalRegister(mod,"Solution",&advect->functional.Solution,PhysicsFunctional_Advect,phys);CHKERRQ(ierr);
344   ierr = ModelFunctionalRegister(mod,"Error",&advect->functional.Error,PhysicsFunctional_Advect,phys);CHKERRQ(ierr);
345   mod->bcs[0] = mod->bcs[1] = mod->bcs[2] = DM_BOUNDARY_GHOSTED;
346   PetscFunctionReturn(0);
347 }
348 
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;
367 
368 static const struct FieldDescription PhysicsFields_SW[] = {{"Height",1},{"Momentum",DIM},{NULL,0}};
369 
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;
380 
381   PetscFunctionBeginUser;
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   PetscFunctionReturn(0);
387 }
388 
389 static PetscErrorCode PhysicsBoundary_SW_Wall(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, void *ctx)
390 {
391   PetscFunctionBeginUser;
392   xG[0] = xI[0];
393   xG[1] = -xI[1];
394   xG[2] = -xI[2];
395   PetscFunctionReturn(0);
396 }
397 
398 static void PhysicsRiemann_SW_HLL(PetscInt dim, PetscInt Nf, const PetscReal *qp, const PetscReal *n, const PetscScalar *xL, const PetscScalar *xR, PetscInt numConstants, const PetscScalar constants[], PetscScalar *flux, Physics phys)
399 {
400   Physics_SW *sw = (Physics_SW *) phys->data;
401   PetscReal aL, aR;
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.;
413 
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) {
420     for (i = 0; i < 1 + dim; i++) flux[i] = zero;
421     return;
422   } /* SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Reconstructed thickness is negative"); */
423   nn[0] = n[0];
424   nn[1] = n[1];
425   Normalize2Real(nn);
426   SWFlux(phys, nn, uL, &(fL.swnode));
427   SWFlux(phys, nn, uR, &(fR.swnode));
428   /* gravity wave speed */
429   aL = PetscSqrtReal(sw->gravity * uL->h);
430   aR = PetscSqrtReal(sw->gravity * uR->h);
431   // Defining u_tilda and v_tilda as u and v
432   PetscReal u_L, u_R;
433   u_L = Dot2Real(uL->uh,nn)/uL->h;
434   u_R = Dot2Real(uR->uh,nn)/uR->h;
435   PetscReal sL, sR;
436   sL = PetscMin(u_L - aL, u_R - aR);
437   sR = PetscMax(u_L + aL, u_R + aR);
438   if (sL > zero) {
439     for (i = 0; i < dim + 1; i++) {
440       flux[i] = fL.vals[i] * Norm2Real(n);
441     }
442   } else if (sR < zero) {
443     for (i = 0; i < dim + 1; i++) {
444       flux[i] = fR.vals[i] * Norm2Real(n);
445     }
446   } else {
447     for (i = 0; i < dim + 1; i++) {
448       flux[i] = ((sR * fL.vals[i] - sL * fR.vals[i] + sR * sL * (xR[i] - xL[i])) / (sR - sL)) * Norm2Real(n);
449     }
450   }
451 }
452 
453 static void PhysicsRiemann_SW_Rusanov(PetscInt dim, PetscInt Nf, const PetscReal *qp, const PetscReal *n, const PetscScalar *xL, const PetscScalar *xR, PetscInt numConstants, const PetscScalar constants[], PetscScalar *flux, Physics phys)
454 {
455   Physics_SW   *sw = (Physics_SW*)phys->data;
456   PetscReal    cL,cR,speed;
457   PetscReal    nn[DIM];
458 #if !defined(PETSC_USE_COMPLEX)
459   const SWNode *uL = (const SWNode*)xL,*uR = (const SWNode*)xR;
460 #else
461   SWNodeUnion  uLreal, uRreal;
462   const SWNode *uL = &uLreal.swnode;
463   const SWNode *uR = &uRreal.swnode;
464 #endif
465   SWNodeUnion  fL,fR;
466   PetscInt     i;
467   PetscReal    zero=0.;
468 
469 #if defined(PETSC_USE_COMPLEX)
470   uLreal.swnode.h = 0; uRreal.swnode.h = 0;
471   for (i = 0; i < 1+dim; i++) uLreal.vals[i] = PetscRealPart(xL[i]);
472   for (i = 0; i < 1+dim; i++) uRreal.vals[i] = PetscRealPart(xR[i]);
473 #endif
474   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"); */
475   nn[0] = n[0];
476   nn[1] = n[1];
477   Normalize2Real(nn);
478   SWFlux(phys,nn,uL,&(fL.swnode));
479   SWFlux(phys,nn,uR,&(fR.swnode));
480   cL    = PetscSqrtReal(sw->gravity*uL->h);
481   cR    = PetscSqrtReal(sw->gravity*uR->h); /* gravity wave speed */
482   speed = PetscMax(PetscAbsReal(Dot2Real(uL->uh,nn)/uL->h) + cL,PetscAbsReal(Dot2Real(uR->uh,nn)/uR->h) + cR);
483   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);
484 }
485 
486 static PetscErrorCode PhysicsSolution_SW(Model mod,PetscReal time,const PetscReal *x,PetscScalar *u,void *ctx)
487 {
488   PetscReal dx[2],r,sigma;
489 
490   PetscFunctionBeginUser;
491   if (time != 0.0) SETERRQ1(mod->comm,PETSC_ERR_SUP,"No solution known for time %g",(double)time);
492   dx[0] = x[0] - 1.5;
493   dx[1] = x[1] - 1.0;
494   r     = Norm2Real(dx);
495   sigma = 0.5;
496   u[0]  = 1 + 2*PetscExpReal(-PetscSqr(r)/(2*PetscSqr(sigma)));
497   u[1]  = 0.0;
498   u[2]  = 0.0;
499   PetscFunctionReturn(0);
500 }
501 
502 static PetscErrorCode PhysicsFunctional_SW(Model mod,PetscReal time,const PetscReal *coord,const PetscScalar *xx,PetscReal *f,void *ctx)
503 {
504   Physics      phys = (Physics)ctx;
505   Physics_SW   *sw  = (Physics_SW*)phys->data;
506   const SWNode *x   = (const SWNode*)xx;
507   PetscReal  u[2];
508   PetscReal    h;
509 
510   PetscFunctionBeginUser;
511   h = x->h;
512   Scale2Real(1./x->h,x->uh,u);
513   f[sw->functional.Height] = h;
514   f[sw->functional.Speed]  = Norm2Real(u) + PetscSqrtReal(sw->gravity*h);
515   f[sw->functional.Energy] = 0.5*(Dot2Real(x->uh,u) + sw->gravity*PetscSqr(h));
516   PetscFunctionReturn(0);
517 }
518 
519 static PetscErrorCode SetUpBC_SW(PetscDS prob,Physics phys)
520 {
521   PetscErrorCode ierr;
522   const PetscInt wallids[] = {100,101,200,300};
523   PetscFunctionBeginUser;
524   ierr = PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "wall", "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_SW_Wall, NULL, ALEN(wallids), wallids, phys);CHKERRQ(ierr);
525   PetscFunctionReturn(0);
526 }
527 
528 static PetscErrorCode PhysicsCreate_SW(Model mod,Physics phys,PetscOptionItems *PetscOptionsObject)
529 {
530   Physics_SW     *sw;
531   char           sw_riemann[64] = "rusanov";
532   PetscErrorCode ierr;
533 
534   PetscFunctionBeginUser;
535   phys->field_desc = PhysicsFields_SW;
536   ierr          = PetscNew(&sw);CHKERRQ(ierr);
537   phys->data    = sw;
538   mod->setupbc  = SetUpBC_SW;
539 
540   PetscFunctionListAdd(&PhysicsRiemannList_SW, "rusanov", PhysicsRiemann_SW_Rusanov);
541   PetscFunctionListAdd(&PhysicsRiemannList_SW, "hll", PhysicsRiemann_SW_HLL);
542 
543   ierr          = PetscOptionsHead(PetscOptionsObject,"SW options");CHKERRQ(ierr);
544   {
545     void (*PhysicsRiemann_SW)(PetscInt, PetscInt, const PetscReal *, const PetscReal *, const PetscScalar *, const PetscScalar *, PetscInt, const PetscScalar, PetscScalar *, Physics);
546     sw->gravity = 1.0;
547     ierr = PetscOptionsReal("-sw_gravity","Gravitational constant","",sw->gravity,&sw->gravity,NULL);CHKERRQ(ierr);
548     ierr = PetscOptionsFList("-sw_riemann","Riemann solver","",PhysicsRiemannList_SW,sw_riemann,sw_riemann,sizeof sw_riemann,NULL);CHKERRQ(ierr);
549     ierr = PetscFunctionListFind(PhysicsRiemannList_SW,sw_riemann,&PhysicsRiemann_SW);CHKERRQ(ierr);
550     phys->riemann = (PetscRiemannFunc) PhysicsRiemann_SW;
551   }
552   ierr = PetscOptionsTail();CHKERRQ(ierr);
553   phys->maxspeed = PetscSqrtReal(2.0*sw->gravity); /* Mach 1 for depth of 2 */
554 
555   ierr = ModelSolutionSetDefault(mod,PhysicsSolution_SW,phys);CHKERRQ(ierr);
556   ierr = ModelFunctionalRegister(mod,"Height",&sw->functional.Height,PhysicsFunctional_SW,phys);CHKERRQ(ierr);
557   ierr = ModelFunctionalRegister(mod,"Speed",&sw->functional.Speed,PhysicsFunctional_SW,phys);CHKERRQ(ierr);
558   ierr = ModelFunctionalRegister(mod,"Energy",&sw->functional.Energy,PhysicsFunctional_SW,phys);CHKERRQ(ierr);
559 
560   mod->bcs[0] = mod->bcs[1] = mod->bcs[2] = DM_BOUNDARY_GHOSTED;
561 
562   PetscFunctionReturn(0);
563 }
564 
565 /******************* Euler Density Shock (EULER_IV_SHOCK,EULER_SS_SHOCK) ********************/
566 /* An initial-value and self-similar solutions of the compressible Euler equations */
567 /* Ravi Samtaney and D. I. Pullin */
568 /* Phys. Fluids 8, 2650 (1996); http://dx.doi.org/10.1063/1.869050 */
569 typedef enum {EULER_PAR_GAMMA,EULER_PAR_RHOR,EULER_PAR_AMACH,EULER_PAR_ITANA,EULER_PAR_SIZE} EulerParamIdx;
570 typedef enum {EULER_IV_SHOCK,EULER_SS_SHOCK,EULER_SHOCK_TUBE,EULER_LINEAR_WAVE} EulerType;
571 typedef struct {
572   PetscReal r;
573   PetscReal ru[DIM];
574   PetscReal E;
575 } EulerNode;
576 typedef union {
577   EulerNode eulernode;
578   PetscReal vals[DIM+2];
579 } EulerNodeUnion;
580 typedef PetscErrorCode (*EquationOfState)(const PetscReal*, const EulerNode*, PetscReal*);
581 typedef struct {
582   EulerType       type;
583   PetscReal       pars[EULER_PAR_SIZE];
584   EquationOfState sound;
585   struct {
586     PetscInt Density;
587     PetscInt Momentum;
588     PetscInt Energy;
589     PetscInt Pressure;
590     PetscInt Speed;
591   } monitor;
592 } Physics_Euler;
593 
594 static const struct FieldDescription PhysicsFields_Euler[] = {{"Density",1},{"Momentum",DIM},{"Energy",1},{NULL,0}};
595 
596 /* initial condition */
597 int initLinearWave(EulerNode *ux, const PetscReal gamma, const PetscReal coord[], const PetscReal Lx);
598 static PetscErrorCode PhysicsSolution_Euler(Model mod, PetscReal time, const PetscReal *x, PetscScalar *u, void *ctx)
599 {
600   PetscInt i;
601   Physics         phys = (Physics)ctx;
602   Physics_Euler   *eu  = (Physics_Euler*)phys->data;
603   EulerNode       *uu  = (EulerNode*)u;
604   PetscReal        p0,gamma,c;
605   PetscFunctionBeginUser;
606   if (time != 0.0) SETERRQ1(mod->comm,PETSC_ERR_SUP,"No solution known for time %g",(double)time);
607 
608   for (i=0; i<DIM; i++) uu->ru[i] = 0.0; /* zero out initial velocity */
609   /* set E and rho */
610   gamma = eu->pars[EULER_PAR_GAMMA];
611 
612   if (eu->type==EULER_IV_SHOCK || eu->type==EULER_SS_SHOCK) {
613     /******************* Euler Density Shock ********************/
614     /* On initial-value and self-similar solutions of the compressible Euler equations */
615     /* Ravi Samtaney and D. I. Pullin */
616     /* Phys. Fluids 8, 2650 (1996); http://dx.doi.org/10.1063/1.869050 */
617     /* initial conditions 1: left of shock, 0: left of discontinuity 2: right of discontinuity,  */
618     p0 = 1.;
619     if (x[0] < 0.0 + x[1]*eu->pars[EULER_PAR_ITANA]) {
620       if (x[0] < mod->bounds[0]*0.5) { /* left of shock (1) */
621         PetscReal amach,rho,press,gas1,p1;
622         amach = eu->pars[EULER_PAR_AMACH];
623         rho = 1.;
624         press = p0;
625         p1 = press*(1.0+2.0*gamma/(gamma+1.0)*(amach*amach-1.0));
626         gas1 = (gamma-1.0)/(gamma+1.0);
627         uu->r = rho*(p1/press+gas1)/(gas1*p1/press+1.0);
628         uu->ru[0]   = ((uu->r - rho)*PetscSqrtReal(gamma*press/rho)*amach);
629         uu->E = p1/(gamma-1.0) + .5/uu->r*uu->ru[0]*uu->ru[0];
630       }
631       else { /* left of discontinuity (0) */
632         uu->r = 1.; /* rho = 1 */
633         uu->E = p0/(gamma-1.0);
634       }
635     }
636     else { /* right of discontinuity (2) */
637       uu->r = eu->pars[EULER_PAR_RHOR];
638       uu->E = p0/(gamma-1.0);
639     }
640   }
641   else if (eu->type==EULER_SHOCK_TUBE) {
642     /* 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. */
643     if (x[0] < 0.0) {
644       uu->r = 8.;
645       uu->E = 10./(gamma-1.);
646     }
647     else {
648       uu->r = 1.;
649       uu->E = 1./(gamma-1.);
650     }
651   }
652   else if (eu->type==EULER_LINEAR_WAVE) {
653     initLinearWave( uu, gamma, x, mod->bounds[1] - mod->bounds[0]);
654   }
655   else SETERRQ1(mod->comm,PETSC_ERR_SUP,"Unknown type %d",eu->type);
656 
657   /* set phys->maxspeed: (mod->maxspeed = phys->maxspeed) in main; */
658   eu->sound(&gamma,uu,&c);
659   c = (uu->ru[0]/uu->r) + c;
660   if (c > phys->maxspeed) phys->maxspeed = c;
661 
662   PetscFunctionReturn(0);
663 }
664 
665 static PetscErrorCode Pressure_PG(const PetscReal gamma,const EulerNode *x,PetscReal *p)
666 {
667   PetscReal ru2;
668 
669   PetscFunctionBeginUser;
670   ru2  = DotDIMReal(x->ru,x->ru);
671   (*p)=(x->E - 0.5*ru2/x->r)*(gamma - 1.0); /* (E - rho V^2/2)(gamma-1) = e rho (gamma-1) */
672   PetscFunctionReturn(0);
673 }
674 
675 static PetscErrorCode SpeedOfSound_PG(const PetscReal *gamma, const EulerNode *x, PetscReal *c)
676 {
677   PetscReal p;
678 
679   PetscFunctionBeginUser;
680   Pressure_PG(*gamma,x,&p);
681   if (p<0.) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"negative pressure time %g -- NEED TO FIX!!!!!!",(double) p);
682   /* pars[EULER_PAR_GAMMA] = heat capacity ratio */
683   (*c)=PetscSqrtReal(*gamma * p / x->r);
684   PetscFunctionReturn(0);
685 }
686 
687 /*
688  * x = (rho,rho*(u_1),...,rho*e)^T
689  * x_t+div(f_1(x))+...+div(f_DIM(x)) = 0
690  *
691  * f_i(x) = u_i*x+(0,0,...,p,...,p*u_i)^T
692  *
693  */
694 static PetscErrorCode EulerFlux(Physics phys,const PetscReal *n,const EulerNode *x,EulerNode *f)
695 {
696   Physics_Euler *eu = (Physics_Euler*)phys->data;
697   PetscReal     nu,p;
698   PetscInt      i;
699 
700   PetscFunctionBeginUser;
701   Pressure_PG(eu->pars[EULER_PAR_GAMMA],x,&p);
702   nu = DotDIMReal(x->ru,n);
703   f->r = nu;   /* A rho u */
704   nu /= x->r;  /* A u */
705   for (i=0; i<DIM; i++) f->ru[i] = nu * x->ru[i] + n[i]*p;  /* r u^2 + p */
706   f->E = nu * (x->E + p); /* u(e+p) */
707   PetscFunctionReturn(0);
708 }
709 
710 /* PetscReal* => EulerNode* conversion */
711 static PetscErrorCode PhysicsBoundary_Euler_Wall(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *a_xI, PetscScalar *a_xG, void *ctx)
712 {
713   PetscInt    i;
714   const EulerNode *xI = (const EulerNode*)a_xI;
715   EulerNode       *xG = (EulerNode*)a_xG;
716   Physics         phys = (Physics)ctx;
717   Physics_Euler   *eu  = (Physics_Euler*)phys->data;
718   PetscFunctionBeginUser;
719   xG->r = xI->r;           /* ghost cell density - same */
720   xG->E = xI->E;           /* ghost cell energy - same */
721   if (n[1] != 0.) {        /* top and bottom */
722     xG->ru[0] =  xI->ru[0]; /* copy tang to wall */
723     xG->ru[1] = -xI->ru[1]; /* reflect perp to t/b wall */
724   }
725   else { /* sides */
726     for (i=0; i<DIM; i++) xG->ru[i] = xI->ru[i]; /* copy */
727   }
728   if (eu->type == EULER_LINEAR_WAVE) { /* debug */
729 #if 0
730     PetscPrintf(PETSC_COMM_WORLD,"%s coord=%g,%g\n",PETSC_FUNCTION_NAME,c[0],c[1]);
731 #endif
732   }
733   PetscFunctionReturn(0);
734 }
735 int godunovflux( const PetscScalar *ul, const PetscScalar *ur, PetscScalar *flux, const PetscReal *nn, const int *ndim, const PetscReal *gamma);
736 /* PetscReal* => EulerNode* conversion */
737 static void PhysicsRiemann_Euler_Godunov( PetscInt dim, PetscInt Nf, const PetscReal *qp, const PetscReal *n,
738                                           const PetscScalar *xL, const PetscScalar *xR, PetscInt numConstants, const PetscScalar constants[], PetscScalar *flux, Physics phys)
739 {
740   Physics_Euler   *eu = (Physics_Euler*)phys->data;
741   PetscReal       cL,cR,speed,velL,velR,nn[DIM],s2;
742   PetscInt        i;
743   PetscErrorCode  ierr;
744   PetscFunctionBeginUser;
745 
746   for (i=0,s2=0.; i<DIM; i++) {
747     nn[i] = n[i];
748     s2 += nn[i]*nn[i];
749   }
750   s2 = PetscSqrtReal(s2); /* |n|_2 = sum(n^2)^1/2 */
751   for (i=0.; i<DIM; i++) nn[i] /= s2;
752   if (0) { /* Rusanov */
753     const EulerNode *uL = (const EulerNode*)xL,*uR = (const EulerNode*)xR;
754     EulerNodeUnion  fL,fR;
755     EulerFlux(phys,nn,uL,&(fL.eulernode));
756     EulerFlux(phys,nn,uR,&(fR.eulernode));
757     ierr = eu->sound(&eu->pars[EULER_PAR_GAMMA],uL,&cL);if (ierr) exit(13);
758     ierr = eu->sound(&eu->pars[EULER_PAR_GAMMA],uR,&cR);if (ierr) exit(14);
759     velL = DotDIMReal(uL->ru,nn)/uL->r;
760     velR = DotDIMReal(uR->ru,nn)/uR->r;
761     speed = PetscMax(velR + cR, velL + cL);
762     for (i=0; i<2+dim; i++) flux[i] = 0.5*((fL.vals[i]+fR.vals[i]) + speed*(xL[i] - xR[i]))*s2;
763   }
764   else {
765     int dim = DIM;
766     /* int iwave =  */
767     godunovflux(xL, xR, flux, nn, &dim, &eu->pars[EULER_PAR_GAMMA]);
768     for (i=0; i<2+dim; i++) flux[i] *= s2;
769   }
770   PetscFunctionReturnVoid();
771 }
772 
773 static PetscErrorCode PhysicsFunctional_Euler(Model mod,PetscReal time,const PetscReal *coord,const PetscScalar *xx,PetscReal *f,void *ctx)
774 {
775   Physics         phys = (Physics)ctx;
776   Physics_Euler   *eu  = (Physics_Euler*)phys->data;
777   const EulerNode *x   = (const EulerNode*)xx;
778   PetscReal       p;
779 
780   PetscFunctionBeginUser;
781   f[eu->monitor.Density]  = x->r;
782   f[eu->monitor.Momentum] = NormDIM(x->ru);
783   f[eu->monitor.Energy]   = x->E;
784   f[eu->monitor.Speed]    = NormDIM(x->ru)/x->r;
785   Pressure_PG(eu->pars[EULER_PAR_GAMMA], x, &p);
786   f[eu->monitor.Pressure] = p;
787   PetscFunctionReturn(0);
788 }
789 
790 static PetscErrorCode SetUpBC_Euler(PetscDS prob,Physics phys)
791 {
792   PetscErrorCode  ierr;
793   Physics_Euler   *eu = (Physics_Euler *) phys->data;
794   if (eu->type == EULER_LINEAR_WAVE) {
795     const PetscInt wallids[] = {100,101};
796     ierr = PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "wall", "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_Euler_Wall, NULL, ALEN(wallids), wallids, phys);CHKERRQ(ierr);
797   }
798   else {
799     const PetscInt wallids[] = {100,101,200,300};
800     ierr = PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "wall", "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_Euler_Wall, NULL, ALEN(wallids), wallids, phys);CHKERRQ(ierr);
801   }
802   PetscFunctionReturn(0);
803 }
804 
805 static PetscErrorCode PhysicsCreate_Euler(Model mod,Physics phys,PetscOptionItems *PetscOptionsObject)
806 {
807   Physics_Euler   *eu;
808   PetscErrorCode  ierr;
809 
810   PetscFunctionBeginUser;
811   phys->field_desc = PhysicsFields_Euler;
812   phys->riemann = (PetscRiemannFunc) PhysicsRiemann_Euler_Godunov;
813   ierr = PetscNew(&eu);CHKERRQ(ierr);
814   phys->data    = eu;
815   mod->setupbc = SetUpBC_Euler;
816   ierr = PetscOptionsHead(PetscOptionsObject,"Euler options");CHKERRQ(ierr);
817   {
818     PetscReal alpha;
819     char type[64] = "linear_wave";
820     PetscBool  is;
821     mod->bcs[0] = mod->bcs[1] = mod->bcs[2] = DM_BOUNDARY_GHOSTED;
822     eu->pars[EULER_PAR_GAMMA] = 1.4;
823     eu->pars[EULER_PAR_AMACH] = 2.02;
824     eu->pars[EULER_PAR_RHOR] = 3.0;
825     eu->pars[EULER_PAR_ITANA] = 0.57735026918963; /* angle of Euler self similar (SS) shock */
826     ierr = PetscOptionsReal("-eu_gamma","Heat capacity ratio","",eu->pars[EULER_PAR_GAMMA],&eu->pars[EULER_PAR_GAMMA],NULL);CHKERRQ(ierr);
827     ierr = PetscOptionsReal("-eu_amach","Shock speed (Mach)","",eu->pars[EULER_PAR_AMACH],&eu->pars[EULER_PAR_AMACH],NULL);CHKERRQ(ierr);
828     ierr = PetscOptionsReal("-eu_rho2","Density right of discontinuity","",eu->pars[EULER_PAR_RHOR],&eu->pars[EULER_PAR_RHOR],NULL);CHKERRQ(ierr);
829     alpha = 60.;
830     ierr = PetscOptionsReal("-eu_alpha","Angle of discontinuity","",alpha,&alpha,NULL);CHKERRQ(ierr);
831     if (alpha<=0. || alpha>90.) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Alpha bust be > 0 and <= 90 (%g)",alpha);
832     eu->pars[EULER_PAR_ITANA] = 1./PetscTanReal( alpha * PETSC_PI / 180.0);
833     ierr = PetscOptionsString("-eu_type","Type of Euler test","",type,type,sizeof(type),NULL);CHKERRQ(ierr);
834     ierr = PetscStrcmp(type,"linear_wave", &is);CHKERRQ(ierr);
835     if (is) {
836       eu->type = EULER_LINEAR_WAVE;
837       mod->bcs[0] = mod->bcs[1] = mod->bcs[2] = DM_BOUNDARY_PERIODIC;
838       mod->bcs[1] = DM_BOUNDARY_GHOSTED; /* debug */
839       ierr = PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",PETSC_FUNCTION_NAME,"linear_wave");CHKERRQ(ierr);
840     }
841     else {
842       if (DIM != 2) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"DIM must be 2 unless linear wave test %s",type);
843       ierr = PetscStrcmp(type,"iv_shock", &is);CHKERRQ(ierr);
844       if (is) {
845         eu->type = EULER_IV_SHOCK;
846         ierr = PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",PETSC_FUNCTION_NAME,"iv_shock");CHKERRQ(ierr);
847       }
848       else {
849         ierr = PetscStrcmp(type,"ss_shock", &is);CHKERRQ(ierr);
850         if (is) {
851           eu->type = EULER_SS_SHOCK;
852           ierr = PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",PETSC_FUNCTION_NAME,"ss_shock");CHKERRQ(ierr);
853         }
854         else {
855           ierr = PetscStrcmp(type,"shock_tube", &is);CHKERRQ(ierr);
856           if (is) eu->type = EULER_SHOCK_TUBE;
857           else SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Unknown Euler type %s",type);
858           ierr = PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",PETSC_FUNCTION_NAME,"shock_tube");CHKERRQ(ierr);
859         }
860       }
861     }
862   }
863   ierr = PetscOptionsTail();CHKERRQ(ierr);
864   eu->sound = SpeedOfSound_PG;
865   phys->maxspeed = 0.; /* will get set in solution */
866   ierr = ModelSolutionSetDefault(mod,PhysicsSolution_Euler,phys);CHKERRQ(ierr);
867   ierr = ModelFunctionalRegister(mod,"Speed",&eu->monitor.Speed,PhysicsFunctional_Euler,phys);CHKERRQ(ierr);
868   ierr = ModelFunctionalRegister(mod,"Energy",&eu->monitor.Energy,PhysicsFunctional_Euler,phys);CHKERRQ(ierr);
869   ierr = ModelFunctionalRegister(mod,"Density",&eu->monitor.Density,PhysicsFunctional_Euler,phys);CHKERRQ(ierr);
870   ierr = ModelFunctionalRegister(mod,"Momentum",&eu->monitor.Momentum,PhysicsFunctional_Euler,phys);CHKERRQ(ierr);
871   ierr = ModelFunctionalRegister(mod,"Pressure",&eu->monitor.Pressure,PhysicsFunctional_Euler,phys);CHKERRQ(ierr);
872 
873   PetscFunctionReturn(0);
874 }
875 
876 static PetscErrorCode ErrorIndicator_Simple(PetscInt dim, PetscReal volume, PetscInt numComps, const PetscScalar u[], const PetscScalar grad[], PetscReal *error, void *ctx)
877 {
878   PetscReal      err = 0.;
879   PetscInt       i, j;
880 
881   PetscFunctionBeginUser;
882   for (i = 0; i < numComps; i++) {
883     for (j = 0; j < dim; j++) {
884       err += PetscSqr(PetscRealPart(grad[i * dim + j]));
885     }
886   }
887   *error = volume * err;
888   PetscFunctionReturn(0);
889 }
890 
891 PetscErrorCode ConstructCellBoundary(DM dm, User user)
892 {
893   const char     *name   = "Cell Sets";
894   const char     *bdname = "split faces";
895   IS             regionIS, innerIS;
896   const PetscInt *regions, *cells;
897   PetscInt       numRegions, innerRegion, numCells, c;
898   PetscInt       cStart, cEnd, cEndInterior, fStart, fEnd;
899   PetscBool      hasLabel;
900   PetscErrorCode ierr;
901 
902   PetscFunctionBeginUser;
903   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
904   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
905   ierr = DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);CHKERRQ(ierr);
906 
907   ierr = DMHasLabel(dm, name, &hasLabel);CHKERRQ(ierr);
908   if (!hasLabel) PetscFunctionReturn(0);
909   ierr = DMGetLabelSize(dm, name, &numRegions);CHKERRQ(ierr);
910   if (numRegions != 2) PetscFunctionReturn(0);
911   /* Get the inner id */
912   ierr = DMGetLabelIdIS(dm, name, &regionIS);CHKERRQ(ierr);
913   ierr = ISGetIndices(regionIS, &regions);CHKERRQ(ierr);
914   innerRegion = regions[0];
915   ierr = ISRestoreIndices(regionIS, &regions);CHKERRQ(ierr);
916   ierr = ISDestroy(&regionIS);CHKERRQ(ierr);
917   /* Find the faces between cells in different regions, could call DMPlexCreateNeighborCSR() */
918   ierr = DMGetStratumIS(dm, name, innerRegion, &innerIS);CHKERRQ(ierr);
919   ierr = ISGetLocalSize(innerIS, &numCells);CHKERRQ(ierr);
920   ierr = ISGetIndices(innerIS, &cells);CHKERRQ(ierr);
921   ierr = DMCreateLabel(dm, bdname);CHKERRQ(ierr);
922   for (c = 0; c < numCells; ++c) {
923     const PetscInt cell = cells[c];
924     const PetscInt *faces;
925     PetscInt       numFaces, f;
926 
927     if ((cell < cStart) || (cell >= cEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Got invalid point %d which is not a cell", cell);
928     ierr = DMPlexGetConeSize(dm, cell, &numFaces);CHKERRQ(ierr);
929     ierr = DMPlexGetCone(dm, cell, &faces);CHKERRQ(ierr);
930     for (f = 0; f < numFaces; ++f) {
931       const PetscInt face = faces[f];
932       const PetscInt *neighbors;
933       PetscInt       nC, regionA, regionB;
934 
935       if ((face < fStart) || (face >= fEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Got invalid point %d which is not a face", face);
936       ierr = DMPlexGetSupportSize(dm, face, &nC);CHKERRQ(ierr);
937       if (nC != 2) continue;
938       ierr = DMPlexGetSupport(dm, face, &neighbors);CHKERRQ(ierr);
939       if ((neighbors[0] >= cEndInterior) || (neighbors[1] >= cEndInterior)) continue;
940       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]);
941       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]);
942       ierr = DMGetLabelValue(dm, name, neighbors[0], &regionA);CHKERRQ(ierr);
943       ierr = DMGetLabelValue(dm, name, neighbors[1], &regionB);CHKERRQ(ierr);
944       if (regionA < 0) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Invalid label %s: Cell %d has no value", name, neighbors[0]);
945       if (regionB < 0) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Invalid label %s: Cell %d has no value", name, neighbors[1]);
946       if (regionA != regionB) {
947         ierr = DMSetLabelValue(dm, bdname, faces[f], 1);CHKERRQ(ierr);
948       }
949     }
950   }
951   ierr = ISRestoreIndices(innerIS, &cells);CHKERRQ(ierr);
952   ierr = ISDestroy(&innerIS);CHKERRQ(ierr);
953   {
954     DMLabel label;
955 
956     ierr = DMGetLabel(dm, bdname, &label);CHKERRQ(ierr);
957     ierr = DMLabelView(label, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
958   }
959   PetscFunctionReturn(0);
960 }
961 
962 /* Right now, I have just added duplicate faces, which see both cells. We can
963 - Add duplicate vertices and decouple the face cones
964 - Disconnect faces from cells across the rotation gap
965 */
966 PetscErrorCode SplitFaces(DM *dmSplit, const char labelName[], User user)
967 {
968   DM             dm = *dmSplit, sdm;
969   PetscSF        sfPoint, gsfPoint;
970   PetscSection   coordSection, newCoordSection;
971   Vec            coordinates;
972   IS             idIS;
973   const PetscInt *ids;
974   PetscInt       *newpoints;
975   PetscInt       dim, depth, maxConeSize, maxSupportSize, numLabels, numGhostCells;
976   PetscInt       numFS, fs, pStart, pEnd, p, cEnd, cEndInterior, vStart, vEnd, v, fStart, fEnd, newf, d, l;
977   PetscBool      hasLabel;
978   PetscErrorCode ierr;
979 
980   PetscFunctionBeginUser;
981   ierr = DMHasLabel(dm, labelName, &hasLabel);CHKERRQ(ierr);
982   if (!hasLabel) PetscFunctionReturn(0);
983   ierr = DMCreate(PetscObjectComm((PetscObject)dm), &sdm);CHKERRQ(ierr);
984   ierr = DMSetType(sdm, DMPLEX);CHKERRQ(ierr);
985   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
986   ierr = DMSetDimension(sdm, dim);CHKERRQ(ierr);
987 
988   ierr = DMGetLabelIdIS(dm, labelName, &idIS);CHKERRQ(ierr);
989   ierr = ISGetLocalSize(idIS, &numFS);CHKERRQ(ierr);
990   ierr = ISGetIndices(idIS, &ids);CHKERRQ(ierr);
991 
992   user->numSplitFaces = 0;
993   for (fs = 0; fs < numFS; ++fs) {
994     PetscInt numBdFaces;
995 
996     ierr = DMGetStratumSize(dm, labelName, ids[fs], &numBdFaces);CHKERRQ(ierr);
997     user->numSplitFaces += numBdFaces;
998   }
999   ierr  = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
1000   pEnd += user->numSplitFaces;
1001   ierr  = DMPlexSetChart(sdm, pStart, pEnd);CHKERRQ(ierr);
1002   ierr  = DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);CHKERRQ(ierr);
1003   ierr  = DMPlexGetHeightStratum(dm, 0, NULL, &cEnd);CHKERRQ(ierr);
1004   numGhostCells = cEnd - cEndInterior;
1005   /* Set cone and support sizes */
1006   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
1007   for (d = 0; d <= depth; ++d) {
1008     ierr = DMPlexGetDepthStratum(dm, d, &pStart, &pEnd);CHKERRQ(ierr);
1009     for (p = pStart; p < pEnd; ++p) {
1010       PetscInt newp = p;
1011       PetscInt size;
1012 
1013       ierr = DMPlexGetConeSize(dm, p, &size);CHKERRQ(ierr);
1014       ierr = DMPlexSetConeSize(sdm, newp, size);CHKERRQ(ierr);
1015       ierr = DMPlexGetSupportSize(dm, p, &size);CHKERRQ(ierr);
1016       ierr = DMPlexSetSupportSize(sdm, newp, size);CHKERRQ(ierr);
1017     }
1018   }
1019   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1020   for (fs = 0, newf = fEnd; fs < numFS; ++fs) {
1021     IS             faceIS;
1022     const PetscInt *faces;
1023     PetscInt       numFaces, f;
1024 
1025     ierr = DMGetStratumIS(dm, labelName, ids[fs], &faceIS);CHKERRQ(ierr);
1026     ierr = ISGetLocalSize(faceIS, &numFaces);CHKERRQ(ierr);
1027     ierr = ISGetIndices(faceIS, &faces);CHKERRQ(ierr);
1028     for (f = 0; f < numFaces; ++f, ++newf) {
1029       PetscInt size;
1030 
1031       /* Right now I think that both faces should see both cells */
1032       ierr = DMPlexGetConeSize(dm, faces[f], &size);CHKERRQ(ierr);
1033       ierr = DMPlexSetConeSize(sdm, newf, size);CHKERRQ(ierr);
1034       ierr = DMPlexGetSupportSize(dm, faces[f], &size);CHKERRQ(ierr);
1035       ierr = DMPlexSetSupportSize(sdm, newf, size);CHKERRQ(ierr);
1036     }
1037     ierr = ISRestoreIndices(faceIS, &faces);CHKERRQ(ierr);
1038     ierr = ISDestroy(&faceIS);CHKERRQ(ierr);
1039   }
1040   ierr = DMSetUp(sdm);CHKERRQ(ierr);
1041   /* Set cones and supports */
1042   ierr = DMPlexGetMaxSizes(dm, &maxConeSize, &maxSupportSize);CHKERRQ(ierr);
1043   ierr = PetscMalloc1(PetscMax(maxConeSize, maxSupportSize), &newpoints);CHKERRQ(ierr);
1044   ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
1045   for (p = pStart; p < pEnd; ++p) {
1046     const PetscInt *points, *orientations;
1047     PetscInt       size, i, newp = p;
1048 
1049     ierr = DMPlexGetConeSize(dm, p, &size);CHKERRQ(ierr);
1050     ierr = DMPlexGetCone(dm, p, &points);CHKERRQ(ierr);
1051     ierr = DMPlexGetConeOrientation(dm, p, &orientations);CHKERRQ(ierr);
1052     for (i = 0; i < size; ++i) newpoints[i] = points[i];
1053     ierr = DMPlexSetCone(sdm, newp, newpoints);CHKERRQ(ierr);
1054     ierr = DMPlexSetConeOrientation(sdm, newp, orientations);CHKERRQ(ierr);
1055     ierr = DMPlexGetSupportSize(dm, p, &size);CHKERRQ(ierr);
1056     ierr = DMPlexGetSupport(dm, p, &points);CHKERRQ(ierr);
1057     for (i = 0; i < size; ++i) newpoints[i] = points[i];
1058     ierr = DMPlexSetSupport(sdm, newp, newpoints);CHKERRQ(ierr);
1059   }
1060   ierr = PetscFree(newpoints);CHKERRQ(ierr);
1061   for (fs = 0, newf = fEnd; fs < numFS; ++fs) {
1062     IS             faceIS;
1063     const PetscInt *faces;
1064     PetscInt       numFaces, f;
1065 
1066     ierr = DMGetStratumIS(dm, labelName, ids[fs], &faceIS);CHKERRQ(ierr);
1067     ierr = ISGetLocalSize(faceIS, &numFaces);CHKERRQ(ierr);
1068     ierr = ISGetIndices(faceIS, &faces);CHKERRQ(ierr);
1069     for (f = 0; f < numFaces; ++f, ++newf) {
1070       const PetscInt *points;
1071 
1072       ierr = DMPlexGetCone(dm, faces[f], &points);CHKERRQ(ierr);
1073       ierr = DMPlexSetCone(sdm, newf, points);CHKERRQ(ierr);
1074       ierr = DMPlexGetSupport(dm, faces[f], &points);CHKERRQ(ierr);
1075       ierr = DMPlexSetSupport(sdm, newf, points);CHKERRQ(ierr);
1076     }
1077     ierr = ISRestoreIndices(faceIS, &faces);CHKERRQ(ierr);
1078     ierr = ISDestroy(&faceIS);CHKERRQ(ierr);
1079   }
1080   ierr = ISRestoreIndices(idIS, &ids);CHKERRQ(ierr);
1081   ierr = ISDestroy(&idIS);CHKERRQ(ierr);
1082   ierr = DMPlexStratify(sdm);CHKERRQ(ierr);
1083   /* Convert coordinates */
1084   ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1085   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1086   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &newCoordSection);CHKERRQ(ierr);
1087   ierr = PetscSectionSetNumFields(newCoordSection, 1);CHKERRQ(ierr);
1088   ierr = PetscSectionSetFieldComponents(newCoordSection, 0, dim);CHKERRQ(ierr);
1089   ierr = PetscSectionSetChart(newCoordSection, vStart, vEnd);CHKERRQ(ierr);
1090   for (v = vStart; v < vEnd; ++v) {
1091     ierr = PetscSectionSetDof(newCoordSection, v, dim);CHKERRQ(ierr);
1092     ierr = PetscSectionSetFieldDof(newCoordSection, v, 0, dim);CHKERRQ(ierr);
1093   }
1094   ierr = PetscSectionSetUp(newCoordSection);CHKERRQ(ierr);
1095   ierr = DMSetCoordinateSection(sdm, PETSC_DETERMINE, newCoordSection);CHKERRQ(ierr);
1096   ierr = PetscSectionDestroy(&newCoordSection);CHKERRQ(ierr); /* relinquish our reference */
1097   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1098   ierr = DMSetCoordinatesLocal(sdm, coordinates);CHKERRQ(ierr);
1099   /* Convert labels */
1100   ierr = DMGetNumLabels(dm, &numLabels);CHKERRQ(ierr);
1101   for (l = 0; l < numLabels; ++l) {
1102     const char *lname;
1103     PetscBool  isDepth, isDim;
1104 
1105     ierr = DMGetLabelName(dm, l, &lname);CHKERRQ(ierr);
1106     ierr = PetscStrcmp(lname, "depth", &isDepth);CHKERRQ(ierr);
1107     if (isDepth) continue;
1108     ierr = PetscStrcmp(lname, "dim", &isDim);CHKERRQ(ierr);
1109     if (isDim) continue;
1110     ierr = DMCreateLabel(sdm, lname);CHKERRQ(ierr);
1111     ierr = DMGetLabelIdIS(dm, lname, &idIS);CHKERRQ(ierr);
1112     ierr = ISGetLocalSize(idIS, &numFS);CHKERRQ(ierr);
1113     ierr = ISGetIndices(idIS, &ids);CHKERRQ(ierr);
1114     for (fs = 0; fs < numFS; ++fs) {
1115       IS             pointIS;
1116       const PetscInt *points;
1117       PetscInt       numPoints;
1118 
1119       ierr = DMGetStratumIS(dm, lname, ids[fs], &pointIS);CHKERRQ(ierr);
1120       ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
1121       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1122       for (p = 0; p < numPoints; ++p) {
1123         PetscInt newpoint = points[p];
1124 
1125         ierr = DMSetLabelValue(sdm, lname, newpoint, ids[fs]);CHKERRQ(ierr);
1126       }
1127       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1128       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1129     }
1130     ierr = ISRestoreIndices(idIS, &ids);CHKERRQ(ierr);
1131     ierr = ISDestroy(&idIS);CHKERRQ(ierr);
1132   }
1133   {
1134     /* Convert pointSF */
1135     const PetscSFNode *remotePoints;
1136     PetscSFNode       *gremotePoints;
1137     const PetscInt    *localPoints;
1138     PetscInt          *glocalPoints,*newLocation,*newRemoteLocation;
1139     PetscInt          numRoots, numLeaves;
1140     PetscMPIInt       size;
1141 
1142     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)dm), &size);CHKERRQ(ierr);
1143     ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
1144     ierr = DMGetPointSF(sdm, &gsfPoint);CHKERRQ(ierr);
1145     ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
1146     ierr = PetscSFGetGraph(sfPoint, &numRoots, &numLeaves, &localPoints, &remotePoints);CHKERRQ(ierr);
1147     if (numRoots >= 0) {
1148       ierr = PetscMalloc2(numRoots,&newLocation,pEnd-pStart,&newRemoteLocation);CHKERRQ(ierr);
1149       for (l=0; l<numRoots; l++) newLocation[l] = l; /* + (l >= cEnd ? numGhostCells : 0); */
1150       ierr = PetscSFBcastBegin(sfPoint, MPIU_INT, newLocation, newRemoteLocation);CHKERRQ(ierr);
1151       ierr = PetscSFBcastEnd(sfPoint, MPIU_INT, newLocation, newRemoteLocation);CHKERRQ(ierr);
1152       ierr = PetscMalloc1(numLeaves,    &glocalPoints);CHKERRQ(ierr);
1153       ierr = PetscMalloc1(numLeaves, &gremotePoints);CHKERRQ(ierr);
1154       for (l = 0; l < numLeaves; ++l) {
1155         glocalPoints[l]        = localPoints[l]; /* localPoints[l] >= cEnd ? localPoints[l] + numGhostCells : localPoints[l]; */
1156         gremotePoints[l].rank  = remotePoints[l].rank;
1157         gremotePoints[l].index = newRemoteLocation[localPoints[l]];
1158       }
1159       ierr = PetscFree2(newLocation,newRemoteLocation);CHKERRQ(ierr);
1160       ierr = PetscSFSetGraph(gsfPoint, numRoots+numGhostCells, numLeaves, glocalPoints, PETSC_OWN_POINTER, gremotePoints, PETSC_OWN_POINTER);CHKERRQ(ierr);
1161     }
1162     ierr     = DMDestroy(dmSplit);CHKERRQ(ierr);
1163     *dmSplit = sdm;
1164   }
1165   PetscFunctionReturn(0);
1166 }
1167 
1168 PetscErrorCode CreatePartitionVec(DM dm, DM *dmCell, Vec *partition)
1169 {
1170   PetscSF        sfPoint;
1171   PetscSection   coordSection;
1172   Vec            coordinates;
1173   PetscSection   sectionCell;
1174   PetscScalar    *part;
1175   PetscInt       cStart, cEnd, c;
1176   PetscMPIInt    rank;
1177   PetscErrorCode ierr;
1178 
1179   PetscFunctionBeginUser;
1180   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1181   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1182   ierr = DMClone(dm, dmCell);CHKERRQ(ierr);
1183   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
1184   ierr = DMSetPointSF(*dmCell, sfPoint);CHKERRQ(ierr);
1185   ierr = DMSetCoordinateSection(*dmCell, PETSC_DETERMINE, coordSection);CHKERRQ(ierr);
1186   ierr = DMSetCoordinatesLocal(*dmCell, coordinates);CHKERRQ(ierr);
1187   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
1188   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionCell);CHKERRQ(ierr);
1189   ierr = DMPlexGetHeightStratum(*dmCell, 0, &cStart, &cEnd);CHKERRQ(ierr);
1190   ierr = PetscSectionSetChart(sectionCell, cStart, cEnd);CHKERRQ(ierr);
1191   for (c = cStart; c < cEnd; ++c) {
1192     ierr = PetscSectionSetDof(sectionCell, c, 1);CHKERRQ(ierr);
1193   }
1194   ierr = PetscSectionSetUp(sectionCell);CHKERRQ(ierr);
1195   ierr = DMSetLocalSection(*dmCell, sectionCell);CHKERRQ(ierr);
1196   ierr = PetscSectionDestroy(&sectionCell);CHKERRQ(ierr);
1197   ierr = DMCreateLocalVector(*dmCell, partition);CHKERRQ(ierr);
1198   ierr = PetscObjectSetName((PetscObject)*partition, "partition");CHKERRQ(ierr);
1199   ierr = VecGetArray(*partition, &part);CHKERRQ(ierr);
1200   for (c = cStart; c < cEnd; ++c) {
1201     PetscScalar *p;
1202 
1203     ierr = DMPlexPointLocalRef(*dmCell, c, part, &p);CHKERRQ(ierr);
1204     p[0] = rank;
1205   }
1206   ierr = VecRestoreArray(*partition, &part);CHKERRQ(ierr);
1207   PetscFunctionReturn(0);
1208 }
1209 
1210 PetscErrorCode CreateMassMatrix(DM dm, Vec *massMatrix, User user)
1211 {
1212   DM                plex, dmMass, dmFace, dmCell, dmCoord;
1213   PetscSection      coordSection;
1214   Vec               coordinates, facegeom, cellgeom;
1215   PetscSection      sectionMass;
1216   PetscScalar       *m;
1217   const PetscScalar *fgeom, *cgeom, *coords;
1218   PetscInt          vStart, vEnd, v;
1219   PetscErrorCode    ierr;
1220 
1221   PetscFunctionBeginUser;
1222   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
1223   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1224   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
1225   ierr = DMClone(dm, &dmMass);CHKERRQ(ierr);
1226   ierr = DMSetCoordinateSection(dmMass, PETSC_DETERMINE, coordSection);CHKERRQ(ierr);
1227   ierr = DMSetCoordinatesLocal(dmMass, coordinates);CHKERRQ(ierr);
1228   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionMass);CHKERRQ(ierr);
1229   ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1230   ierr = PetscSectionSetChart(sectionMass, vStart, vEnd);CHKERRQ(ierr);
1231   for (v = vStart; v < vEnd; ++v) {
1232     PetscInt numFaces;
1233 
1234     ierr = DMPlexGetSupportSize(dmMass, v, &numFaces);CHKERRQ(ierr);
1235     ierr = PetscSectionSetDof(sectionMass, v, numFaces*numFaces);CHKERRQ(ierr);
1236   }
1237   ierr = PetscSectionSetUp(sectionMass);CHKERRQ(ierr);
1238   ierr = DMSetLocalSection(dmMass, sectionMass);CHKERRQ(ierr);
1239   ierr = PetscSectionDestroy(&sectionMass);CHKERRQ(ierr);
1240   ierr = DMGetLocalVector(dmMass, massMatrix);CHKERRQ(ierr);
1241   ierr = VecGetArray(*massMatrix, &m);CHKERRQ(ierr);
1242   ierr = DMPlexGetGeometryFVM(plex, &facegeom, &cellgeom, NULL);CHKERRQ(ierr);
1243   ierr = VecGetDM(facegeom, &dmFace);CHKERRQ(ierr);
1244   ierr = VecGetArrayRead(facegeom, &fgeom);CHKERRQ(ierr);
1245   ierr = VecGetDM(cellgeom, &dmCell);CHKERRQ(ierr);
1246   ierr = VecGetArrayRead(cellgeom, &cgeom);CHKERRQ(ierr);
1247   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
1248   ierr = VecGetArrayRead(coordinates, &coords);CHKERRQ(ierr);
1249   for (v = vStart; v < vEnd; ++v) {
1250     const PetscInt        *faces;
1251     PetscFVFaceGeom       *fgA, *fgB, *cg;
1252     PetscScalar           *vertex;
1253     PetscInt               numFaces, sides[2], f, g;
1254 
1255     ierr = DMPlexPointLocalRead(dmCoord, v, coords, &vertex);CHKERRQ(ierr);
1256     ierr = DMPlexGetSupportSize(dmMass, v, &numFaces);CHKERRQ(ierr);
1257     ierr = DMPlexGetSupport(dmMass, v, &faces);CHKERRQ(ierr);
1258     for (f = 0; f < numFaces; ++f) {
1259       sides[0] = faces[f];
1260       ierr = DMPlexPointLocalRead(dmFace, faces[f], fgeom, &fgA);CHKERRQ(ierr);
1261       for (g = 0; g < numFaces; ++g) {
1262         const PetscInt *cells = NULL;
1263         PetscReal      area   = 0.0;
1264         PetscInt       numCells;
1265 
1266         sides[1] = faces[g];
1267         ierr = DMPlexPointLocalRead(dmFace, faces[g], fgeom, &fgB);CHKERRQ(ierr);
1268         ierr = DMPlexGetJoin(dmMass, 2, sides, &numCells, &cells);CHKERRQ(ierr);
1269         if (numCells != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Invalid join for faces");
1270         ierr = DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cg);CHKERRQ(ierr);
1271         area += PetscAbsScalar((vertex[0] - cg->centroid[0])*(fgA->centroid[1] - cg->centroid[1]) - (vertex[1] - cg->centroid[1])*(fgA->centroid[0] - cg->centroid[0]));
1272         area += PetscAbsScalar((vertex[0] - cg->centroid[0])*(fgB->centroid[1] - cg->centroid[1]) - (vertex[1] - cg->centroid[1])*(fgB->centroid[0] - cg->centroid[0]));
1273         m[f*numFaces+g] = Dot2Real(fgA->normal, fgB->normal)*area*0.5;
1274         ierr = DMPlexRestoreJoin(dmMass, 2, sides, &numCells, &cells);CHKERRQ(ierr);
1275       }
1276     }
1277   }
1278   ierr = VecRestoreArrayRead(facegeom, &fgeom);CHKERRQ(ierr);
1279   ierr = VecRestoreArrayRead(cellgeom, &cgeom);CHKERRQ(ierr);
1280   ierr = VecRestoreArrayRead(coordinates, &coords);CHKERRQ(ierr);
1281   ierr = VecRestoreArray(*massMatrix, &m);CHKERRQ(ierr);
1282   ierr = DMDestroy(&dmMass);CHKERRQ(ierr);
1283   ierr = DMDestroy(&plex);CHKERRQ(ierr);
1284   PetscFunctionReturn(0);
1285 }
1286 
1287 /* Behavior will be different for multi-physics or when using non-default boundary conditions */
1288 static PetscErrorCode ModelSolutionSetDefault(Model mod,SolutionFunction func,void *ctx)
1289 {
1290   PetscFunctionBeginUser;
1291   mod->solution    = func;
1292   mod->solutionctx = ctx;
1293   PetscFunctionReturn(0);
1294 }
1295 
1296 static PetscErrorCode ModelFunctionalRegister(Model mod,const char *name,PetscInt *offset,FunctionalFunction func,void *ctx)
1297 {
1298   PetscErrorCode ierr;
1299   FunctionalLink link,*ptr;
1300   PetscInt       lastoffset = -1;
1301 
1302   PetscFunctionBeginUser;
1303   for (ptr=&mod->functionalRegistry; *ptr; ptr = &(*ptr)->next) lastoffset = (*ptr)->offset;
1304   ierr         = PetscNew(&link);CHKERRQ(ierr);
1305   ierr         = PetscStrallocpy(name,&link->name);CHKERRQ(ierr);
1306   link->offset = lastoffset + 1;
1307   link->func   = func;
1308   link->ctx    = ctx;
1309   link->next   = NULL;
1310   *ptr         = link;
1311   *offset      = link->offset;
1312   PetscFunctionReturn(0);
1313 }
1314 
1315 static PetscErrorCode ModelFunctionalSetFromOptions(Model mod,PetscOptionItems *PetscOptionsObject)
1316 {
1317   PetscErrorCode ierr;
1318   PetscInt       i,j;
1319   FunctionalLink link;
1320   char           *names[256];
1321 
1322   PetscFunctionBeginUser;
1323   mod->numMonitored = ALEN(names);
1324   ierr = PetscOptionsStringArray("-monitor","list of functionals to monitor","",names,&mod->numMonitored,NULL);CHKERRQ(ierr);
1325   /* Create list of functionals that will be computed somehow */
1326   ierr = PetscMalloc1(mod->numMonitored,&mod->functionalMonitored);CHKERRQ(ierr);
1327   /* Create index of calls that we will have to make to compute these functionals (over-allocation in general). */
1328   ierr = PetscMalloc1(mod->numMonitored,&mod->functionalCall);CHKERRQ(ierr);
1329   mod->numCall = 0;
1330   for (i=0; i<mod->numMonitored; i++) {
1331     for (link=mod->functionalRegistry; link; link=link->next) {
1332       PetscBool match;
1333       ierr = PetscStrcasecmp(names[i],link->name,&match);CHKERRQ(ierr);
1334       if (match) break;
1335     }
1336     if (!link) SETERRQ1(mod->comm,PETSC_ERR_USER,"No known functional '%s'",names[i]);
1337     mod->functionalMonitored[i] = link;
1338     for (j=0; j<i; j++) {
1339       if (mod->functionalCall[j]->func == link->func && mod->functionalCall[j]->ctx == link->ctx) goto next_name;
1340     }
1341     mod->functionalCall[mod->numCall++] = link; /* Just points to the first link using the result. There may be more results. */
1342 next_name:
1343     ierr = PetscFree(names[i]);CHKERRQ(ierr);
1344   }
1345 
1346   /* Find out the maximum index of any functional computed by a function we will be calling (even if we are not using it) */
1347   mod->maxComputed = -1;
1348   for (link=mod->functionalRegistry; link; link=link->next) {
1349     for (i=0; i<mod->numCall; i++) {
1350       FunctionalLink call = mod->functionalCall[i];
1351       if (link->func == call->func && link->ctx == call->ctx) {
1352         mod->maxComputed = PetscMax(mod->maxComputed,link->offset);
1353       }
1354     }
1355   }
1356   PetscFunctionReturn(0);
1357 }
1358 
1359 static PetscErrorCode FunctionalLinkDestroy(FunctionalLink *link)
1360 {
1361   PetscErrorCode ierr;
1362   FunctionalLink l,next;
1363 
1364   PetscFunctionBeginUser;
1365   if (!link) PetscFunctionReturn(0);
1366   l     = *link;
1367   *link = NULL;
1368   for (; l; l=next) {
1369     next = l->next;
1370     ierr = PetscFree(l->name);CHKERRQ(ierr);
1371     ierr = PetscFree(l);CHKERRQ(ierr);
1372   }
1373   PetscFunctionReturn(0);
1374 }
1375 
1376 /* put the solution callback into a functional callback */
1377 static PetscErrorCode SolutionFunctional(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *modctx)
1378 {
1379   Model          mod;
1380   PetscErrorCode ierr;
1381   PetscFunctionBegin;
1382   mod  = (Model) modctx;
1383   ierr = (*mod->solution)(mod, time, x, u, mod->solutionctx);CHKERRQ(ierr);
1384   PetscFunctionReturn(0);
1385 }
1386 
1387 PetscErrorCode SetInitialCondition(DM dm, Vec X, User user)
1388 {
1389   PetscErrorCode     (*func[1]) (PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
1390   void               *ctx[1];
1391   Model              mod = user->model;
1392   PetscErrorCode     ierr;
1393 
1394   PetscFunctionBeginUser;
1395   func[0] = SolutionFunctional;
1396   ctx[0]  = (void *) mod;
1397   ierr    = DMProjectFunction(dm,0.0,func,ctx,INSERT_ALL_VALUES,X);CHKERRQ(ierr);
1398   PetscFunctionReturn(0);
1399 }
1400 
1401 static PetscErrorCode OutputVTK(DM dm, const char *filename, PetscViewer *viewer)
1402 {
1403   PetscErrorCode ierr;
1404 
1405   PetscFunctionBeginUser;
1406   ierr = PetscViewerCreate(PetscObjectComm((PetscObject)dm), viewer);CHKERRQ(ierr);
1407   ierr = PetscViewerSetType(*viewer, PETSCVIEWERVTK);CHKERRQ(ierr);
1408   ierr = PetscViewerFileSetName(*viewer, filename);CHKERRQ(ierr);
1409   PetscFunctionReturn(0);
1410 }
1411 
1412 static PetscErrorCode MonitorVTK(TS ts,PetscInt stepnum,PetscReal time,Vec X,void *ctx)
1413 {
1414   User           user = (User)ctx;
1415   DM             dm, plex;
1416   PetscViewer    viewer;
1417   char           filename[PETSC_MAX_PATH_LEN],*ftable = NULL;
1418   PetscReal      xnorm;
1419   PetscErrorCode ierr;
1420 
1421   PetscFunctionBeginUser;
1422   ierr = PetscObjectSetName((PetscObject) X, "u");CHKERRQ(ierr);
1423   ierr = VecGetDM(X,&dm);CHKERRQ(ierr);
1424   ierr = VecNorm(X,NORM_INFINITY,&xnorm);CHKERRQ(ierr);
1425 
1426   if (stepnum >= 0) {
1427     stepnum += user->monitorStepOffset;
1428   }
1429   if (stepnum >= 0) {           /* No summary for final time */
1430     Model             mod = user->model;
1431     Vec               cellgeom;
1432     PetscInt          c,cStart,cEnd,fcount,i;
1433     size_t            ftableused,ftablealloc;
1434     const PetscScalar *cgeom,*x;
1435     DM                dmCell;
1436     DMLabel           vtkLabel;
1437     PetscReal         *fmin,*fmax,*fintegral,*ftmp;
1438 
1439     ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
1440     ierr = DMPlexGetGeometryFVM(plex, NULL, &cellgeom, NULL);CHKERRQ(ierr);
1441     fcount = mod->maxComputed+1;
1442     ierr   = PetscMalloc4(fcount,&fmin,fcount,&fmax,fcount,&fintegral,fcount,&ftmp);CHKERRQ(ierr);
1443     for (i=0; i<fcount; i++) {
1444       fmin[i]      = PETSC_MAX_REAL;
1445       fmax[i]      = PETSC_MIN_REAL;
1446       fintegral[i] = 0;
1447     }
1448     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
1449     ierr = DMPlexGetSimplexOrBoxCells(dmCell,0,&cStart,&cEnd);CHKERRQ(ierr);
1450     ierr = VecGetArrayRead(cellgeom,&cgeom);CHKERRQ(ierr);
1451     ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr);
1452     ierr = DMGetLabel(dm,"vtk",&vtkLabel);CHKERRQ(ierr);
1453     for (c = cStart; c < cEnd; ++c) {
1454       PetscFVCellGeom       *cg;
1455       const PetscScalar     *cx    = NULL;
1456       PetscInt              vtkVal = 0;
1457 
1458       /* not that these two routines as currently implemented work for any dm with a
1459        * localSection/globalSection */
1460       ierr = DMPlexPointLocalRead(dmCell,c,cgeom,&cg);CHKERRQ(ierr);
1461       ierr = DMPlexPointGlobalRead(dm,c,x,&cx);CHKERRQ(ierr);
1462       if (vtkLabel) {ierr = DMLabelGetValue(vtkLabel,c,&vtkVal);CHKERRQ(ierr);}
1463       if (!vtkVal || !cx) continue;        /* ghost, or not a global cell */
1464       for (i=0; i<mod->numCall; i++) {
1465         FunctionalLink flink = mod->functionalCall[i];
1466         ierr = (*flink->func)(mod,time,cg->centroid,cx,ftmp,flink->ctx);CHKERRQ(ierr);
1467       }
1468       for (i=0; i<fcount; i++) {
1469         fmin[i]       = PetscMin(fmin[i],ftmp[i]);
1470         fmax[i]       = PetscMax(fmax[i],ftmp[i]);
1471         fintegral[i] += cg->volume * ftmp[i];
1472       }
1473     }
1474     ierr = VecRestoreArrayRead(cellgeom,&cgeom);CHKERRQ(ierr);
1475     ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr);
1476     ierr = DMDestroy(&plex);CHKERRQ(ierr);
1477     ierr = MPI_Allreduce(MPI_IN_PLACE,fmin,fcount,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
1478     ierr = MPI_Allreduce(MPI_IN_PLACE,fmax,fcount,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
1479     ierr = MPI_Allreduce(MPI_IN_PLACE,fintegral,fcount,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
1480 
1481     ftablealloc = fcount * 100;
1482     ftableused  = 0;
1483     ierr        = PetscMalloc1(ftablealloc,&ftable);CHKERRQ(ierr);
1484     for (i=0; i<mod->numMonitored; i++) {
1485       size_t         countused;
1486       char           buffer[256],*p;
1487       FunctionalLink flink = mod->functionalMonitored[i];
1488       PetscInt       id    = flink->offset;
1489       if (i % 3) {
1490         ierr = PetscArraycpy(buffer,"  ",2);CHKERRQ(ierr);
1491         p    = buffer + 2;
1492       } else if (i) {
1493         char newline[] = "\n";
1494         ierr = PetscMemcpy(buffer,newline,sizeof(newline)-1);CHKERRQ(ierr);
1495         p    = buffer + sizeof(newline) - 1;
1496       } else {
1497         p = buffer;
1498       }
1499       ierr = 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]);CHKERRQ(ierr);
1500       countused--;
1501       countused += p - buffer;
1502       if (countused > ftablealloc-ftableused-1) { /* reallocate */
1503         char *ftablenew;
1504         ftablealloc = 2*ftablealloc + countused;
1505         ierr = PetscMalloc(ftablealloc,&ftablenew);CHKERRQ(ierr);
1506         ierr = PetscArraycpy(ftablenew,ftable,ftableused);CHKERRQ(ierr);
1507         ierr = PetscFree(ftable);CHKERRQ(ierr);
1508         ftable = ftablenew;
1509       }
1510       ierr = PetscArraycpy(ftable+ftableused,buffer,countused);CHKERRQ(ierr);
1511       ftableused += countused;
1512       ftable[ftableused] = 0;
1513     }
1514     ierr = PetscFree4(fmin,fmax,fintegral,ftmp);CHKERRQ(ierr);
1515 
1516     ierr = PetscPrintf(PetscObjectComm((PetscObject)ts),"% 3D  time %8.4g  |x| %8.4g  %s\n",stepnum,(double)time,(double)xnorm,ftable ? ftable : "");CHKERRQ(ierr);
1517     ierr = PetscFree(ftable);CHKERRQ(ierr);
1518   }
1519   if (user->vtkInterval < 1) PetscFunctionReturn(0);
1520   if ((stepnum == -1) ^ (stepnum % user->vtkInterval == 0)) {
1521     if (stepnum == -1) {        /* Final time is not multiple of normal time interval, write it anyway */
1522       ierr = TSGetStepNumber(ts,&stepnum);CHKERRQ(ierr);
1523     }
1524     ierr = PetscSNPrintf(filename,sizeof filename,"%s-%03D.vtu",user->outputBasename,stepnum);CHKERRQ(ierr);
1525     ierr = OutputVTK(dm,filename,&viewer);CHKERRQ(ierr);
1526     ierr = VecView(X,viewer);CHKERRQ(ierr);
1527     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
1528   }
1529   PetscFunctionReturn(0);
1530 }
1531 
1532 static PetscErrorCode initializeTS(DM dm, User user, TS *ts)
1533 {
1534   PetscErrorCode ierr;
1535 
1536   PetscFunctionBegin;
1537   ierr = TSCreate(PetscObjectComm((PetscObject)dm), ts);CHKERRQ(ierr);
1538   ierr = TSSetType(*ts, TSSSP);CHKERRQ(ierr);
1539   ierr = TSSetDM(*ts, dm);CHKERRQ(ierr);
1540   if (user->vtkmon) {
1541     ierr = TSMonitorSet(*ts,MonitorVTK,user,NULL);CHKERRQ(ierr);
1542   }
1543   ierr = DMTSSetBoundaryLocal(dm, DMPlexTSComputeBoundary, user);CHKERRQ(ierr);
1544   ierr = DMTSSetRHSFunctionLocal(dm, DMPlexTSComputeRHSFunctionFVM, user);CHKERRQ(ierr);
1545   ierr = TSSetMaxTime(*ts,2.0);CHKERRQ(ierr);
1546   ierr = TSSetExactFinalTime(*ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr);
1547   PetscFunctionReturn(0);
1548 }
1549 
1550 static PetscErrorCode adaptToleranceFVM(PetscFV fvm, TS ts, Vec sol, VecTagger refineTag, VecTagger coarsenTag, User user, TS *tsNew, Vec *solNew)
1551 {
1552   DM                dm, gradDM, plex, cellDM, adaptedDM = NULL;
1553   Vec               cellGeom, faceGeom;
1554   PetscBool         isForest, computeGradient;
1555   Vec               grad, locGrad, locX, errVec;
1556   PetscInt          cStart, cEnd, c, dim, nRefine, nCoarsen;
1557   PetscReal         minMaxInd[2] = {PETSC_MAX_REAL, PETSC_MIN_REAL}, minMaxIndGlobal[2], minInd, maxInd, time;
1558   PetscScalar       *errArray;
1559   const PetscScalar *pointVals;
1560   const PetscScalar *pointGrads;
1561   const PetscScalar *pointGeom;
1562   DMLabel           adaptLabel = NULL;
1563   IS                refineIS, coarsenIS;
1564   PetscErrorCode    ierr;
1565 
1566   PetscFunctionBegin;
1567   ierr = TSGetTime(ts,&time);CHKERRQ(ierr);
1568   ierr = VecGetDM(sol, &dm);CHKERRQ(ierr);
1569   ierr = DMGetDimension(dm,&dim);CHKERRQ(ierr);
1570   ierr = PetscFVGetComputeGradients(fvm,&computeGradient);CHKERRQ(ierr);
1571   ierr = PetscFVSetComputeGradients(fvm,PETSC_TRUE);CHKERRQ(ierr);
1572   ierr = DMIsForest(dm, &isForest);CHKERRQ(ierr);
1573   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
1574   ierr = DMPlexGetDataFVM(plex, fvm, &cellGeom, &faceGeom, &gradDM);CHKERRQ(ierr);
1575   ierr = DMCreateLocalVector(plex,&locX);CHKERRQ(ierr);
1576   ierr = DMPlexInsertBoundaryValues(plex, PETSC_TRUE, locX, 0.0, faceGeom, cellGeom, NULL);CHKERRQ(ierr);
1577   ierr = DMGlobalToLocalBegin(plex, sol, INSERT_VALUES, locX);CHKERRQ(ierr);
1578   ierr = DMGlobalToLocalEnd  (plex, sol, INSERT_VALUES, locX);CHKERRQ(ierr);
1579   ierr = DMCreateGlobalVector(gradDM, &grad);CHKERRQ(ierr);
1580   ierr = DMPlexReconstructGradientsFVM(plex, locX, grad);CHKERRQ(ierr);
1581   ierr = DMCreateLocalVector(gradDM, &locGrad);CHKERRQ(ierr);
1582   ierr = DMGlobalToLocalBegin(gradDM, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1583   ierr = DMGlobalToLocalEnd(gradDM, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1584   ierr = VecDestroy(&grad);CHKERRQ(ierr);
1585   ierr = DMPlexGetSimplexOrBoxCells(plex,0,&cStart,&cEnd);CHKERRQ(ierr);
1586   ierr = VecGetArrayRead(locGrad,&pointGrads);CHKERRQ(ierr);
1587   ierr = VecGetArrayRead(cellGeom,&pointGeom);CHKERRQ(ierr);
1588   ierr = VecGetArrayRead(locX,&pointVals);CHKERRQ(ierr);
1589   ierr = VecGetDM(cellGeom,&cellDM);CHKERRQ(ierr);
1590   ierr = DMLabelCreate(PETSC_COMM_SELF,"adapt",&adaptLabel);CHKERRQ(ierr);
1591   ierr = VecCreateMPI(PetscObjectComm((PetscObject)plex),cEnd-cStart,PETSC_DETERMINE,&errVec);CHKERRQ(ierr);
1592   ierr = VecSetUp(errVec);CHKERRQ(ierr);
1593   ierr = VecGetArray(errVec,&errArray);CHKERRQ(ierr);
1594   for (c = cStart; c < cEnd; c++) {
1595     PetscReal             errInd = 0.;
1596     PetscScalar           *pointGrad;
1597     PetscScalar           *pointVal;
1598     PetscFVCellGeom       *cg;
1599 
1600     ierr = DMPlexPointLocalRead(gradDM,c,pointGrads,&pointGrad);CHKERRQ(ierr);
1601     ierr = DMPlexPointLocalRead(cellDM,c,pointGeom,&cg);CHKERRQ(ierr);
1602     ierr = DMPlexPointLocalRead(plex,c,pointVals,&pointVal);CHKERRQ(ierr);
1603 
1604     ierr = (user->model->errorIndicator)(dim,cg->volume,user->model->physics->dof,pointVal,pointGrad,&errInd,user->model->errorCtx);CHKERRQ(ierr);
1605     errArray[c-cStart] = errInd;
1606     minMaxInd[0] = PetscMin(minMaxInd[0],errInd);
1607     minMaxInd[1] = PetscMax(minMaxInd[1],errInd);
1608   }
1609   ierr = VecRestoreArray(errVec,&errArray);CHKERRQ(ierr);
1610   ierr = VecRestoreArrayRead(locX,&pointVals);CHKERRQ(ierr);
1611   ierr = VecRestoreArrayRead(cellGeom,&pointGeom);CHKERRQ(ierr);
1612   ierr = VecRestoreArrayRead(locGrad,&pointGrads);CHKERRQ(ierr);
1613   ierr = VecDestroy(&locGrad);CHKERRQ(ierr);
1614   ierr = VecDestroy(&locX);CHKERRQ(ierr);
1615   ierr = DMDestroy(&plex);CHKERRQ(ierr);
1616 
1617   ierr = VecTaggerComputeIS(refineTag,errVec,&refineIS);CHKERRQ(ierr);
1618   ierr = VecTaggerComputeIS(coarsenTag,errVec,&coarsenIS);CHKERRQ(ierr);
1619   ierr = ISGetSize(refineIS,&nRefine);CHKERRQ(ierr);
1620   ierr = ISGetSize(coarsenIS,&nCoarsen);CHKERRQ(ierr);
1621   if (nRefine) {ierr = DMLabelSetStratumIS(adaptLabel,DM_ADAPT_REFINE,refineIS);CHKERRQ(ierr);}
1622   if (nCoarsen) {ierr = DMLabelSetStratumIS(adaptLabel,DM_ADAPT_COARSEN,coarsenIS);CHKERRQ(ierr);}
1623   ierr = ISDestroy(&coarsenIS);CHKERRQ(ierr);
1624   ierr = ISDestroy(&refineIS);CHKERRQ(ierr);
1625   ierr = VecDestroy(&errVec);CHKERRQ(ierr);
1626 
1627   ierr = PetscFVSetComputeGradients(fvm,computeGradient);CHKERRQ(ierr);
1628   minMaxInd[1] = -minMaxInd[1];
1629   ierr = MPI_Allreduce(minMaxInd,minMaxIndGlobal,2,MPIU_REAL,MPI_MIN,PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
1630   minInd = minMaxIndGlobal[0];
1631   maxInd = -minMaxIndGlobal[1];
1632   ierr = PetscInfo2(ts, "error indicator range (%E, %E)\n", minInd, maxInd);CHKERRQ(ierr);
1633   if (nRefine || nCoarsen) { /* at least one cell is over the refinement threshold */
1634     ierr = DMAdaptLabel(dm,adaptLabel,&adaptedDM);CHKERRQ(ierr);
1635   }
1636   ierr = DMLabelDestroy(&adaptLabel);CHKERRQ(ierr);
1637   if (adaptedDM) {
1638     ierr = PetscInfo2(ts, "Adapted mesh, marking %D cells for refinement, and %D cells for coarsening\n", nRefine, nCoarsen);CHKERRQ(ierr);
1639     if (tsNew) {ierr = initializeTS(adaptedDM, user, tsNew);CHKERRQ(ierr);}
1640     if (solNew) {
1641       ierr = DMCreateGlobalVector(adaptedDM, solNew);CHKERRQ(ierr);
1642       ierr = PetscObjectSetName((PetscObject) *solNew, "solution");CHKERRQ(ierr);
1643       ierr = DMForestTransferVec(dm, sol, adaptedDM, *solNew, PETSC_TRUE, time);CHKERRQ(ierr);
1644     }
1645     if (isForest) {ierr = DMForestSetAdaptivityForest(adaptedDM,NULL);CHKERRQ(ierr);} /* clear internal references to the previous dm */
1646     ierr = DMDestroy(&adaptedDM);CHKERRQ(ierr);
1647   } else {
1648     if (tsNew)  *tsNew  = NULL;
1649     if (solNew) *solNew = NULL;
1650   }
1651   PetscFunctionReturn(0);
1652 }
1653 
1654 int main(int argc, char **argv)
1655 {
1656   MPI_Comm          comm;
1657   PetscDS           prob;
1658   PetscFV           fvm;
1659   PetscLimiter      limiter = NULL, noneLimiter = NULL;
1660   User              user;
1661   Model             mod;
1662   Physics           phys;
1663   DM                dm, plex;
1664   PetscReal         ftime, cfl, dt, minRadius;
1665   PetscInt          dim, nsteps;
1666   TS                ts;
1667   TSConvergedReason reason;
1668   Vec               X;
1669   PetscViewer       viewer;
1670   PetscBool         simplex = PETSC_FALSE, vtkCellGeom, splitFaces, useAMR;
1671   PetscInt          overlap, adaptInterval;
1672   char              filename[PETSC_MAX_PATH_LEN] = "";
1673   char              physname[256]  = "advect";
1674   VecTagger         refineTag = NULL, coarsenTag = NULL;
1675   PetscErrorCode    ierr;
1676 
1677   ierr = PetscInitialize(&argc, &argv, (char*) 0, help);if (ierr) return ierr;
1678   comm = PETSC_COMM_WORLD;
1679 
1680   ierr          = PetscNew(&user);CHKERRQ(ierr);
1681   ierr          = PetscNew(&user->model);CHKERRQ(ierr);
1682   ierr          = PetscNew(&user->model->physics);CHKERRQ(ierr);
1683   mod           = user->model;
1684   phys          = mod->physics;
1685   mod->comm     = comm;
1686   useAMR        = PETSC_FALSE;
1687   adaptInterval = 1;
1688 
1689   /* Register physical models to be available on the command line */
1690   ierr = PetscFunctionListAdd(&PhysicsList,"advect"          ,PhysicsCreate_Advect);CHKERRQ(ierr);
1691   ierr = PetscFunctionListAdd(&PhysicsList,"sw"              ,PhysicsCreate_SW);CHKERRQ(ierr);
1692   ierr = PetscFunctionListAdd(&PhysicsList,"euler"           ,PhysicsCreate_Euler);CHKERRQ(ierr);
1693 
1694 
1695   ierr = PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Mesh Options","");CHKERRQ(ierr);
1696   {
1697     cfl  = 0.9 * 4; /* default SSPRKS2 with s=5 stages is stable for CFL number s-1 */
1698     ierr = PetscOptionsReal("-ufv_cfl","CFL number per step","",cfl,&cfl,NULL);CHKERRQ(ierr);
1699     ierr = PetscOptionsString("-f","Exodus.II filename to read","",filename,filename,sizeof(filename),NULL);CHKERRQ(ierr);
1700     ierr = PetscOptionsBool("-simplex","Flag to use a simplex mesh","",simplex,&simplex,NULL);CHKERRQ(ierr);
1701     splitFaces = PETSC_FALSE;
1702     ierr = PetscOptionsBool("-ufv_split_faces","Split faces between cell sets","",splitFaces,&splitFaces,NULL);CHKERRQ(ierr);
1703     overlap = 1;
1704     ierr = PetscOptionsInt("-ufv_mesh_overlap","Number of cells to overlap partitions","",overlap,&overlap,NULL);CHKERRQ(ierr);
1705     user->vtkInterval = 1;
1706     ierr = PetscOptionsInt("-ufv_vtk_interval","VTK output interval (0 to disable)","",user->vtkInterval,&user->vtkInterval,NULL);CHKERRQ(ierr);
1707     user->vtkmon = PETSC_TRUE;
1708     ierr = PetscOptionsBool("-ufv_vtk_monitor","Use VTKMonitor routine","",user->vtkmon,&user->vtkmon,NULL);CHKERRQ(ierr);
1709     vtkCellGeom = PETSC_FALSE;
1710     ierr = PetscStrcpy(user->outputBasename, "ex11");CHKERRQ(ierr);
1711     ierr = PetscOptionsString("-ufv_vtk_basename","VTK output basename","",user->outputBasename,user->outputBasename,sizeof(user->outputBasename),NULL);CHKERRQ(ierr);
1712     ierr = PetscOptionsBool("-ufv_vtk_cellgeom","Write cell geometry (for debugging)","",vtkCellGeom,&vtkCellGeom,NULL);CHKERRQ(ierr);
1713     ierr = PetscOptionsBool("-ufv_use_amr","use local adaptive mesh refinement","",useAMR,&useAMR,NULL);CHKERRQ(ierr);
1714     ierr = PetscOptionsInt("-ufv_adapt_interval","time steps between AMR","",adaptInterval,&adaptInterval,NULL);CHKERRQ(ierr);
1715   }
1716   ierr = PetscOptionsEnd();CHKERRQ(ierr);
1717 
1718   if (useAMR) {
1719     VecTaggerBox refineBox, coarsenBox;
1720 
1721     refineBox.min  = refineBox.max  = PETSC_MAX_REAL;
1722     coarsenBox.min = coarsenBox.max = PETSC_MIN_REAL;
1723 
1724     ierr = VecTaggerCreate(comm,&refineTag);CHKERRQ(ierr);
1725     ierr = PetscObjectSetOptionsPrefix((PetscObject)refineTag,"refine_");CHKERRQ(ierr);
1726     ierr = VecTaggerSetType(refineTag,VECTAGGERABSOLUTE);CHKERRQ(ierr);
1727     ierr = VecTaggerAbsoluteSetBox(refineTag,&refineBox);CHKERRQ(ierr);
1728     ierr = VecTaggerSetFromOptions(refineTag);CHKERRQ(ierr);
1729     ierr = VecTaggerSetUp(refineTag);CHKERRQ(ierr);
1730     ierr = PetscObjectViewFromOptions((PetscObject)refineTag,NULL,"-tag_view");CHKERRQ(ierr);
1731 
1732     ierr = VecTaggerCreate(comm,&coarsenTag);CHKERRQ(ierr);
1733     ierr = PetscObjectSetOptionsPrefix((PetscObject)coarsenTag,"coarsen_");CHKERRQ(ierr);
1734     ierr = VecTaggerSetType(coarsenTag,VECTAGGERABSOLUTE);CHKERRQ(ierr);
1735     ierr = VecTaggerAbsoluteSetBox(coarsenTag,&coarsenBox);CHKERRQ(ierr);
1736     ierr = VecTaggerSetFromOptions(coarsenTag);CHKERRQ(ierr);
1737     ierr = VecTaggerSetUp(coarsenTag);CHKERRQ(ierr);
1738     ierr = PetscObjectViewFromOptions((PetscObject)coarsenTag,NULL,"-tag_view");CHKERRQ(ierr);
1739   }
1740 
1741   ierr = PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Physics Options","");CHKERRQ(ierr);
1742   {
1743     PetscErrorCode (*physcreate)(Model,Physics,PetscOptionItems*);
1744     ierr = PetscOptionsFList("-physics","Physics module to solve","",PhysicsList,physname,physname,sizeof physname,NULL);CHKERRQ(ierr);
1745     ierr = PetscFunctionListFind(PhysicsList,physname,&physcreate);CHKERRQ(ierr);
1746     ierr = PetscMemzero(phys,sizeof(struct _n_Physics));CHKERRQ(ierr);
1747     ierr = (*physcreate)(mod,phys,PetscOptionsObject);CHKERRQ(ierr);
1748     /* Count number of fields and dofs */
1749     for (phys->nfields=0,phys->dof=0; phys->field_desc[phys->nfields].name; phys->nfields++) phys->dof += phys->field_desc[phys->nfields].dof;
1750     if (phys->dof <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set dof",physname);
1751     ierr = ModelFunctionalSetFromOptions(mod,PetscOptionsObject);CHKERRQ(ierr);
1752   }
1753   ierr = PetscOptionsEnd();CHKERRQ(ierr);
1754 
1755   /* Create mesh */
1756   {
1757     size_t len,i;
1758     for (i = 0; i < DIM; i++) { mod->bounds[2*i] = 0.; mod->bounds[2*i+1] = 1.;};
1759     ierr = PetscStrlen(filename,&len);CHKERRQ(ierr);
1760     dim = DIM;
1761     if (!len) { /* a null name means just do a hex box */
1762       PetscInt cells[3] = {1, 1, 1}; /* coarse mesh is one cell; refine from there */
1763       PetscBool flg1, flg2, skew = PETSC_FALSE;
1764       PetscInt nret1 = DIM;
1765       PetscInt nret2 = 2*DIM;
1766       ierr = PetscOptionsBegin(comm,NULL,"Rectangular mesh options","");CHKERRQ(ierr);
1767       ierr = PetscOptionsIntArray("-grid_size","number of cells in each direction","",cells,&nret1,&flg1);CHKERRQ(ierr);
1768       ierr = PetscOptionsRealArray("-grid_bounds","bounds of the mesh in each direction (i.e., x_min,x_max,y_min,y_max","",mod->bounds,&nret2,&flg2);CHKERRQ(ierr);
1769       ierr = PetscOptionsBool("-grid_skew_60","Skew grid for 60 degree shock mesh","",skew,&skew,NULL);CHKERRQ(ierr);
1770       ierr = PetscOptionsEnd();CHKERRQ(ierr);
1771       if (flg1) {
1772         dim = nret1;
1773         if (dim != DIM) SETERRQ1(comm,PETSC_ERR_ARG_SIZ,"Dim wrong size %D in -grid_size",dim);
1774       }
1775       ierr = DMPlexCreateBoxMesh(comm, dim, simplex, cells, NULL, NULL, mod->bcs, PETSC_TRUE, &dm);CHKERRQ(ierr);
1776       if (flg2) {
1777         PetscInt dimEmbed, i;
1778         PetscInt nCoords;
1779         PetscScalar *coords;
1780         Vec coordinates;
1781 
1782         ierr = DMGetCoordinatesLocal(dm,&coordinates);CHKERRQ(ierr);
1783         ierr = DMGetCoordinateDim(dm,&dimEmbed);CHKERRQ(ierr);
1784         ierr = VecGetLocalSize(coordinates,&nCoords);CHKERRQ(ierr);
1785         if (nCoords % dimEmbed) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Coordinate vector the wrong size");
1786         ierr = VecGetArray(coordinates,&coords);CHKERRQ(ierr);
1787         for (i = 0; i < nCoords; i += dimEmbed) {
1788           PetscInt j;
1789 
1790           PetscScalar *coord = &coords[i];
1791           for (j = 0; j < dimEmbed; j++) {
1792             coord[j] = mod->bounds[2 * j] + coord[j] * (mod->bounds[2 * j + 1] - mod->bounds[2 * j]);
1793             if (dim==2 && cells[1]==1 && j==0 && skew) {
1794               if (cells[0]==2 && i==8) {
1795                 coord[j] = .57735026918963; /* hack to get 60 deg skewed mesh */
1796               }
1797               else if (cells[0]==3) {
1798                 if (i==2 || i==10) coord[j] = mod->bounds[1]/4.;
1799                 else if (i==4) coord[j] = mod->bounds[1]/2.;
1800                 else if (i==12) coord[j] = 1.57735026918963*mod->bounds[1]/2.;
1801               }
1802             }
1803           }
1804         }
1805         ierr = VecRestoreArray(coordinates,&coords);CHKERRQ(ierr);
1806         ierr = DMSetCoordinatesLocal(dm,coordinates);CHKERRQ(ierr);
1807       }
1808     } else {
1809       ierr = DMPlexCreateFromFile(comm, filename, PETSC_TRUE, &dm);CHKERRQ(ierr);
1810     }
1811   }
1812   ierr = DMViewFromOptions(dm, NULL, "-orig_dm_view");CHKERRQ(ierr);
1813   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1814 
1815   /* set up BCs, functions, tags */
1816   ierr = DMCreateLabel(dm, "Face Sets");CHKERRQ(ierr);
1817 
1818   mod->errorIndicator = ErrorIndicator_Simple;
1819 
1820   {
1821     DM dmDist;
1822 
1823     ierr = DMSetBasicAdjacency(dm, PETSC_TRUE, PETSC_FALSE);CHKERRQ(ierr);
1824     ierr = DMPlexDistribute(dm, overlap, NULL, &dmDist);CHKERRQ(ierr);
1825     if (dmDist) {
1826       ierr = DMDestroy(&dm);CHKERRQ(ierr);
1827       dm   = dmDist;
1828     }
1829   }
1830 
1831   ierr = DMSetFromOptions(dm);CHKERRQ(ierr);
1832 
1833   {
1834     DM gdm;
1835 
1836     ierr = DMPlexConstructGhostCells(dm, NULL, NULL, &gdm);CHKERRQ(ierr);
1837     ierr = DMDestroy(&dm);CHKERRQ(ierr);
1838     dm   = gdm;
1839     ierr = DMViewFromOptions(dm, NULL, "-dm_view");CHKERRQ(ierr);
1840   }
1841   if (splitFaces) {ierr = ConstructCellBoundary(dm, user);CHKERRQ(ierr);}
1842   ierr = SplitFaces(&dm, "split faces", user);CHKERRQ(ierr);
1843 
1844   ierr = PetscFVCreate(comm, &fvm);CHKERRQ(ierr);
1845   ierr = PetscFVSetFromOptions(fvm);CHKERRQ(ierr);
1846   ierr = PetscFVSetNumComponents(fvm, phys->dof);CHKERRQ(ierr);
1847   ierr = PetscFVSetSpatialDimension(fvm, dim);CHKERRQ(ierr);
1848   ierr = PetscObjectSetName((PetscObject) fvm,"");CHKERRQ(ierr);
1849   {
1850     PetscInt f, dof;
1851     for (f=0,dof=0; f < phys->nfields; f++) {
1852       PetscInt newDof = phys->field_desc[f].dof;
1853 
1854       if (newDof == 1) {
1855         ierr = PetscFVSetComponentName(fvm,dof,phys->field_desc[f].name);CHKERRQ(ierr);
1856       }
1857       else {
1858         PetscInt j;
1859 
1860         for (j = 0; j < newDof; j++) {
1861           char     compName[256]  = "Unknown";
1862 
1863           ierr = PetscSNPrintf(compName,sizeof(compName),"%s_%d",phys->field_desc[f].name,j);CHKERRQ(ierr);
1864           ierr = PetscFVSetComponentName(fvm,dof+j,compName);CHKERRQ(ierr);
1865         }
1866       }
1867       dof += newDof;
1868     }
1869   }
1870   /* FV is now structured with one field having all physics as components */
1871   ierr = DMAddField(dm, NULL, (PetscObject) fvm);CHKERRQ(ierr);
1872   ierr = DMCreateDS(dm);CHKERRQ(ierr);
1873   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1874   ierr = PetscDSSetRiemannSolver(prob, 0, user->model->physics->riemann);CHKERRQ(ierr);
1875   ierr = PetscDSSetContext(prob, 0, user->model->physics);CHKERRQ(ierr);
1876   ierr = (*mod->setupbc)(prob,phys);CHKERRQ(ierr);
1877   ierr = PetscDSSetFromOptions(prob);CHKERRQ(ierr);
1878   {
1879     char      convType[256];
1880     PetscBool flg;
1881 
1882     ierr = PetscOptionsBegin(comm, "", "Mesh conversion options", "DMPLEX");CHKERRQ(ierr);
1883     ierr = PetscOptionsFList("-dm_type","Convert DMPlex to another format","ex12",DMList,DMPLEX,convType,256,&flg);CHKERRQ(ierr);
1884     ierr = PetscOptionsEnd();CHKERRQ(ierr);
1885     if (flg) {
1886       DM dmConv;
1887 
1888       ierr = DMConvert(dm,convType,&dmConv);CHKERRQ(ierr);
1889       if (dmConv) {
1890         ierr = DMViewFromOptions(dmConv, NULL, "-dm_conv_view");CHKERRQ(ierr);
1891         ierr = DMDestroy(&dm);CHKERRQ(ierr);
1892         dm   = dmConv;
1893         ierr = DMSetFromOptions(dm);CHKERRQ(ierr);
1894       }
1895     }
1896   }
1897 
1898   ierr = initializeTS(dm, user, &ts);CHKERRQ(ierr);
1899 
1900   ierr = DMCreateGlobalVector(dm, &X);CHKERRQ(ierr);
1901   ierr = PetscObjectSetName((PetscObject) X, "solution");CHKERRQ(ierr);
1902   ierr = SetInitialCondition(dm, X, user);CHKERRQ(ierr);
1903   if (useAMR) {
1904     PetscInt adaptIter;
1905 
1906     /* use no limiting when reconstructing gradients for adaptivity */
1907     ierr = PetscFVGetLimiter(fvm, &limiter);CHKERRQ(ierr);
1908     ierr = PetscObjectReference((PetscObject) limiter);CHKERRQ(ierr);
1909     ierr = PetscLimiterCreate(PetscObjectComm((PetscObject) fvm), &noneLimiter);CHKERRQ(ierr);
1910     ierr = PetscLimiterSetType(noneLimiter, PETSCLIMITERNONE);CHKERRQ(ierr);
1911 
1912     ierr = PetscFVSetLimiter(fvm, noneLimiter);CHKERRQ(ierr);
1913     for (adaptIter = 0; ; ++adaptIter) {
1914       PetscLogDouble bytes;
1915       TS             tsNew = NULL;
1916 
1917       ierr = PetscMemoryGetCurrentUsage(&bytes);CHKERRQ(ierr);
1918       ierr = PetscInfo2(ts, "refinement loop %D: memory used %g\n", adaptIter, bytes);CHKERRQ(ierr);
1919       ierr = DMViewFromOptions(dm, NULL, "-initial_dm_view");CHKERRQ(ierr);
1920       ierr = VecViewFromOptions(X, NULL, "-initial_vec_view");CHKERRQ(ierr);
1921 #if 0
1922       if (viewInitial) {
1923         PetscViewer viewer;
1924         char        buf[256];
1925         PetscBool   isHDF5, isVTK;
1926 
1927         ierr = PetscViewerCreate(comm,&viewer);CHKERRQ(ierr);
1928         ierr = PetscViewerSetType(viewer,PETSCVIEWERVTK);CHKERRQ(ierr);
1929         ierr = PetscViewerSetOptionsPrefix(viewer,"initial_");CHKERRQ(ierr);
1930         ierr = PetscViewerSetFromOptions(viewer);CHKERRQ(ierr);
1931         ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERHDF5,&isHDF5);CHKERRQ(ierr);
1932         ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERVTK,&isVTK);CHKERRQ(ierr);
1933         if (isHDF5) {
1934           ierr = PetscSNPrintf(buf, 256, "ex11-initial-%d.h5", adaptIter);CHKERRQ(ierr);
1935         } else if (isVTK) {
1936           ierr = PetscSNPrintf(buf, 256, "ex11-initial-%d.vtu", adaptIter);CHKERRQ(ierr);
1937           ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_VTK_VTU);CHKERRQ(ierr);
1938         }
1939         ierr = PetscViewerFileSetMode(viewer,FILE_MODE_WRITE);CHKERRQ(ierr);
1940         ierr = PetscViewerFileSetName(viewer,buf);CHKERRQ(ierr);
1941         if (isHDF5) {
1942           ierr = DMView(dm,viewer);CHKERRQ(ierr);
1943           ierr = PetscViewerFileSetMode(viewer,FILE_MODE_UPDATE);CHKERRQ(ierr);
1944         }
1945         ierr = VecView(X,viewer);CHKERRQ(ierr);
1946         ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
1947       }
1948 #endif
1949 
1950       ierr = adaptToleranceFVM(fvm, ts, X, refineTag, coarsenTag, user, &tsNew, NULL);CHKERRQ(ierr);
1951       if (!tsNew) {
1952         break;
1953       } else {
1954         ierr = DMDestroy(&dm);CHKERRQ(ierr);
1955         ierr = VecDestroy(&X);CHKERRQ(ierr);
1956         ierr = TSDestroy(&ts);CHKERRQ(ierr);
1957         ts   = tsNew;
1958         ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1959         ierr = PetscObjectReference((PetscObject)dm);CHKERRQ(ierr);
1960         ierr = DMCreateGlobalVector(dm,&X);CHKERRQ(ierr);
1961         ierr = PetscObjectSetName((PetscObject) X, "solution");CHKERRQ(ierr);
1962         ierr = SetInitialCondition(dm, X, user);CHKERRQ(ierr);
1963       }
1964     }
1965     /* restore original limiter */
1966     ierr = PetscFVSetLimiter(fvm, limiter);CHKERRQ(ierr);
1967   }
1968 
1969   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
1970   if (vtkCellGeom) {
1971     DM  dmCell;
1972     Vec cellgeom, partition;
1973 
1974     ierr = DMPlexGetGeometryFVM(plex, NULL, &cellgeom, NULL);CHKERRQ(ierr);
1975     ierr = OutputVTK(dm, "ex11-cellgeom.vtk", &viewer);CHKERRQ(ierr);
1976     ierr = VecView(cellgeom, viewer);CHKERRQ(ierr);
1977     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
1978     ierr = CreatePartitionVec(dm, &dmCell, &partition);CHKERRQ(ierr);
1979     ierr = OutputVTK(dmCell, "ex11-partition.vtk", &viewer);CHKERRQ(ierr);
1980     ierr = VecView(partition, viewer);CHKERRQ(ierr);
1981     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
1982     ierr = VecDestroy(&partition);CHKERRQ(ierr);
1983     ierr = DMDestroy(&dmCell);CHKERRQ(ierr);
1984   }
1985   /* collect max maxspeed from all processes -- todo */
1986   ierr = DMPlexGetGeometryFVM(plex, NULL, NULL, &minRadius);CHKERRQ(ierr);
1987   ierr = DMDestroy(&plex);CHKERRQ(ierr);
1988   ierr = MPI_Allreduce(&phys->maxspeed,&mod->maxspeed,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
1989   if (mod->maxspeed <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set maxspeed",physname);
1990   dt   = cfl * minRadius / mod->maxspeed;
1991   ierr = TSSetTimeStep(ts,dt);CHKERRQ(ierr);
1992   ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
1993   if (!useAMR) {
1994     ierr = TSSolve(ts,X);CHKERRQ(ierr);
1995     ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
1996     ierr = TSGetStepNumber(ts,&nsteps);CHKERRQ(ierr);
1997   } else {
1998     PetscReal finalTime;
1999     PetscInt  adaptIter;
2000     TS        tsNew = NULL;
2001     Vec       solNew = NULL;
2002 
2003     ierr   = TSGetMaxTime(ts,&finalTime);CHKERRQ(ierr);
2004     ierr   = TSSetMaxSteps(ts,adaptInterval);CHKERRQ(ierr);
2005     ierr   = TSSolve(ts,X);CHKERRQ(ierr);
2006     ierr   = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
2007     ierr   = TSGetStepNumber(ts,&nsteps);CHKERRQ(ierr);
2008     for (adaptIter = 0;ftime < finalTime;adaptIter++) {
2009       PetscLogDouble bytes;
2010 
2011       ierr = PetscMemoryGetCurrentUsage(&bytes);CHKERRQ(ierr);
2012       ierr = PetscInfo2(ts, "AMR time step loop %D: memory used %g\n", adaptIter, bytes);CHKERRQ(ierr);
2013       ierr = PetscFVSetLimiter(fvm,noneLimiter);CHKERRQ(ierr);
2014       ierr = adaptToleranceFVM(fvm,ts,X,refineTag,coarsenTag,user,&tsNew,&solNew);CHKERRQ(ierr);
2015       ierr = PetscFVSetLimiter(fvm,limiter);CHKERRQ(ierr);
2016       if (tsNew) {
2017         ierr = PetscInfo(ts, "AMR used\n");CHKERRQ(ierr);
2018         ierr = DMDestroy(&dm);CHKERRQ(ierr);
2019         ierr = VecDestroy(&X);CHKERRQ(ierr);
2020         ierr = TSDestroy(&ts);CHKERRQ(ierr);
2021         ts   = tsNew;
2022         X    = solNew;
2023         ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
2024         ierr = VecGetDM(X,&dm);CHKERRQ(ierr);
2025         ierr = PetscObjectReference((PetscObject)dm);CHKERRQ(ierr);
2026         ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
2027         ierr = DMPlexGetGeometryFVM(dm, NULL, NULL, &minRadius);CHKERRQ(ierr);
2028         ierr = DMDestroy(&plex);CHKERRQ(ierr);
2029         ierr = MPI_Allreduce(&phys->maxspeed,&mod->maxspeed,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
2030         if (mod->maxspeed <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set maxspeed",physname);
2031         dt   = cfl * minRadius / mod->maxspeed;
2032         ierr = TSSetStepNumber(ts,nsteps);CHKERRQ(ierr);
2033         ierr = TSSetTime(ts,ftime);CHKERRQ(ierr);
2034         ierr = TSSetTimeStep(ts,dt);CHKERRQ(ierr);
2035       } else {
2036         ierr = PetscInfo(ts, "AMR not used\n");CHKERRQ(ierr);
2037       }
2038       user->monitorStepOffset = nsteps;
2039       ierr = TSSetMaxSteps(ts,nsteps+adaptInterval);CHKERRQ(ierr);
2040       ierr = TSSolve(ts,X);CHKERRQ(ierr);
2041       ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
2042       ierr = TSGetStepNumber(ts,&nsteps);CHKERRQ(ierr);
2043     }
2044   }
2045   ierr = TSGetConvergedReason(ts,&reason);CHKERRQ(ierr);
2046   ierr = PetscPrintf(PETSC_COMM_WORLD,"%s at time %g after %D steps\n",TSConvergedReasons[reason],(double)ftime,nsteps);CHKERRQ(ierr);
2047   ierr = TSDestroy(&ts);CHKERRQ(ierr);
2048 
2049   ierr = VecTaggerDestroy(&refineTag);CHKERRQ(ierr);
2050   ierr = VecTaggerDestroy(&coarsenTag);CHKERRQ(ierr);
2051   ierr = PetscFunctionListDestroy(&PhysicsList);CHKERRQ(ierr);
2052   ierr = PetscFunctionListDestroy(&PhysicsRiemannList_SW);CHKERRQ(ierr);
2053   ierr = FunctionalLinkDestroy(&user->model->functionalRegistry);CHKERRQ(ierr);
2054   ierr = PetscFree(user->model->functionalMonitored);CHKERRQ(ierr);
2055   ierr = PetscFree(user->model->functionalCall);CHKERRQ(ierr);
2056   ierr = PetscFree(user->model->physics->data);CHKERRQ(ierr);
2057   ierr = PetscFree(user->model->physics);CHKERRQ(ierr);
2058   ierr = PetscFree(user->model);CHKERRQ(ierr);
2059   ierr = PetscFree(user);CHKERRQ(ierr);
2060   ierr = VecDestroy(&X);CHKERRQ(ierr);
2061   ierr = PetscLimiterDestroy(&limiter);CHKERRQ(ierr);
2062   ierr = PetscLimiterDestroy(&noneLimiter);CHKERRQ(ierr);
2063   ierr = PetscFVDestroy(&fvm);CHKERRQ(ierr);
2064   ierr = DMDestroy(&dm);CHKERRQ(ierr);
2065   ierr = PetscFinalize();
2066   return ierr;
2067 }
2068 
2069 /* Godunov fluxs */
2070 PetscScalar cvmgp_(PetscScalar *a, PetscScalar *b, PetscScalar *test)
2071 {
2072     /* System generated locals */
2073     PetscScalar ret_val;
2074 
2075     if (PetscRealPart(*test) > 0.) {
2076         goto L10;
2077     }
2078     ret_val = *b;
2079     return ret_val;
2080 L10:
2081     ret_val = *a;
2082     return ret_val;
2083 } /* cvmgp_ */
2084 
2085 PetscScalar cvmgm_(PetscScalar *a, PetscScalar *b, PetscScalar *test)
2086 {
2087     /* System generated locals */
2088     PetscScalar ret_val;
2089 
2090     if (PetscRealPart(*test) < 0.) {
2091         goto L10;
2092     }
2093     ret_val = *b;
2094     return ret_val;
2095 L10:
2096     ret_val = *a;
2097     return ret_val;
2098 } /* cvmgm_ */
2099 
2100 int riem1mdt( PetscScalar *gaml, PetscScalar *gamr, PetscScalar *rl, PetscScalar *pl,
2101               PetscScalar *uxl, PetscScalar *rr, PetscScalar *pr,
2102               PetscScalar *uxr, PetscScalar *rstarl, PetscScalar *rstarr, PetscScalar *
2103               pstar, PetscScalar *ustar)
2104 {
2105     /* Initialized data */
2106 
2107     static PetscScalar smallp = 1e-8;
2108 
2109     /* System generated locals */
2110     int i__1;
2111     PetscScalar d__1, d__2;
2112 
2113     /* Local variables */
2114     static int i0;
2115     static PetscScalar cl, cr, wl, zl, wr, zr, pst, durl, skpr1, skpr2;
2116     static int iwave;
2117     static PetscScalar gascl4, gascr4, cstarl, dpstar, cstarr;
2118     /* static PetscScalar csqrl, csqrr, gascl1, gascl2, gascl3, gascr1, gascr2, gascr3; */
2119     static int iterno;
2120     static PetscScalar ustarl, ustarr, rarepr1, rarepr2;
2121 
2122 
2123 
2124     /* gascl1 = *gaml - 1.; */
2125     /* gascl2 = (*gaml + 1.) * .5; */
2126     /* gascl3 = gascl2 / *gaml; */
2127     gascl4 = 1. / (*gaml - 1.);
2128 
2129     /* gascr1 = *gamr - 1.; */
2130     /* gascr2 = (*gamr + 1.) * .5; */
2131     /* gascr3 = gascr2 / *gamr; */
2132     gascr4 = 1. / (*gamr - 1.);
2133     iterno = 10;
2134 /*        find pstar: */
2135     cl = PetscSqrtScalar(*gaml * *pl / *rl);
2136     cr = PetscSqrtScalar(*gamr * *pr / *rr);
2137     wl = *rl * cl;
2138     wr = *rr * cr;
2139     /* csqrl = wl * wl; */
2140     /* csqrr = wr * wr; */
2141     *pstar = (wl * *pr + wr * *pl) / (wl + wr);
2142     *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
2143     pst = *pl / *pr;
2144     skpr1 = cr * (pst - 1.) * PetscSqrtScalar(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
2145     d__1 = (*gamr - 1.) / (*gamr * 2.);
2146     rarepr2 = gascr4 * 2. * cr * (1. - PetscPowScalar(pst, d__1));
2147     pst = *pr / *pl;
2148     skpr2 = cl * (pst - 1.) * PetscSqrtScalar(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
2149     d__1 = (*gaml - 1.) / (*gaml * 2.);
2150     rarepr1 = gascl4 * 2. * cl * (1. - PetscPowScalar(pst, d__1));
2151     durl = *uxr - *uxl;
2152     if (PetscRealPart(*pr) < PetscRealPart(*pl)) {
2153         if (PetscRealPart(durl) >= PetscRealPart(rarepr1)) {
2154             iwave = 100;
2155         } else if (PetscRealPart(durl) <= PetscRealPart(-skpr1)) {
2156             iwave = 300;
2157         } else {
2158             iwave = 400;
2159         }
2160     } else {
2161         if (PetscRealPart(durl) >= PetscRealPart(rarepr2)) {
2162             iwave = 100;
2163         } else if (PetscRealPart(durl) <= PetscRealPart(-skpr2)) {
2164             iwave = 300;
2165         } else {
2166             iwave = 200;
2167         }
2168     }
2169     if (iwave == 100) {
2170 /*     1-wave: rarefaction wave, 3-wave: rarefaction wave */
2171 /*     case (100) */
2172         i__1 = iterno;
2173         for (i0 = 1; i0 <= i__1; ++i0) {
2174             d__1 = *pstar / *pl;
2175             d__2 = 1. / *gaml;
2176             *rstarl = *rl * PetscPowScalar(d__1, d__2);
2177             cstarl = PetscSqrtScalar(*gaml * *pstar / *rstarl);
2178             ustarl = *uxl - gascl4 * 2. * (cstarl - cl);
2179             zl = *rstarl * cstarl;
2180             d__1 = *pstar / *pr;
2181             d__2 = 1. / *gamr;
2182             *rstarr = *rr * PetscPowScalar(d__1, d__2);
2183             cstarr = PetscSqrtScalar(*gamr * *pstar / *rstarr);
2184             ustarr = *uxr + gascr4 * 2. * (cstarr - cr);
2185             zr = *rstarr * cstarr;
2186             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
2187             *pstar -= dpstar;
2188             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
2189             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
2190 #if 0
2191         break;
2192 #endif
2193             }
2194         }
2195 /*     1-wave: shock wave, 3-wave: rarefaction wave */
2196     } else if (iwave == 200) {
2197 /*     case (200) */
2198         i__1 = iterno;
2199         for (i0 = 1; i0 <= i__1; ++i0) {
2200             pst = *pstar / *pl;
2201             ustarl = *uxl - (pst - 1.) * cl * PetscSqrtScalar(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
2202             zl = *pl / cl * PetscSqrtScalar(*gaml * 2. * (*gaml - 1. + (*gaml + 1.) * pst)) * (*gaml - 1. + (*gaml + 1.) * pst) / (*gaml * 3. - 1. + (*gaml + 1.) * pst);
2203             d__1 = *pstar / *pr;
2204             d__2 = 1. / *gamr;
2205             *rstarr = *rr * PetscPowScalar(d__1, d__2);
2206             cstarr = PetscSqrtScalar(*gamr * *pstar / *rstarr);
2207             zr = *rstarr * cstarr;
2208             ustarr = *uxr + gascr4 * 2. * (cstarr - cr);
2209             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
2210             *pstar -= dpstar;
2211             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
2212             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
2213 #if 0
2214         break;
2215 #endif
2216             }
2217         }
2218 /*     1-wave: shock wave, 3-wave: shock */
2219     } else if (iwave == 300) {
2220 /*     case (300) */
2221         i__1 = iterno;
2222         for (i0 = 1; i0 <= i__1; ++i0) {
2223             pst = *pstar / *pl;
2224             ustarl = *uxl - (pst - 1.) * cl * PetscSqrtScalar(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
2225             zl = *pl / cl * PetscSqrtScalar(*gaml * 2. * (*gaml - 1. + (*gaml + 1.) * pst)) * (*gaml - 1. + (*gaml + 1.) * pst) / (*gaml * 3. - 1. + (*gaml + 1.) * pst);
2226             pst = *pstar / *pr;
2227             ustarr = *uxr + (pst - 1.) * cr * PetscSqrtScalar(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
2228             zr = *pr / cr * PetscSqrtScalar(*gamr * 2. * (*gamr - 1. + (*gamr + 1.) * pst)) * (*gamr - 1. + (*gamr + 1.) * pst) / (*gamr * 3. - 1. + (*gamr + 1.) * pst);
2229             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
2230             *pstar -= dpstar;
2231             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
2232             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
2233 #if 0
2234         break;
2235 #endif
2236             }
2237         }
2238 /*     1-wave: rarefaction wave, 3-wave: shock */
2239     } else if (iwave == 400) {
2240 /*     case (400) */
2241         i__1 = iterno;
2242         for (i0 = 1; i0 <= i__1; ++i0) {
2243             d__1 = *pstar / *pl;
2244             d__2 = 1. / *gaml;
2245             *rstarl = *rl * PetscPowScalar(d__1, d__2);
2246             cstarl = PetscSqrtScalar(*gaml * *pstar / *rstarl);
2247             ustarl = *uxl - gascl4 * 2. * (cstarl - cl);
2248             zl = *rstarl * cstarl;
2249             pst = *pstar / *pr;
2250             ustarr = *uxr + (pst - 1.) * cr * PetscSqrtScalar(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
2251             zr = *pr / cr * PetscSqrtScalar(*gamr * 2. * (*gamr - 1. + (*gamr + 1.) * pst)) * (*gamr - 1. + (*gamr + 1.) * pst) / (*gamr * 3. - 1. + (*gamr + 1.) * pst);
2252             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
2253             *pstar -= dpstar;
2254             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
2255             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
2256 #if 0
2257               break;
2258 #endif
2259             }
2260         }
2261     }
2262 
2263     *ustar = (zl * ustarr + zr * ustarl) / (zl + zr);
2264     if (PetscRealPart(*pstar) > PetscRealPart(*pl)) {
2265         pst = *pstar / *pl;
2266         *rstarl = ((*gaml + 1.) * pst + *gaml - 1.) / ((*gaml - 1.) * pst + *
2267                 gaml + 1.) * *rl;
2268     }
2269     if (PetscRealPart(*pstar) > PetscRealPart(*pr)) {
2270         pst = *pstar / *pr;
2271         *rstarr = ((*gamr + 1.) * pst + *gamr - 1.) / ((*gamr - 1.) * pst + *
2272                 gamr + 1.) * *rr;
2273     }
2274     return iwave;
2275 }
2276 
2277 PetscScalar sign(PetscScalar x)
2278 {
2279     if (PetscRealPart(x) > 0) return 1.0;
2280     if (PetscRealPart(x) < 0) return -1.0;
2281     return 0.0;
2282 }
2283 /*        Riemann Solver */
2284 /* -------------------------------------------------------------------- */
2285 int riemannsolver(PetscScalar *xcen, PetscScalar *xp,
2286                    PetscScalar *dtt, PetscScalar *rl, PetscScalar *uxl, PetscScalar *pl,
2287                    PetscScalar *utl, PetscScalar *ubl, PetscScalar *gaml, PetscScalar *rho1l,
2288                    PetscScalar *rr, PetscScalar *uxr, PetscScalar *pr, PetscScalar *utr,
2289                    PetscScalar *ubr, PetscScalar *gamr, PetscScalar *rho1r, PetscScalar *rx,
2290                    PetscScalar *uxm, PetscScalar *px, PetscScalar *utx, PetscScalar *ubx,
2291                    PetscScalar *gam, PetscScalar *rho1)
2292 {
2293     /* System generated locals */
2294     PetscScalar d__1, d__2;
2295 
2296     /* Local variables */
2297     static PetscScalar s, c0, p0, r0, u0, w0, x0, x2, ri, cx, sgn0, wsp0, gasc1, gasc2, gasc3, gasc4;
2298     static PetscScalar cstar, pstar, rstar, ustar, xstar, wspst, ushock, streng, rstarl, rstarr, rstars;
2299     int iwave;
2300 
2301     if (*rl == *rr && *pr == *pl && *uxl == *uxr && *gaml == *gamr) {
2302         *rx = *rl;
2303         *px = *pl;
2304         *uxm = *uxl;
2305         *gam = *gaml;
2306         x2 = *xcen + *uxm * *dtt;
2307 
2308         if (PetscRealPart(*xp) >= PetscRealPart(x2)) {
2309             *utx = *utr;
2310             *ubx = *ubr;
2311             *rho1 = *rho1r;
2312         } else {
2313             *utx = *utl;
2314             *ubx = *ubl;
2315             *rho1 = *rho1l;
2316         }
2317         return 0;
2318     }
2319     iwave = riem1mdt(gaml, gamr, rl, pl, uxl, rr, pr, uxr, &rstarl, &rstarr, &pstar, &ustar);
2320 
2321     x2 = *xcen + ustar * *dtt;
2322     d__1 = *xp - x2;
2323     sgn0 = sign(d__1);
2324 /*            x is in 3-wave if sgn0 = 1 */
2325 /*            x is in 1-wave if sgn0 = -1 */
2326     r0 = cvmgm_(rl, rr, &sgn0);
2327     p0 = cvmgm_(pl, pr, &sgn0);
2328     u0 = cvmgm_(uxl, uxr, &sgn0);
2329     *gam = cvmgm_(gaml, gamr, &sgn0);
2330     gasc1 = *gam - 1.;
2331     gasc2 = (*gam + 1.) * .5;
2332     gasc3 = gasc2 / *gam;
2333     gasc4 = 1. / (*gam - 1.);
2334     c0 = PetscSqrtScalar(*gam * p0 / r0);
2335     streng = pstar - p0;
2336     w0 = *gam * r0 * p0 * (gasc3 * streng / p0 + 1.);
2337     rstars = r0 / (1. - r0 * streng / w0);
2338     d__1 = p0 / pstar;
2339     d__2 = -1. / *gam;
2340     rstarr = r0 * PetscPowScalar(d__1, d__2);
2341     rstar = cvmgm_(&rstarr, &rstars, &streng);
2342     w0 = PetscSqrtScalar(w0);
2343     cstar = PetscSqrtScalar(*gam * pstar / rstar);
2344     wsp0 = u0 + sgn0 * c0;
2345     wspst = ustar + sgn0 * cstar;
2346     ushock = ustar + sgn0 * w0 / rstar;
2347     wspst = cvmgp_(&ushock, &wspst, &streng);
2348     wsp0 = cvmgp_(&ushock, &wsp0, &streng);
2349     x0 = *xcen + wsp0 * *dtt;
2350     xstar = *xcen + wspst * *dtt;
2351 /*           using gas formula to evaluate rarefaction wave */
2352 /*            ri : reiman invariant */
2353     ri = u0 - sgn0 * 2. * gasc4 * c0;
2354     cx = sgn0 * .5 * gasc1 / gasc2 * ((*xp - *xcen) / *dtt - ri);
2355     *uxm = ri + sgn0 * 2. * gasc4 * cx;
2356     s = p0 / PetscPowScalar(r0, *gam);
2357     d__1 = cx * cx / (*gam * s);
2358     *rx = PetscPowScalar(d__1, gasc4);
2359     *px = cx * cx * *rx / *gam;
2360     d__1 = sgn0 * (x0 - *xp);
2361     *rx = cvmgp_(rx, &r0, &d__1);
2362     d__1 = sgn0 * (x0 - *xp);
2363     *px = cvmgp_(px, &p0, &d__1);
2364     d__1 = sgn0 * (x0 - *xp);
2365     *uxm = cvmgp_(uxm, &u0, &d__1);
2366     d__1 = sgn0 * (xstar - *xp);
2367     *rx = cvmgm_(rx, &rstar, &d__1);
2368     d__1 = sgn0 * (xstar - *xp);
2369     *px = cvmgm_(px, &pstar, &d__1);
2370     d__1 = sgn0 * (xstar - *xp);
2371     *uxm = cvmgm_(uxm, &ustar, &d__1);
2372     if (PetscRealPart(*xp) >= PetscRealPart(x2)) {
2373         *utx = *utr;
2374         *ubx = *ubr;
2375         *rho1 = *rho1r;
2376     } else {
2377         *utx = *utl;
2378         *ubx = *ubl;
2379         *rho1 = *rho1l;
2380     }
2381     return iwave;
2382 }
2383 int godunovflux( const PetscScalar *ul, const PetscScalar *ur,
2384                  PetscScalar *flux, const PetscReal *nn, const int *ndim,
2385                  const PetscReal *gamma)
2386 {
2387     /* System generated locals */
2388   int i__1,iwave;
2389     PetscScalar d__1, d__2, d__3;
2390 
2391     /* Local variables */
2392     static int k;
2393     static PetscScalar bn[3], fn, ft, tg[3], pl, rl, pm, pr, rr, xp, ubl, ubm,
2394             ubr, dtt, unm, tmp, utl, utm, uxl, utr, uxr, gaml, gamm, gamr,
2395             xcen, rhom, rho1l, rho1m, rho1r;
2396     /* Parameter adjustments */
2397     --nn;
2398     --flux;
2399     --ur;
2400     --ul;
2401 
2402     /* Function Body */
2403     xcen = 0.;
2404     xp = 0.;
2405     i__1 = *ndim;
2406     for (k = 1; k <= i__1; ++k) {
2407         tg[k - 1] = 0.;
2408         bn[k - 1] = 0.;
2409     }
2410     dtt = 1.;
2411     if (*ndim == 3) {
2412         if (nn[1] == 0. && nn[2] == 0.) {
2413             tg[0] = 1.;
2414         } else {
2415             tg[0] = -nn[2];
2416             tg[1] = nn[1];
2417         }
2418 /*           tmp=dsqrt(tg(1)**2+tg(2)**2) */
2419 /*           tg=tg/tmp */
2420         bn[0] = -nn[3] * tg[1];
2421         bn[1] = nn[3] * tg[0];
2422         bn[2] = nn[1] * tg[1] - nn[2] * tg[0];
2423 /* Computing 2nd power */
2424         d__1 = bn[0];
2425 /* Computing 2nd power */
2426         d__2 = bn[1];
2427 /* Computing 2nd power */
2428         d__3 = bn[2];
2429         tmp = PetscSqrtScalar(d__1 * d__1 + d__2 * d__2 + d__3 * d__3);
2430         i__1 = *ndim;
2431         for (k = 1; k <= i__1; ++k) {
2432             bn[k - 1] /= tmp;
2433         }
2434     } else if (*ndim == 2) {
2435         tg[0] = -nn[2];
2436         tg[1] = nn[1];
2437 /*           tmp=dsqrt(tg(1)**2+tg(2)**2) */
2438 /*           tg=tg/tmp */
2439         bn[0] = 0.;
2440         bn[1] = 0.;
2441         bn[2] = 1.;
2442     }
2443     rl = ul[1];
2444     rr = ur[1];
2445     uxl = 0.;
2446     uxr = 0.;
2447     utl = 0.;
2448     utr = 0.;
2449     ubl = 0.;
2450     ubr = 0.;
2451     i__1 = *ndim;
2452     for (k = 1; k <= i__1; ++k) {
2453         uxl += ul[k + 1] * nn[k];
2454         uxr += ur[k + 1] * nn[k];
2455         utl += ul[k + 1] * tg[k - 1];
2456         utr += ur[k + 1] * tg[k - 1];
2457         ubl += ul[k + 1] * bn[k - 1];
2458         ubr += ur[k + 1] * bn[k - 1];
2459     }
2460     uxl /= rl;
2461     uxr /= rr;
2462     utl /= rl;
2463     utr /= rr;
2464     ubl /= rl;
2465     ubr /= rr;
2466 
2467     gaml = *gamma;
2468     gamr = *gamma;
2469 /* Computing 2nd power */
2470     d__1 = uxl;
2471 /* Computing 2nd power */
2472     d__2 = utl;
2473 /* Computing 2nd power */
2474     d__3 = ubl;
2475     pl = (*gamma - 1.) * (ul[*ndim + 2] - rl * .5 * (d__1 * d__1 + d__2 * d__2 + d__3 * d__3));
2476 /* Computing 2nd power */
2477     d__1 = uxr;
2478 /* Computing 2nd power */
2479     d__2 = utr;
2480 /* Computing 2nd power */
2481     d__3 = ubr;
2482     pr = (*gamma - 1.) * (ur[*ndim + 2] - rr * .5 * (d__1 * d__1 + d__2 * d__2 + d__3 * d__3));
2483     rho1l = rl;
2484     rho1r = rr;
2485 
2486     iwave = riemannsolver(&xcen, &xp, &dtt, &rl, &uxl, &pl, &utl, &ubl, &gaml, &
2487                           rho1l, &rr, &uxr, &pr, &utr, &ubr, &gamr, &rho1r, &rhom, &unm, &
2488                           pm, &utm, &ubm, &gamm, &rho1m);
2489 
2490     flux[1] = rhom * unm;
2491     fn = rhom * unm * unm + pm;
2492     ft = rhom * unm * utm;
2493 /*           flux(2)=fn*nn(1)+ft*nn(2) */
2494 /*           flux(3)=fn*tg(1)+ft*tg(2) */
2495     flux[2] = fn * nn[1] + ft * tg[0];
2496     flux[3] = fn * nn[2] + ft * tg[1];
2497 /*           flux(2)=rhom*unm*(unm)+pm */
2498 /*           flux(3)=rhom*(unm)*utm */
2499     if (*ndim == 3) {
2500         flux[4] = rhom * unm * ubm;
2501     }
2502     flux[*ndim + 2] = (rhom * .5 * (unm * unm + utm * utm + ubm * ubm) + gamm / (gamm - 1.) * pm) * unm;
2503     return iwave;
2504 } /* godunovflux_ */
2505 
2506 /* Subroutine to set up the initial conditions for the */
2507 /* Shock Interface interaction or linear wave (Ravi Samtaney,Mark Adams). */
2508 /* ----------------------------------------------------------------------- */
2509 int projecteqstate(PetscReal wc[], const PetscReal ueq[], PetscReal lv[][3])
2510 {
2511   int j,k;
2512 /*      Wc=matmul(lv,Ueq) 3 vars */
2513   for (k = 0; k < 3; ++k) {
2514     wc[k] = 0.;
2515     for (j = 0; j < 3; ++j) {
2516       wc[k] += lv[k][j]*ueq[j];
2517     }
2518   }
2519   return 0;
2520 }
2521 /* ----------------------------------------------------------------------- */
2522 int projecttoprim(PetscReal v[], const PetscReal wc[], PetscReal rv[][3])
2523 {
2524   int k,j;
2525   /*      V=matmul(rv,WC) 3 vars */
2526   for (k = 0; k < 3; ++k) {
2527     v[k] = 0.;
2528     for (j = 0; j < 3; ++j) {
2529       v[k] += rv[k][j]*wc[j];
2530     }
2531   }
2532   return 0;
2533 }
2534 /* ---------------------------------------------------------------------- */
2535 int eigenvectors(PetscReal rv[][3], PetscReal lv[][3], const PetscReal ueq[], PetscReal gamma)
2536 {
2537   int j,k;
2538   PetscReal rho,csnd,p0;
2539   /* PetscScalar u; */
2540 
2541   for (k = 0; k < 3; ++k) for (j = 0; j < 3; ++j) { lv[k][j] = 0.; rv[k][j] = 0.; }
2542   rho = ueq[0];
2543   /* u = ueq[1]; */
2544   p0 = ueq[2];
2545   csnd = PetscSqrtReal(gamma * p0 / rho);
2546   lv[0][1] = rho * .5;
2547   lv[0][2] = -.5 / csnd;
2548   lv[1][0] = csnd;
2549   lv[1][2] = -1. / csnd;
2550   lv[2][1] = rho * .5;
2551   lv[2][2] = .5 / csnd;
2552   rv[0][0] = -1. / csnd;
2553   rv[1][0] = 1. / rho;
2554   rv[2][0] = -csnd;
2555   rv[0][1] = 1. / csnd;
2556   rv[0][2] = 1. / csnd;
2557   rv[1][2] = 1. / rho;
2558   rv[2][2] = csnd;
2559   return 0;
2560 }
2561 
2562 int initLinearWave(EulerNode *ux, const PetscReal gamma, const PetscReal coord[], const PetscReal Lx)
2563 {
2564   PetscReal p0,u0,wcp[3],wc[3];
2565   PetscReal lv[3][3];
2566   PetscReal vp[3];
2567   PetscReal rv[3][3];
2568   PetscReal eps, ueq[3], rho0, twopi;
2569 
2570   /* Function Body */
2571   twopi = 2.*PETSC_PI;
2572   eps = 1e-4; /* perturbation */
2573   rho0 = 1e3;   /* density of water */
2574   p0 = 101325.; /* init pressure of 1 atm (?) */
2575   u0 = 0.;
2576   ueq[0] = rho0;
2577   ueq[1] = u0;
2578   ueq[2] = p0;
2579   /* Project initial state to characteristic variables */
2580   eigenvectors(rv, lv, ueq, gamma);
2581   projecteqstate(wc, ueq, lv);
2582   wcp[0] = wc[0];
2583   wcp[1] = wc[1];
2584   wcp[2] = wc[2] + eps * PetscCosReal(coord[0] * 2. * twopi / Lx);
2585   projecttoprim(vp, wcp, rv);
2586   ux->r = vp[0]; /* density */
2587   ux->ru[0] = vp[0] * vp[1]; /* x momentum */
2588   ux->ru[1] = 0.;
2589 #if defined DIM > 2
2590   if (dim>2) ux->ru[2] = 0.;
2591 #endif
2592   /* E = rho * e + rho * v^2/2 = p/(gam-1) + rho*v^2/2 */
2593   ux->E = vp[2]/(gamma - 1.) + 0.5*vp[0]*vp[1]*vp[1];
2594   return 0;
2595 }
2596 
2597 /*TEST
2598 
2599   # 2D Advection 0-10
2600   test:
2601     suffix: 0
2602     requires: exodusii
2603     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo
2604 
2605   test:
2606     suffix: 1
2607     requires: exodusii
2608     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo
2609 
2610   test:
2611     suffix: 2
2612     requires: exodusii
2613     nsize: 2
2614     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo
2615 
2616   test:
2617     suffix: 3
2618     requires: exodusii
2619     nsize: 2
2620     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo
2621 
2622   test:
2623     suffix: 4
2624     requires: exodusii
2625     nsize: 8
2626     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad.exo
2627 
2628   test:
2629     suffix: 5
2630     requires: exodusii
2631     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo -ts_type rosw -ts_adapt_reject_safety 1
2632 
2633   test:
2634     suffix: 6
2635     requires: exodusii
2636     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/squaremotor-30.exo -ufv_split_faces
2637 
2638   test:
2639     suffix: 7
2640     requires: exodusii
2641     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 1
2642 
2643   test:
2644     suffix: 8
2645     requires: exodusii
2646     nsize: 2
2647     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 1
2648 
2649   test:
2650     suffix: 9
2651     requires: exodusii
2652     nsize: 8
2653     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 1
2654 
2655   test:
2656     suffix: 10
2657     requires: exodusii
2658     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad.exo
2659 
2660   # 2D Shallow water
2661   test:
2662     suffix: sw_0
2663     requires: exodusii
2664     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
2665 
2666   test:
2667     suffix: sw_hll
2668     args: -ufv_vtk_interval 0 -bc_wall 1,2,3,4 -physics sw -ufv_cfl 3 -petscfv_type leastsquares -petsclimiter_type sin -ts_max_steps 5 -ts_ssp_type rks2 -ts_ssp_nstages 10 -monitor height,energy -grid_bounds 0,5,0,5 -grid_size 25,25 -sw_riemann hll
2669 
2670   # 2D Advection: p4est
2671   test:
2672     suffix: p4est_advec_2d
2673     requires: p4est
2674     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
2675 
2676   # Advection in a box
2677   test:
2678     suffix: adv_2d_quad_0
2679     args: -ufv_vtk_interval 0 -dm_refine 3 -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3
2680 
2681   test:
2682     suffix: adv_2d_quad_1
2683     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
2684     timeoutfactor: 3
2685 
2686   test:
2687     suffix: adv_2d_quad_p4est_0
2688     requires: p4est
2689     args: -ufv_vtk_interval 0 -dm_refine 5 -dm_type p4est -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3
2690 
2691   test:
2692     suffix: adv_2d_quad_p4est_1
2693     requires: p4est
2694     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
2695     timeoutfactor: 3
2696 
2697   test:
2698     suffix: adv_2d_quad_p4est_adapt_0
2699     requires: p4est !__float128 #broken for quad precision
2700     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
2701     timeoutfactor: 3
2702 
2703   test:
2704     suffix: adv_2d_tri_0
2705     requires: triangle
2706     TODO: how did this ever get in master when there is no support for this
2707     args: -ufv_vtk_interval 0 -simplex -dm_refine 3 -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3
2708 
2709   test:
2710     suffix: adv_2d_tri_1
2711     requires: triangle
2712     TODO: how did this ever get in master when there is no support for this
2713     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
2714 
2715   test:
2716     suffix: adv_0
2717     requires: exodusii
2718     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/blockcylinder-50.exo -bc_inflow 100,101,200 -bc_outflow 201
2719 
2720   test:
2721     suffix: shock_0
2722     requires: p4est !single !complex
2723     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
2724     timeoutfactor: 3
2725 
2726   # Test GLVis visualization of PetscFV fields
2727   test:
2728     suffix: glvis_adv_2d_tet
2729     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 -dm_plex_gmsh_periodic 0
2730 
2731   test:
2732     suffix: glvis_adv_2d_quad
2733     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
2734 
2735   test:
2736     suffix: tut_1
2737     requires: exodusii
2738     nsize: 1
2739     args: -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo
2740 
2741   test:
2742     suffix: tut_2
2743     requires: exodusii
2744     nsize: 1
2745     args: -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo -ts_type rosw
2746 
2747   test:
2748     suffix: tut_3
2749     requires: exodusii
2750     nsize: 4
2751     args: -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/annulus-20.exo -monitor Error -advect_sol_type bump -petscfv_type leastsquares -petsclimiter_type sin
2752 
2753   test:
2754     suffix: tut_4
2755     requires: exodusii
2756     nsize: 4
2757     args: -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/annulus-20.exo -physics sw -monitor Height,Energy -petscfv_type leastsquares -petsclimiter_type minmod
2758 
2759 TEST*/
2760