Actual source code: ex11.c

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

We use a second order TVD finite volume method to evolve a system of PDEs. Our simple upwinded residual evaluation loops
over all mesh faces and uses a Riemann solver to produce the flux given the face geometry and cell values,
\begin{equation}
f_i = \mathrm{riemann}(\mathrm{phys}, p_\mathrm{centroid}, \hat n, x^L, x^R)
\end{equation}
and then update the cell values given the cell volume.
\begin{eqnarray}
f^L_i &-=& \frac{f_i}{vol^L} \\
f^R_i &+=& \frac{f_i}{vol^R}
\end{eqnarray}
As an example, we can consider the shallow water wave equation,
\begin{eqnarray}
h_t + \nabla\cdot \left( uh \right) &=& 0 \\
(uh)_t + \nabla\cdot \left( u\otimes uh + \frac{g h^2}{2} I \right) &=& 0
\end{eqnarray}
where $h$ is wave height, $u$ is wave velocity, and $g$ is the acceleration due to gravity.
A representative Riemann solver for the shallow water equations is given in the PhysicsRiemann_SW() function,
\begin{eqnarray}
f^{L,R}_h &=& uh^{L,R} \cdot \hat n \\
f^{L,R}_{uh} &=& \frac{f^{L,R}_h}{h^{L,R}} uh^{L,R} + g (h^{L,R})^2 \hat n \\
c^{L,R} &=& \sqrt{g h^{L,R}} \\
s &=& \max\left( \left|\frac{uh^L \cdot \hat n}{h^L}\right| + c^L, \left|\frac{uh^R \cdot \hat n}{h^R}\right| + c^R \right) \\
f_i &=& \frac{A_\mathrm{face}}{2} \left( f^L_i + f^R_i + s \left( x^L_i - x^R_i \right) \right)
\end{eqnarray}
where $c$ is the local gravity wave speed and $f_i$ is a Rusanov flux.
The more sophisticated residual evaluation in RHSFunctionLocal_LS() uses a least-squares fit to a quadratic polynomial
over a neighborhood of the given element.
The mesh is read in from an ExodusII file, usually generated by Cubit.

     37: #include <petscdmplex.h>
     38: #include <petscdmforest.h>
     39: #include <petscds.h>
     40: #include <petscts.h>
     41: #include <petscsf.h>

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

     46: static PetscFunctionList PhysicsList, PhysicsRiemannList_SW;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    398: static void PhysicsRiemann_SW_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.;

    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: }

    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.;

    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: }

    486: static PetscErrorCode PhysicsSolution_SW(Model mod,PetscReal time,const PetscReal *x,PetscScalar *u,void *ctx)
    487: {
    488:   PetscReal dx[2],r,sigma;

    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:   return(0);
    500: }

    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;

    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:   return(0);
    517: }

    519: static PetscErrorCode SetUpBC_SW(PetscDS prob,Physics phys)
    520: {
    522:   const PetscInt wallids[] = {100,101,200,300};
    524:   PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "wall", "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_SW_Wall, NULL, ALEN(wallids), wallids, phys);
    525:   return(0);
    526: }

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

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

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

    543:   PetscOptionsHead(PetscOptionsObject,"SW options");
    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:     PetscOptionsReal("-sw_gravity","Gravitational constant","",sw->gravity,&sw->gravity,NULL);
    548:     PetscOptionsFList("-sw_riemann","Riemann solver","",PhysicsRiemannList_SW,sw_riemann,sw_riemann,sizeof sw_riemann,NULL);
    549:     PetscFunctionListFind(PhysicsRiemannList_SW,sw_riemann,&PhysicsRiemann_SW);
    550:     phys->riemann = (PetscRiemannFunc) PhysicsRiemann_SW;
    551:   }
    552:   PetscOptionsTail();
    553:   phys->maxspeed = PetscSqrtReal(2.0*sw->gravity); /* Mach 1 for depth of 2 */

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

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

    562:   return(0);
    563: }

    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;

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

    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;
    606:   if (time != 0.0) SETERRQ1(mod->comm,PETSC_ERR_SUP,"No solution known for time %g",(double)time);

    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];

    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);

    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;

    662:   return(0);
    663: }

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

    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:   return(0);
    673: }

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

    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:   return(0);
    685: }

    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;

    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:   return(0);
    708: }

    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;
    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:   return(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;

    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:     eu->sound(&eu->pars[EULER_PAR_GAMMA],uL,&cL);if (ierr) exit(13);
    758:     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: }

    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;

    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:   return(0);
    788: }

    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:     PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "wall", "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_Euler_Wall, NULL, ALEN(wallids), wallids, phys);
    797:   }
    798:   else {
    799:     const PetscInt wallids[] = {100,101,200,300};
    800:     PetscDSAddBoundary(prob, DM_BC_NATURAL_RIEMANN, "wall", "Face Sets", 0, 0, NULL, (void (*)(void)) PhysicsBoundary_Euler_Wall, NULL, ALEN(wallids), wallids, phys);
    801:   }
    802:   return(0);
    803: }

    805: static PetscErrorCode PhysicsCreate_Euler(Model mod,Physics phys,PetscOptionItems *PetscOptionsObject)
    806: {
    807:   Physics_Euler   *eu;
    808:   PetscErrorCode  ierr;

    811:   phys->field_desc = PhysicsFields_Euler;
    812:   phys->riemann = (PetscRiemannFunc) PhysicsRiemann_Euler_Godunov;
    813:   PetscNew(&eu);
    814:   phys->data    = eu;
    815:   mod->setupbc = SetUpBC_Euler;
    816:   PetscOptionsHead(PetscOptionsObject,"Euler options");
    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:     PetscOptionsReal("-eu_gamma","Heat capacity ratio","",eu->pars[EULER_PAR_GAMMA],&eu->pars[EULER_PAR_GAMMA],NULL);
    827:     PetscOptionsReal("-eu_amach","Shock speed (Mach)","",eu->pars[EULER_PAR_AMACH],&eu->pars[EULER_PAR_AMACH],NULL);
    828:     PetscOptionsReal("-eu_rho2","Density right of discontinuity","",eu->pars[EULER_PAR_RHOR],&eu->pars[EULER_PAR_RHOR],NULL);
    829:     alpha = 60.;
    830:     PetscOptionsReal("-eu_alpha","Angle of discontinuity","",alpha,&alpha,NULL);
    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:     PetscOptionsString("-eu_type","Type of Euler test","",type,type,sizeof(type),NULL);
    834:     PetscStrcmp(type,"linear_wave", &is);
    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:       PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",PETSC_FUNCTION_NAME,"linear_wave");
    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:       PetscStrcmp(type,"iv_shock", &is);
    844:       if (is) {
    845:         eu->type = EULER_IV_SHOCK;
    846:         PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",PETSC_FUNCTION_NAME,"iv_shock");
    847:       }
    848:       else {
    849:         PetscStrcmp(type,"ss_shock", &is);
    850:         if (is) {
    851:           eu->type = EULER_SS_SHOCK;
    852:           PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",PETSC_FUNCTION_NAME,"ss_shock");
    853:         }
    854:         else {
    855:           PetscStrcmp(type,"shock_tube", &is);
    856:           if (is) eu->type = EULER_SHOCK_TUBE;
    857:           else SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Unknown Euler type %s",type);
    858:           PetscPrintf(PETSC_COMM_WORLD,"%s set Euler type: %s\n",PETSC_FUNCTION_NAME,"shock_tube");
    859:         }
    860:       }
    861:     }
    862:   }
    863:   PetscOptionsTail();
    864:   eu->sound = SpeedOfSound_PG;
    865:   phys->maxspeed = 0.; /* will get set in solution */
    866:   ModelSolutionSetDefault(mod,PhysicsSolution_Euler,phys);
    867:   ModelFunctionalRegister(mod,"Speed",&eu->monitor.Speed,PhysicsFunctional_Euler,phys);
    868:   ModelFunctionalRegister(mod,"Energy",&eu->monitor.Energy,PhysicsFunctional_Euler,phys);
    869:   ModelFunctionalRegister(mod,"Density",&eu->monitor.Density,PhysicsFunctional_Euler,phys);
    870:   ModelFunctionalRegister(mod,"Momentum",&eu->monitor.Momentum,PhysicsFunctional_Euler,phys);
    871:   ModelFunctionalRegister(mod,"Pressure",&eu->monitor.Pressure,PhysicsFunctional_Euler,phys);

    873:   return(0);
    874: }

    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;

    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:   return(0);
    889: }

    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;

    903:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
    904:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
    905:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);

    907:   DMHasLabel(dm, name, &hasLabel);
    908:   if (!hasLabel) return(0);
    909:   DMGetLabelSize(dm, name, &numRegions);
    910:   if (numRegions != 2) return(0);
    911:   /* Get the inner id */
    912:   DMGetLabelIdIS(dm, name, &regionIS);
    913:   ISGetIndices(regionIS, &regions);
    914:   innerRegion = regions[0];
    915:   ISRestoreIndices(regionIS, &regions);
    916:   ISDestroy(&regionIS);
    917:   /* Find the faces between cells in different regions, could call DMPlexCreateNeighborCSR() */
    918:   DMGetStratumIS(dm, name, innerRegion, &innerIS);
    919:   ISGetLocalSize(innerIS, &numCells);
    920:   ISGetIndices(innerIS, &cells);
    921:   DMCreateLabel(dm, bdname);
    922:   for (c = 0; c < numCells; ++c) {
    923:     const PetscInt cell = cells[c];
    924:     const PetscInt *faces;
    925:     PetscInt       numFaces, f;

    927:     if ((cell < cStart) || (cell >= cEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Got invalid point %d which is not a cell", cell);
    928:     DMPlexGetConeSize(dm, cell, &numFaces);
    929:     DMPlexGetCone(dm, cell, &faces);
    930:     for (f = 0; f < numFaces; ++f) {
    931:       const PetscInt face = faces[f];
    932:       const PetscInt *neighbors;
    933:       PetscInt       nC, regionA, regionB;

    935:       if ((face < fStart) || (face >= fEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Got invalid point %d which is not a face", face);
    936:       DMPlexGetSupportSize(dm, face, &nC);
    937:       if (nC != 2) continue;
    938:       DMPlexGetSupport(dm, face, &neighbors);
    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:       DMGetLabelValue(dm, name, neighbors[0], &regionA);
    943:       DMGetLabelValue(dm, name, neighbors[1], &regionB);
    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:         DMSetLabelValue(dm, bdname, faces[f], 1);
    948:       }
    949:     }
    950:   }
    951:   ISRestoreIndices(innerIS, &cells);
    952:   ISDestroy(&innerIS);
    953:   {
    954:     DMLabel label;

    956:     DMGetLabel(dm, bdname, &label);
    957:     DMLabelView(label, PETSC_VIEWER_STDOUT_WORLD);
    958:   }
    959:   return(0);
    960: }

    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;

    981:   DMHasLabel(dm, labelName, &hasLabel);
    982:   if (!hasLabel) return(0);
    983:   DMCreate(PetscObjectComm((PetscObject)dm), &sdm);
    984:   DMSetType(sdm, DMPLEX);
    985:   DMGetDimension(dm, &dim);
    986:   DMSetDimension(sdm, dim);

    988:   DMGetLabelIdIS(dm, labelName, &idIS);
    989:   ISGetLocalSize(idIS, &numFS);
    990:   ISGetIndices(idIS, &ids);

    992:   user->numSplitFaces = 0;
    993:   for (fs = 0; fs < numFS; ++fs) {
    994:     PetscInt numBdFaces;

    996:     DMGetStratumSize(dm, labelName, ids[fs], &numBdFaces);
    997:     user->numSplitFaces += numBdFaces;
    998:   }
    999:   DMPlexGetChart(dm, &pStart, &pEnd);
    1000:   pEnd += user->numSplitFaces;
    1001:   DMPlexSetChart(sdm, pStart, pEnd);
    1002:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
    1003:   DMPlexGetHeightStratum(dm, 0, NULL, &cEnd);
    1004:   numGhostCells = cEnd - cEndInterior;
    1005:   /* Set cone and support sizes */
    1006:   DMPlexGetDepth(dm, &depth);
    1007:   for (d = 0; d <= depth; ++d) {
    1008:     DMPlexGetDepthStratum(dm, d, &pStart, &pEnd);
    1009:     for (p = pStart; p < pEnd; ++p) {
    1010:       PetscInt newp = p;
    1011:       PetscInt size;

    1013:       DMPlexGetConeSize(dm, p, &size);
    1014:       DMPlexSetConeSize(sdm, newp, size);
    1015:       DMPlexGetSupportSize(dm, p, &size);
    1016:       DMPlexSetSupportSize(sdm, newp, size);
    1017:     }
    1018:   }
    1019:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
    1020:   for (fs = 0, newf = fEnd; fs < numFS; ++fs) {
    1021:     IS             faceIS;
    1022:     const PetscInt *faces;
    1023:     PetscInt       numFaces, f;

    1025:     DMGetStratumIS(dm, labelName, ids[fs], &faceIS);
    1026:     ISGetLocalSize(faceIS, &numFaces);
    1027:     ISGetIndices(faceIS, &faces);
    1028:     for (f = 0; f < numFaces; ++f, ++newf) {
    1029:       PetscInt size;

    1031:       /* Right now I think that both faces should see both cells */
    1032:       DMPlexGetConeSize(dm, faces[f], &size);
    1033:       DMPlexSetConeSize(sdm, newf, size);
    1034:       DMPlexGetSupportSize(dm, faces[f], &size);
    1035:       DMPlexSetSupportSize(sdm, newf, size);
    1036:     }
    1037:     ISRestoreIndices(faceIS, &faces);
    1038:     ISDestroy(&faceIS);
    1039:   }
    1040:   DMSetUp(sdm);
    1041:   /* Set cones and supports */
    1042:   DMPlexGetMaxSizes(dm, &maxConeSize, &maxSupportSize);
    1043:   PetscMalloc1(PetscMax(maxConeSize, maxSupportSize), &newpoints);
    1044:   DMPlexGetChart(dm, &pStart, &pEnd);
    1045:   for (p = pStart; p < pEnd; ++p) {
    1046:     const PetscInt *points, *orientations;
    1047:     PetscInt       size, i, newp = p;

    1049:     DMPlexGetConeSize(dm, p, &size);
    1050:     DMPlexGetCone(dm, p, &points);
    1051:     DMPlexGetConeOrientation(dm, p, &orientations);
    1052:     for (i = 0; i < size; ++i) newpoints[i] = points[i];
    1053:     DMPlexSetCone(sdm, newp, newpoints);
    1054:     DMPlexSetConeOrientation(sdm, newp, orientations);
    1055:     DMPlexGetSupportSize(dm, p, &size);
    1056:     DMPlexGetSupport(dm, p, &points);
    1057:     for (i = 0; i < size; ++i) newpoints[i] = points[i];
    1058:     DMPlexSetSupport(sdm, newp, newpoints);
    1059:   }
    1060:   PetscFree(newpoints);
    1061:   for (fs = 0, newf = fEnd; fs < numFS; ++fs) {
    1062:     IS             faceIS;
    1063:     const PetscInt *faces;
    1064:     PetscInt       numFaces, f;

    1066:     DMGetStratumIS(dm, labelName, ids[fs], &faceIS);
    1067:     ISGetLocalSize(faceIS, &numFaces);
    1068:     ISGetIndices(faceIS, &faces);
    1069:     for (f = 0; f < numFaces; ++f, ++newf) {
    1070:       const PetscInt *points;

    1072:       DMPlexGetCone(dm, faces[f], &points);
    1073:       DMPlexSetCone(sdm, newf, points);
    1074:       DMPlexGetSupport(dm, faces[f], &points);
    1075:       DMPlexSetSupport(sdm, newf, points);
    1076:     }
    1077:     ISRestoreIndices(faceIS, &faces);
    1078:     ISDestroy(&faceIS);
    1079:   }
    1080:   ISRestoreIndices(idIS, &ids);
    1081:   ISDestroy(&idIS);
    1082:   DMPlexStratify(sdm);
    1083:   /* Convert coordinates */
    1084:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
    1085:   DMGetCoordinateSection(dm, &coordSection);
    1086:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &newCoordSection);
    1087:   PetscSectionSetNumFields(newCoordSection, 1);
    1088:   PetscSectionSetFieldComponents(newCoordSection, 0, dim);
    1089:   PetscSectionSetChart(newCoordSection, vStart, vEnd);
    1090:   for (v = vStart; v < vEnd; ++v) {
    1091:     PetscSectionSetDof(newCoordSection, v, dim);
    1092:     PetscSectionSetFieldDof(newCoordSection, v, 0, dim);
    1093:   }
    1094:   PetscSectionSetUp(newCoordSection);
    1095:   DMSetCoordinateSection(sdm, PETSC_DETERMINE, newCoordSection);
    1096:   PetscSectionDestroy(&newCoordSection); /* relinquish our reference */
    1097:   DMGetCoordinatesLocal(dm, &coordinates);
    1098:   DMSetCoordinatesLocal(sdm, coordinates);
    1099:   /* Convert labels */
    1100:   DMGetNumLabels(dm, &numLabels);
    1101:   for (l = 0; l < numLabels; ++l) {
    1102:     const char *lname;
    1103:     PetscBool  isDepth, isDim;

    1105:     DMGetLabelName(dm, l, &lname);
    1106:     PetscStrcmp(lname, "depth", &isDepth);
    1107:     if (isDepth) continue;
    1108:     PetscStrcmp(lname, "dim", &isDim);
    1109:     if (isDim) continue;
    1110:     DMCreateLabel(sdm, lname);
    1111:     DMGetLabelIdIS(dm, lname, &idIS);
    1112:     ISGetLocalSize(idIS, &numFS);
    1113:     ISGetIndices(idIS, &ids);
    1114:     for (fs = 0; fs < numFS; ++fs) {
    1115:       IS             pointIS;
    1116:       const PetscInt *points;
    1117:       PetscInt       numPoints;

    1119:       DMGetStratumIS(dm, lname, ids[fs], &pointIS);
    1120:       ISGetLocalSize(pointIS, &numPoints);
    1121:       ISGetIndices(pointIS, &points);
    1122:       for (p = 0; p < numPoints; ++p) {
    1123:         PetscInt newpoint = points[p];

    1125:         DMSetLabelValue(sdm, lname, newpoint, ids[fs]);
    1126:       }
    1127:       ISRestoreIndices(pointIS, &points);
    1128:       ISDestroy(&pointIS);
    1129:     }
    1130:     ISRestoreIndices(idIS, &ids);
    1131:     ISDestroy(&idIS);
    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;

    1142:     MPI_Comm_size(PetscObjectComm((PetscObject)dm), &size);
    1143:     DMGetPointSF(dm, &sfPoint);
    1144:     DMGetPointSF(sdm, &gsfPoint);
    1145:     DMPlexGetChart(dm,&pStart,&pEnd);
    1146:     PetscSFGetGraph(sfPoint, &numRoots, &numLeaves, &localPoints, &remotePoints);
    1147:     if (numRoots >= 0) {
    1148:       PetscMalloc2(numRoots,&newLocation,pEnd-pStart,&newRemoteLocation);
    1149:       for (l=0; l<numRoots; l++) newLocation[l] = l; /* + (l >= cEnd ? numGhostCells : 0); */
    1150:       PetscSFBcastBegin(sfPoint, MPIU_INT, newLocation, newRemoteLocation,MPI_REPLACE);
    1151:       PetscSFBcastEnd(sfPoint, MPIU_INT, newLocation, newRemoteLocation,MPI_REPLACE);
    1152:       PetscMalloc1(numLeaves,    &glocalPoints);
    1153:       PetscMalloc1(numLeaves, &gremotePoints);
    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:       PetscFree2(newLocation,newRemoteLocation);
    1160:       PetscSFSetGraph(gsfPoint, numRoots+numGhostCells, numLeaves, glocalPoints, PETSC_OWN_POINTER, gremotePoints, PETSC_OWN_POINTER);
    1161:     }
    1162:     DMDestroy(dmSplit);
    1163:     *dmSplit = sdm;
    1164:   }
    1165:   return(0);
    1166: }

    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;

    1180:   DMGetCoordinateSection(dm, &coordSection);
    1181:   DMGetCoordinatesLocal(dm, &coordinates);
    1182:   DMClone(dm, dmCell);
    1183:   DMGetPointSF(dm, &sfPoint);
    1184:   DMSetPointSF(*dmCell, sfPoint);
    1185:   DMSetCoordinateSection(*dmCell, PETSC_DETERMINE, coordSection);
    1186:   DMSetCoordinatesLocal(*dmCell, coordinates);
    1187:   MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);
    1188:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionCell);
    1189:   DMPlexGetHeightStratum(*dmCell, 0, &cStart, &cEnd);
    1190:   PetscSectionSetChart(sectionCell, cStart, cEnd);
    1191:   for (c = cStart; c < cEnd; ++c) {
    1192:     PetscSectionSetDof(sectionCell, c, 1);
    1193:   }
    1194:   PetscSectionSetUp(sectionCell);
    1195:   DMSetLocalSection(*dmCell, sectionCell);
    1196:   PetscSectionDestroy(&sectionCell);
    1197:   DMCreateLocalVector(*dmCell, partition);
    1198:   PetscObjectSetName((PetscObject)*partition, "partition");
    1199:   VecGetArray(*partition, &part);
    1200:   for (c = cStart; c < cEnd; ++c) {
    1201:     PetscScalar *p;

    1203:     DMPlexPointLocalRef(*dmCell, c, part, &p);
    1204:     p[0] = rank;
    1205:   }
    1206:   VecRestoreArray(*partition, &part);
    1207:   return(0);
    1208: }

    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;

    1222:   DMConvert(dm, DMPLEX, &plex);
    1223:   DMGetCoordinateSection(dm, &coordSection);
    1224:   DMGetCoordinatesLocal(dm, &coordinates);
    1225:   DMClone(dm, &dmMass);
    1226:   DMSetCoordinateSection(dmMass, PETSC_DETERMINE, coordSection);
    1227:   DMSetCoordinatesLocal(dmMass, coordinates);
    1228:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionMass);
    1229:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
    1230:   PetscSectionSetChart(sectionMass, vStart, vEnd);
    1231:   for (v = vStart; v < vEnd; ++v) {
    1232:     PetscInt numFaces;

    1234:     DMPlexGetSupportSize(dmMass, v, &numFaces);
    1235:     PetscSectionSetDof(sectionMass, v, numFaces*numFaces);
    1236:   }
    1237:   PetscSectionSetUp(sectionMass);
    1238:   DMSetLocalSection(dmMass, sectionMass);
    1239:   PetscSectionDestroy(&sectionMass);
    1240:   DMGetLocalVector(dmMass, massMatrix);
    1241:   VecGetArray(*massMatrix, &m);
    1242:   DMPlexGetGeometryFVM(plex, &facegeom, &cellgeom, NULL);
    1243:   VecGetDM(facegeom, &dmFace);
    1244:   VecGetArrayRead(facegeom, &fgeom);
    1245:   VecGetDM(cellgeom, &dmCell);
    1246:   VecGetArrayRead(cellgeom, &cgeom);
    1247:   DMGetCoordinateDM(dm, &dmCoord);
    1248:   VecGetArrayRead(coordinates, &coords);
    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;

    1255:     DMPlexPointLocalRead(dmCoord, v, coords, &vertex);
    1256:     DMPlexGetSupportSize(dmMass, v, &numFaces);
    1257:     DMPlexGetSupport(dmMass, v, &faces);
    1258:     for (f = 0; f < numFaces; ++f) {
    1259:       sides[0] = faces[f];
    1260:       DMPlexPointLocalRead(dmFace, faces[f], fgeom, &fgA);
    1261:       for (g = 0; g < numFaces; ++g) {
    1262:         const PetscInt *cells = NULL;
    1263:         PetscReal      area   = 0.0;
    1264:         PetscInt       numCells;

    1266:         sides[1] = faces[g];
    1267:         DMPlexPointLocalRead(dmFace, faces[g], fgeom, &fgB);
    1268:         DMPlexGetJoin(dmMass, 2, sides, &numCells, &cells);
    1269:         if (numCells != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Invalid join for faces");
    1270:         DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cg);
    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:         DMPlexRestoreJoin(dmMass, 2, sides, &numCells, &cells);
    1275:       }
    1276:     }
    1277:   }
    1278:   VecRestoreArrayRead(facegeom, &fgeom);
    1279:   VecRestoreArrayRead(cellgeom, &cgeom);
    1280:   VecRestoreArrayRead(coordinates, &coords);
    1281:   VecRestoreArray(*massMatrix, &m);
    1282:   DMDestroy(&dmMass);
    1283:   DMDestroy(&plex);
    1284:   return(0);
    1285: }

    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: {
    1291:   mod->solution    = func;
    1292:   mod->solutionctx = ctx;
    1293:   return(0);
    1294: }

    1296: static PetscErrorCode ModelFunctionalRegister(Model mod,const char *name,PetscInt *offset,FunctionalFunction func,void *ctx)
    1297: {
    1299:   FunctionalLink link,*ptr;
    1300:   PetscInt       lastoffset = -1;

    1303:   for (ptr=&mod->functionalRegistry; *ptr; ptr = &(*ptr)->next) lastoffset = (*ptr)->offset;
    1304:   PetscNew(&link);
    1305:   PetscStrallocpy(name,&link->name);
    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:   return(0);
    1313: }

    1315: static PetscErrorCode ModelFunctionalSetFromOptions(Model mod,PetscOptionItems *PetscOptionsObject)
    1316: {
    1318:   PetscInt       i,j;
    1319:   FunctionalLink link;
    1320:   char           *names[256];

    1323:   mod->numMonitored = ALEN(names);
    1324:   PetscOptionsStringArray("-monitor","list of functionals to monitor","",names,&mod->numMonitored,NULL);
    1325:   /* Create list of functionals that will be computed somehow */
    1326:   PetscMalloc1(mod->numMonitored,&mod->functionalMonitored);
    1327:   /* Create index of calls that we will have to make to compute these functionals (over-allocation in general). */
    1328:   PetscMalloc1(mod->numMonitored,&mod->functionalCall);
    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:       PetscStrcasecmp(names[i],link->name,&match);
    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:     PetscFree(names[i]);
    1344:   }

    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:   return(0);
    1357: }

    1359: static PetscErrorCode FunctionalLinkDestroy(FunctionalLink *link)
    1360: {
    1362:   FunctionalLink l,next;

    1365:   if (!link) return(0);
    1366:   l     = *link;
    1367:   *link = NULL;
    1368:   for (; l; l=next) {
    1369:     next = l->next;
    1370:     PetscFree(l->name);
    1371:     PetscFree(l);
    1372:   }
    1373:   return(0);
    1374: }

    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;
    1382:   mod  = (Model) modctx;
    1383:   (*mod->solution)(mod, time, x, u, mod->solutionctx);
    1384:   return(0);
    1385: }

    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;

    1395:   func[0] = SolutionFunctional;
    1396:   ctx[0]  = (void *) mod;
    1397:   DMProjectFunction(dm,0.0,func,ctx,INSERT_ALL_VALUES,X);
    1398:   return(0);
    1399: }

    1401: static PetscErrorCode OutputVTK(DM dm, const char *filename, PetscViewer *viewer)
    1402: {

    1406:   PetscViewerCreate(PetscObjectComm((PetscObject)dm), viewer);
    1407:   PetscViewerSetType(*viewer, PETSCVIEWERVTK);
    1408:   PetscViewerFileSetName(*viewer, filename);
    1409:   return(0);
    1410: }

    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;

    1422:   PetscObjectSetName((PetscObject) X, "u");
    1423:   VecGetDM(X,&dm);
    1424:   VecNorm(X,NORM_INFINITY,&xnorm);

    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;

    1439:     DMConvert(dm, DMPLEX, &plex);
    1440:     DMPlexGetGeometryFVM(plex, NULL, &cellgeom, NULL);
    1441:     fcount = mod->maxComputed+1;
    1442:     PetscMalloc4(fcount,&fmin,fcount,&fmax,fcount,&fintegral,fcount,&ftmp);
    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:     VecGetDM(cellgeom,&dmCell);
    1449:     DMPlexGetSimplexOrBoxCells(dmCell,0,&cStart,&cEnd);
    1450:     VecGetArrayRead(cellgeom,&cgeom);
    1451:     VecGetArrayRead(X,&x);
    1452:     DMGetLabel(dm,"vtk",&vtkLabel);
    1453:     for (c = cStart; c < cEnd; ++c) {
    1454:       PetscFVCellGeom       *cg;
    1455:       const PetscScalar     *cx    = NULL;
    1456:       PetscInt              vtkVal = 0;

    1458:       /* not that these two routines as currently implemented work for any dm with a
    1459:        * localSection/globalSection */
    1460:       DMPlexPointLocalRead(dmCell,c,cgeom,&cg);
    1461:       DMPlexPointGlobalRead(dm,c,x,&cx);
    1462:       if (vtkLabel) {DMLabelGetValue(vtkLabel,c,&vtkVal);}
    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:         (*flink->func)(mod,time,cg->centroid,cx,ftmp,flink->ctx);
    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:     VecRestoreArrayRead(cellgeom,&cgeom);
    1475:     VecRestoreArrayRead(X,&x);
    1476:     DMDestroy(&plex);
    1477:     MPI_Allreduce(MPI_IN_PLACE,fmin,fcount,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)ts));
    1478:     MPI_Allreduce(MPI_IN_PLACE,fmax,fcount,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
    1479:     MPI_Allreduce(MPI_IN_PLACE,fintegral,fcount,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));

    1481:     ftablealloc = fcount * 100;
    1482:     ftableused  = 0;
    1483:     PetscMalloc1(ftablealloc,&ftable);
    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:         PetscArraycpy(buffer,"  ",2);
    1491:         p    = buffer + 2;
    1492:       } else if (i) {
    1493:         char newline[] = "\n";
    1494:         PetscMemcpy(buffer,newline,sizeof(newline)-1);
    1495:         p    = buffer + sizeof(newline) - 1;
    1496:       } else {
    1497:         p = buffer;
    1498:       }
    1499:       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]);
    1500:       countused--;
    1501:       countused += p - buffer;
    1502:       if (countused > ftablealloc-ftableused-1) { /* reallocate */
    1503:         char *ftablenew;
    1504:         ftablealloc = 2*ftablealloc + countused;
    1505:         PetscMalloc(ftablealloc,&ftablenew);
    1506:         PetscArraycpy(ftablenew,ftable,ftableused);
    1507:         PetscFree(ftable);
    1508:         ftable = ftablenew;
    1509:       }
    1510:       PetscArraycpy(ftable+ftableused,buffer,countused);
    1511:       ftableused += countused;
    1512:       ftable[ftableused] = 0;
    1513:     }
    1514:     PetscFree4(fmin,fmax,fintegral,ftmp);

    1516:     PetscPrintf(PetscObjectComm((PetscObject)ts),"% 3D  time %8.4g  |x| %8.4g  %s\n",stepnum,(double)time,(double)xnorm,ftable ? ftable : "");
    1517:     PetscFree(ftable);
    1518:   }
    1519:   if (user->vtkInterval < 1) return(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:       TSGetStepNumber(ts,&stepnum);
    1523:     }
    1524:     PetscSNPrintf(filename,sizeof filename,"%s-%03D.vtu",user->outputBasename,stepnum);
    1525:     OutputVTK(dm,filename,&viewer);
    1526:     VecView(X,viewer);
    1527:     PetscViewerDestroy(&viewer);
    1528:   }
    1529:   return(0);
    1530: }

    1532: static PetscErrorCode initializeTS(DM dm, User user, TS *ts)
    1533: {

    1537:   TSCreate(PetscObjectComm((PetscObject)dm), ts);
    1538:   TSSetType(*ts, TSSSP);
    1539:   TSSetDM(*ts, dm);
    1540:   if (user->vtkmon) {
    1541:     TSMonitorSet(*ts,MonitorVTK,user,NULL);
    1542:   }
    1543:   DMTSSetBoundaryLocal(dm, DMPlexTSComputeBoundary, user);
    1544:   DMTSSetRHSFunctionLocal(dm, DMPlexTSComputeRHSFunctionFVM, user);
    1545:   TSSetMaxTime(*ts,2.0);
    1546:   TSSetExactFinalTime(*ts,TS_EXACTFINALTIME_STEPOVER);
    1547:   return(0);
    1548: }

    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;

    1567:   TSGetTime(ts,&time);
    1568:   VecGetDM(sol, &dm);
    1569:   DMGetDimension(dm,&dim);
    1570:   PetscFVGetComputeGradients(fvm,&computeGradient);
    1571:   PetscFVSetComputeGradients(fvm,PETSC_TRUE);
    1572:   DMIsForest(dm, &isForest);
    1573:   DMConvert(dm, DMPLEX, &plex);
    1574:   DMPlexGetDataFVM(plex, fvm, &cellGeom, &faceGeom, &gradDM);
    1575:   DMCreateLocalVector(plex,&locX);
    1576:   DMPlexInsertBoundaryValues(plex, PETSC_TRUE, locX, 0.0, faceGeom, cellGeom, NULL);
    1577:   DMGlobalToLocalBegin(plex, sol, INSERT_VALUES, locX);
    1578:   DMGlobalToLocalEnd  (plex, sol, INSERT_VALUES, locX);
    1579:   DMCreateGlobalVector(gradDM, &grad);
    1580:   DMPlexReconstructGradientsFVM(plex, locX, grad);
    1581:   DMCreateLocalVector(gradDM, &locGrad);
    1582:   DMGlobalToLocalBegin(gradDM, grad, INSERT_VALUES, locGrad);
    1583:   DMGlobalToLocalEnd(gradDM, grad, INSERT_VALUES, locGrad);
    1584:   VecDestroy(&grad);
    1585:   DMPlexGetSimplexOrBoxCells(plex,0,&cStart,&cEnd);
    1586:   VecGetArrayRead(locGrad,&pointGrads);
    1587:   VecGetArrayRead(cellGeom,&pointGeom);
    1588:   VecGetArrayRead(locX,&pointVals);
    1589:   VecGetDM(cellGeom,&cellDM);
    1590:   DMLabelCreate(PETSC_COMM_SELF,"adapt",&adaptLabel);
    1591:   VecCreateMPI(PetscObjectComm((PetscObject)plex),cEnd-cStart,PETSC_DETERMINE,&errVec);
    1592:   VecSetUp(errVec);
    1593:   VecGetArray(errVec,&errArray);
    1594:   for (c = cStart; c < cEnd; c++) {
    1595:     PetscReal             errInd = 0.;
    1596:     PetscScalar           *pointGrad;
    1597:     PetscScalar           *pointVal;
    1598:     PetscFVCellGeom       *cg;

    1600:     DMPlexPointLocalRead(gradDM,c,pointGrads,&pointGrad);
    1601:     DMPlexPointLocalRead(cellDM,c,pointGeom,&cg);
    1602:     DMPlexPointLocalRead(plex,c,pointVals,&pointVal);

    1604:     (user->model->errorIndicator)(dim,cg->volume,user->model->physics->dof,pointVal,pointGrad,&errInd,user->model->errorCtx);
    1605:     errArray[c-cStart] = errInd;
    1606:     minMaxInd[0] = PetscMin(minMaxInd[0],errInd);
    1607:     minMaxInd[1] = PetscMax(minMaxInd[1],errInd);
    1608:   }
    1609:   VecRestoreArray(errVec,&errArray);
    1610:   VecRestoreArrayRead(locX,&pointVals);
    1611:   VecRestoreArrayRead(cellGeom,&pointGeom);
    1612:   VecRestoreArrayRead(locGrad,&pointGrads);
    1613:   VecDestroy(&locGrad);
    1614:   VecDestroy(&locX);
    1615:   DMDestroy(&plex);

    1617:   VecTaggerComputeIS(refineTag,errVec,&refineIS);
    1618:   VecTaggerComputeIS(coarsenTag,errVec,&coarsenIS);
    1619:   ISGetSize(refineIS,&nRefine);
    1620:   ISGetSize(coarsenIS,&nCoarsen);
    1621:   if (nRefine) {DMLabelSetStratumIS(adaptLabel,DM_ADAPT_REFINE,refineIS);}
    1622:   if (nCoarsen) {DMLabelSetStratumIS(adaptLabel,DM_ADAPT_COARSEN,coarsenIS);}
    1623:   ISDestroy(&coarsenIS);
    1624:   ISDestroy(&refineIS);
    1625:   VecDestroy(&errVec);

    1627:   PetscFVSetComputeGradients(fvm,computeGradient);
    1628:   minMaxInd[1] = -minMaxInd[1];
    1629:   MPI_Allreduce(minMaxInd,minMaxIndGlobal,2,MPIU_REAL,MPI_MIN,PetscObjectComm((PetscObject)dm));
    1630:   minInd = minMaxIndGlobal[0];
    1631:   maxInd = -minMaxIndGlobal[1];
    1632:   PetscInfo2(ts, "error indicator range (%E, %E)\n", minInd, maxInd);
    1633:   if (nRefine || nCoarsen) { /* at least one cell is over the refinement threshold */
    1634:     DMAdaptLabel(dm,adaptLabel,&adaptedDM);
    1635:   }
    1636:   DMLabelDestroy(&adaptLabel);
    1637:   if (adaptedDM) {
    1638:     PetscInfo2(ts, "Adapted mesh, marking %D cells for refinement, and %D cells for coarsening\n", nRefine, nCoarsen);
    1639:     if (tsNew) {initializeTS(adaptedDM, user, tsNew);}
    1640:     if (solNew) {
    1641:       DMCreateGlobalVector(adaptedDM, solNew);
    1642:       PetscObjectSetName((PetscObject) *solNew, "solution");
    1643:       DMForestTransferVec(dm, sol, adaptedDM, *solNew, PETSC_TRUE, time);
    1644:     }
    1645:     if (isForest) {DMForestSetAdaptivityForest(adaptedDM,NULL);} /* clear internal references to the previous dm */
    1646:     DMDestroy(&adaptedDM);
    1647:   } else {
    1648:     if (tsNew)  *tsNew  = NULL;
    1649:     if (solNew) *solNew = NULL;
    1650:   }
    1651:   return(0);
    1652: }

    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;

    1677:   PetscInitialize(&argc, &argv, (char*) 0, help);if (ierr) return ierr;
    1678:   comm = PETSC_COMM_WORLD;

    1680:   PetscNew(&user);
    1681:   PetscNew(&user->model);
    1682:   PetscNew(&user->model->physics);
    1683:   mod           = user->model;
    1684:   phys          = mod->physics;
    1685:   mod->comm     = comm;
    1686:   useAMR        = PETSC_FALSE;
    1687:   adaptInterval = 1;

    1689:   /* Register physical models to be available on the command line */
    1690:   PetscFunctionListAdd(&PhysicsList,"advect"          ,PhysicsCreate_Advect);
    1691:   PetscFunctionListAdd(&PhysicsList,"sw"              ,PhysicsCreate_SW);
    1692:   PetscFunctionListAdd(&PhysicsList,"euler"           ,PhysicsCreate_Euler);

    1695:   PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Mesh Options","");
    1696:   {
    1697:     cfl  = 0.9 * 4; /* default SSPRKS2 with s=5 stages is stable for CFL number s-1 */
    1698:     PetscOptionsReal("-ufv_cfl","CFL number per step","",cfl,&cfl,NULL);
    1699:     PetscOptionsString("-f","Exodus.II filename to read","",filename,filename,sizeof(filename),NULL);
    1700:     PetscOptionsBool("-simplex","Flag to use a simplex mesh","",simplex,&simplex,NULL);
    1701:     splitFaces = PETSC_FALSE;
    1702:     PetscOptionsBool("-ufv_split_faces","Split faces between cell sets","",splitFaces,&splitFaces,NULL);
    1703:     overlap = 1;
    1704:     PetscOptionsInt("-ufv_mesh_overlap","Number of cells to overlap partitions","",overlap,&overlap,NULL);
    1705:     user->vtkInterval = 1;
    1706:     PetscOptionsInt("-ufv_vtk_interval","VTK output interval (0 to disable)","",user->vtkInterval,&user->vtkInterval,NULL);
    1707:     user->vtkmon = PETSC_TRUE;
    1708:     PetscOptionsBool("-ufv_vtk_monitor","Use VTKMonitor routine","",user->vtkmon,&user->vtkmon,NULL);
    1709:     vtkCellGeom = PETSC_FALSE;
    1710:     PetscStrcpy(user->outputBasename, "ex11");
    1711:     PetscOptionsString("-ufv_vtk_basename","VTK output basename","",user->outputBasename,user->outputBasename,sizeof(user->outputBasename),NULL);
    1712:     PetscOptionsBool("-ufv_vtk_cellgeom","Write cell geometry (for debugging)","",vtkCellGeom,&vtkCellGeom,NULL);
    1713:     PetscOptionsBool("-ufv_use_amr","use local adaptive mesh refinement","",useAMR,&useAMR,NULL);
    1714:     PetscOptionsInt("-ufv_adapt_interval","time steps between AMR","",adaptInterval,&adaptInterval,NULL);
    1715:   }
    1716:   PetscOptionsEnd();

    1718:   if (useAMR) {
    1719:     VecTaggerBox refineBox, coarsenBox;

    1721:     refineBox.min  = refineBox.max  = PETSC_MAX_REAL;
    1722:     coarsenBox.min = coarsenBox.max = PETSC_MIN_REAL;

    1724:     VecTaggerCreate(comm,&refineTag);
    1725:     PetscObjectSetOptionsPrefix((PetscObject)refineTag,"refine_");
    1726:     VecTaggerSetType(refineTag,VECTAGGERABSOLUTE);
    1727:     VecTaggerAbsoluteSetBox(refineTag,&refineBox);
    1728:     VecTaggerSetFromOptions(refineTag);
    1729:     VecTaggerSetUp(refineTag);
    1730:     PetscObjectViewFromOptions((PetscObject)refineTag,NULL,"-tag_view");

    1732:     VecTaggerCreate(comm,&coarsenTag);
    1733:     PetscObjectSetOptionsPrefix((PetscObject)coarsenTag,"coarsen_");
    1734:     VecTaggerSetType(coarsenTag,VECTAGGERABSOLUTE);
    1735:     VecTaggerAbsoluteSetBox(coarsenTag,&coarsenBox);
    1736:     VecTaggerSetFromOptions(coarsenTag);
    1737:     VecTaggerSetUp(coarsenTag);
    1738:     PetscObjectViewFromOptions((PetscObject)coarsenTag,NULL,"-tag_view");
    1739:   }

    1741:   PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Physics Options","");
    1742:   {
    1743:     PetscErrorCode (*physcreate)(Model,Physics,PetscOptionItems*);
    1744:     PetscOptionsFList("-physics","Physics module to solve","",PhysicsList,physname,physname,sizeof physname,NULL);
    1745:     PetscFunctionListFind(PhysicsList,physname,&physcreate);
    1746:     PetscMemzero(phys,sizeof(struct _n_Physics));
    1747:     (*physcreate)(mod,phys,PetscOptionsObject);
    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:     ModelFunctionalSetFromOptions(mod,PetscOptionsObject);
    1752:   }
    1753:   PetscOptionsEnd();

    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:     PetscStrlen(filename,&len);
    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:       PetscOptionsBegin(comm,NULL,"Rectangular mesh options","");
    1767:       PetscOptionsIntArray("-grid_size","number of cells in each direction","",cells,&nret1,&flg1);
    1768:       PetscOptionsRealArray("-grid_bounds","bounds of the mesh in each direction (i.e., x_min,x_max,y_min,y_max","",mod->bounds,&nret2,&flg2);
    1769:       PetscOptionsBool("-grid_skew_60","Skew grid for 60 degree shock mesh","",skew,&skew,NULL);
    1770:       PetscOptionsEnd();
    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:       DMPlexCreateBoxMesh(comm, dim, simplex, cells, NULL, NULL, mod->bcs, PETSC_TRUE, &dm);
    1776:       if (flg2) {
    1777:         PetscInt dimEmbed, i;
    1778:         PetscInt nCoords;
    1779:         PetscScalar *coords;
    1780:         Vec coordinates;

    1782:         DMGetCoordinatesLocal(dm,&coordinates);
    1783:         DMGetCoordinateDim(dm,&dimEmbed);
    1784:         VecGetLocalSize(coordinates,&nCoords);
    1785:         if (nCoords % dimEmbed) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Coordinate vector the wrong size");
    1786:         VecGetArray(coordinates,&coords);
    1787:         for (i = 0; i < nCoords; i += dimEmbed) {
    1788:           PetscInt j;

    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:         VecRestoreArray(coordinates,&coords);
    1806:         DMSetCoordinatesLocal(dm,coordinates);
    1807:       }
    1808:     } else {
    1809:       DMPlexCreateFromFile(comm, filename, PETSC_TRUE, &dm);
    1810:     }
    1811:   }
    1812:   DMViewFromOptions(dm, NULL, "-orig_dm_view");
    1813:   DMGetDimension(dm, &dim);

    1815:   /* set up BCs, functions, tags */
    1816:   DMCreateLabel(dm, "Face Sets");

    1818:   mod->errorIndicator = ErrorIndicator_Simple;

    1820:   {
    1821:     DM dmDist;

    1823:     DMSetBasicAdjacency(dm, PETSC_TRUE, PETSC_FALSE);
    1824:     DMPlexDistribute(dm, overlap, NULL, &dmDist);
    1825:     if (dmDist) {
    1826:       DMDestroy(&dm);
    1827:       dm   = dmDist;
    1828:     }
    1829:   }

    1831:   DMSetFromOptions(dm);

    1833:   {
    1834:     DM gdm;

    1836:     DMPlexConstructGhostCells(dm, NULL, NULL, &gdm);
    1837:     DMDestroy(&dm);
    1838:     dm   = gdm;
    1839:     DMViewFromOptions(dm, NULL, "-dm_view");
    1840:   }
    1841:   if (splitFaces) {ConstructCellBoundary(dm, user);}
    1842:   SplitFaces(&dm, "split faces", user);

    1844:   PetscFVCreate(comm, &fvm);
    1845:   PetscFVSetFromOptions(fvm);
    1846:   PetscFVSetNumComponents(fvm, phys->dof);
    1847:   PetscFVSetSpatialDimension(fvm, dim);
    1848:   PetscObjectSetName((PetscObject) fvm,"");
    1849:   {
    1850:     PetscInt f, dof;
    1851:     for (f=0,dof=0; f < phys->nfields; f++) {
    1852:       PetscInt newDof = phys->field_desc[f].dof;

    1854:       if (newDof == 1) {
    1855:         PetscFVSetComponentName(fvm,dof,phys->field_desc[f].name);
    1856:       }
    1857:       else {
    1858:         PetscInt j;

    1860:         for (j = 0; j < newDof; j++) {
    1861:           char     compName[256]  = "Unknown";

    1863:           PetscSNPrintf(compName,sizeof(compName),"%s_%d",phys->field_desc[f].name,j);
    1864:           PetscFVSetComponentName(fvm,dof+j,compName);
    1865:         }
    1866:       }
    1867:       dof += newDof;
    1868:     }
    1869:   }
    1870:   /* FV is now structured with one field having all physics as components */
    1871:   DMAddField(dm, NULL, (PetscObject) fvm);
    1872:   DMCreateDS(dm);
    1873:   DMGetDS(dm, &prob);
    1874:   PetscDSSetRiemannSolver(prob, 0, user->model->physics->riemann);
    1875:   PetscDSSetContext(prob, 0, user->model->physics);
    1876:   (*mod->setupbc)(prob,phys);
    1877:   PetscDSSetFromOptions(prob);
    1878:   {
    1879:     char      convType[256];
    1880:     PetscBool flg;

    1882:     PetscOptionsBegin(comm, "", "Mesh conversion options", "DMPLEX");
    1883:     PetscOptionsFList("-dm_type","Convert DMPlex to another format","ex12",DMList,DMPLEX,convType,256,&flg);
    1884:     PetscOptionsEnd();
    1885:     if (flg) {
    1886:       DM dmConv;

    1888:       DMConvert(dm,convType,&dmConv);
    1889:       if (dmConv) {
    1890:         DMViewFromOptions(dmConv, NULL, "-dm_conv_view");
    1891:         DMDestroy(&dm);
    1892:         dm   = dmConv;
    1893:         DMSetFromOptions(dm);
    1894:       }
    1895:     }
    1896:   }

    1898:   initializeTS(dm, user, &ts);

    1900:   DMCreateGlobalVector(dm, &X);
    1901:   PetscObjectSetName((PetscObject) X, "solution");
    1902:   SetInitialCondition(dm, X, user);
    1903:   if (useAMR) {
    1904:     PetscInt adaptIter;

    1906:     /* use no limiting when reconstructing gradients for adaptivity */
    1907:     PetscFVGetLimiter(fvm, &limiter);
    1908:     PetscObjectReference((PetscObject) limiter);
    1909:     PetscLimiterCreate(PetscObjectComm((PetscObject) fvm), &noneLimiter);
    1910:     PetscLimiterSetType(noneLimiter, PETSCLIMITERNONE);

    1912:     PetscFVSetLimiter(fvm, noneLimiter);
    1913:     for (adaptIter = 0; ; ++adaptIter) {
    1914:       PetscLogDouble bytes;
    1915:       TS             tsNew = NULL;

    1917:       PetscMemoryGetCurrentUsage(&bytes);
    1918:       PetscInfo2(ts, "refinement loop %D: memory used %g\n", adaptIter, bytes);
    1919:       DMViewFromOptions(dm, NULL, "-initial_dm_view");
    1920:       VecViewFromOptions(X, NULL, "-initial_vec_view");
    1921: #if 0
    1922:       if (viewInitial) {
    1923:         PetscViewer viewer;
    1924:         char        buf[256];
    1925:         PetscBool   isHDF5, isVTK;

    1927:         PetscViewerCreate(comm,&viewer);
    1928:         PetscViewerSetType(viewer,PETSCVIEWERVTK);
    1929:         PetscViewerSetOptionsPrefix(viewer,"initial_");
    1930:         PetscViewerSetFromOptions(viewer);
    1931:         PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERHDF5,&isHDF5);
    1932:         PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERVTK,&isVTK);
    1933:         if (isHDF5) {
    1934:           PetscSNPrintf(buf, 256, "ex11-initial-%d.h5", adaptIter);
    1935:         } else if (isVTK) {
    1936:           PetscSNPrintf(buf, 256, "ex11-initial-%d.vtu", adaptIter);
    1937:           PetscViewerPushFormat(viewer,PETSC_VIEWER_VTK_VTU);
    1938:         }
    1939:         PetscViewerFileSetMode(viewer,FILE_MODE_WRITE);
    1940:         PetscViewerFileSetName(viewer,buf);
    1941:         if (isHDF5) {
    1942:           DMView(dm,viewer);
    1943:           PetscViewerFileSetMode(viewer,FILE_MODE_UPDATE);
    1944:         }
    1945:         VecView(X,viewer);
    1946:         PetscViewerDestroy(&viewer);
    1947:       }
    1948: #endif

    1950:       adaptToleranceFVM(fvm, ts, X, refineTag, coarsenTag, user, &tsNew, NULL);
    1951:       if (!tsNew) {
    1952:         break;
    1953:       } else {
    1954:         DMDestroy(&dm);
    1955:         VecDestroy(&X);
    1956:         TSDestroy(&ts);
    1957:         ts   = tsNew;
    1958:         TSGetDM(ts,&dm);
    1959:         PetscObjectReference((PetscObject)dm);
    1960:         DMCreateGlobalVector(dm,&X);
    1961:         PetscObjectSetName((PetscObject) X, "solution");
    1962:         SetInitialCondition(dm, X, user);
    1963:       }
    1964:     }
    1965:     /* restore original limiter */
    1966:     PetscFVSetLimiter(fvm, limiter);
    1967:   }

    1969:   DMConvert(dm, DMPLEX, &plex);
    1970:   if (vtkCellGeom) {
    1971:     DM  dmCell;
    1972:     Vec cellgeom, partition;

    1974:     DMPlexGetGeometryFVM(plex, NULL, &cellgeom, NULL);
    1975:     OutputVTK(dm, "ex11-cellgeom.vtk", &viewer);
    1976:     VecView(cellgeom, viewer);
    1977:     PetscViewerDestroy(&viewer);
    1978:     CreatePartitionVec(dm, &dmCell, &partition);
    1979:     OutputVTK(dmCell, "ex11-partition.vtk", &viewer);
    1980:     VecView(partition, viewer);
    1981:     PetscViewerDestroy(&viewer);
    1982:     VecDestroy(&partition);
    1983:     DMDestroy(&dmCell);
    1984:   }
    1985:   /* collect max maxspeed from all processes -- todo */
    1986:   DMPlexGetGeometryFVM(plex, NULL, NULL, &minRadius);
    1987:   DMDestroy(&plex);
    1988:   MPI_Allreduce(&phys->maxspeed,&mod->maxspeed,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
    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:   TSSetTimeStep(ts,dt);
    1992:   TSSetFromOptions(ts);
    1993:   if (!useAMR) {
    1994:     TSSolve(ts,X);
    1995:     TSGetSolveTime(ts,&ftime);
    1996:     TSGetStepNumber(ts,&nsteps);
    1997:   } else {
    1998:     PetscReal finalTime;
    1999:     PetscInt  adaptIter;
    2000:     TS        tsNew = NULL;
    2001:     Vec       solNew = NULL;

    2003:     TSGetMaxTime(ts,&finalTime);
    2004:     TSSetMaxSteps(ts,adaptInterval);
    2005:     TSSolve(ts,X);
    2006:     TSGetSolveTime(ts,&ftime);
    2007:     TSGetStepNumber(ts,&nsteps);
    2008:     for (adaptIter = 0;ftime < finalTime;adaptIter++) {
    2009:       PetscLogDouble bytes;

    2011:       PetscMemoryGetCurrentUsage(&bytes);
    2012:       PetscInfo2(ts, "AMR time step loop %D: memory used %g\n", adaptIter, bytes);
    2013:       PetscFVSetLimiter(fvm,noneLimiter);
    2014:       adaptToleranceFVM(fvm,ts,X,refineTag,coarsenTag,user,&tsNew,&solNew);
    2015:       PetscFVSetLimiter(fvm,limiter);
    2016:       if (tsNew) {
    2017:         PetscInfo(ts, "AMR used\n");
    2018:         DMDestroy(&dm);
    2019:         VecDestroy(&X);
    2020:         TSDestroy(&ts);
    2021:         ts   = tsNew;
    2022:         X    = solNew;
    2023:         TSSetFromOptions(ts);
    2024:         VecGetDM(X,&dm);
    2025:         PetscObjectReference((PetscObject)dm);
    2026:         DMConvert(dm, DMPLEX, &plex);
    2027:         DMPlexGetGeometryFVM(dm, NULL, NULL, &minRadius);
    2028:         DMDestroy(&plex);
    2029:         MPI_Allreduce(&phys->maxspeed,&mod->maxspeed,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
    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:         TSSetStepNumber(ts,nsteps);
    2033:         TSSetTime(ts,ftime);
    2034:         TSSetTimeStep(ts,dt);
    2035:       } else {
    2036:         PetscInfo(ts, "AMR not used\n");
    2037:       }
    2038:       user->monitorStepOffset = nsteps;
    2039:       TSSetMaxSteps(ts,nsteps+adaptInterval);
    2040:       TSSolve(ts,X);
    2041:       TSGetSolveTime(ts,&ftime);
    2042:       TSGetStepNumber(ts,&nsteps);
    2043:     }
    2044:   }
    2045:   TSGetConvergedReason(ts,&reason);
    2046:   PetscPrintf(PETSC_COMM_WORLD,"%s at time %g after %D steps\n",TSConvergedReasons[reason],(double)ftime,nsteps);
    2047:   TSDestroy(&ts);

    2049:   VecTaggerDestroy(&refineTag);
    2050:   VecTaggerDestroy(&coarsenTag);
    2051:   PetscFunctionListDestroy(&PhysicsList);
    2052:   PetscFunctionListDestroy(&PhysicsRiemannList_SW);
    2053:   FunctionalLinkDestroy(&user->model->functionalRegistry);
    2054:   PetscFree(user->model->functionalMonitored);
    2055:   PetscFree(user->model->functionalCall);
    2056:   PetscFree(user->model->physics->data);
    2057:   PetscFree(user->model->physics);
    2058:   PetscFree(user->model);
    2059:   PetscFree(user);
    2060:   VecDestroy(&X);
    2061:   PetscLimiterDestroy(&limiter);
    2062:   PetscLimiterDestroy(&noneLimiter);
    2063:   PetscFVDestroy(&fvm);
    2064:   DMDestroy(&dm);
    2065:   PetscFinalize();
    2066:   return ierr;
    2067: }

    2069: /* Godunov fluxs */
    2070: PetscScalar cvmgp_(PetscScalar *a, PetscScalar *b, PetscScalar *test)
    2071: {
    2072:     /* System generated locals */
    2073:     PetscScalar ret_val;

    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_ */

    2085: PetscScalar cvmgm_(PetscScalar *a, PetscScalar *b, PetscScalar *test)
    2086: {
    2087:     /* System generated locals */
    2088:     PetscScalar ret_val;

    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_ */

    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 */

    2107:     static PetscScalar smallp = 1e-8;

    2109:     /* System generated locals */
    2110:     int i__1;
    2111:     PetscScalar d__1, d__2;

    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;

    2124:     /* gascl1 = *gaml - 1.; */
    2125:     /* gascl2 = (*gaml + 1.) * .5; */
    2126:     /* gascl3 = gascl2 / *gaml; */
    2127:     gascl4 = 1. / (*gaml - 1.);

    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:     }

    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: }

    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;

    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;

    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;

    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);

    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;

    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;

    2397:     /* Function Body */
    2398:     xcen = 0.;
    2399:     xp = 0.;
    2400:     i__1 = *ndim;
    2401:     for (k = 1; k <= i__1; ++k) {
    2402:         tg[k - 1] = 0.;
    2403:         bn[k - 1] = 0.;
    2404:     }
    2405:     dtt = 1.;
    2406:     if (*ndim == 3) {
    2407:         if (nn[0] == 0. && nn[1] == 0.) {
    2408:             tg[0] = 1.;
    2409:         } else {
    2410:             tg[0] = -nn[1];
    2411:             tg[1] = nn[0];
    2412:         }
    2413: /*           tmp=dsqrt(tg(1)**2+tg(2)**2) */
    2414: /*           tg=tg/tmp */
    2415:         bn[0] = -nn[2] * tg[1];
    2416:         bn[1] = nn[2] * tg[0];
    2417:         bn[2] = nn[0] * tg[1] - nn[1] * tg[0];
    2418: /* Computing 2nd power */
    2419:         d__1 = bn[0];
    2420: /* Computing 2nd power */
    2421:         d__2 = bn[1];
    2422: /* Computing 2nd power */
    2423:         d__3 = bn[2];
    2424:         tmp = PetscSqrtScalar(d__1 * d__1 + d__2 * d__2 + d__3 * d__3);
    2425:         i__1 = *ndim;
    2426:         for (k = 1; k <= i__1; ++k) {
    2427:             bn[k - 1] /= tmp;
    2428:         }
    2429:     } else if (*ndim == 2) {
    2430:         tg[0] = -nn[1];
    2431:         tg[1] = nn[0];
    2432: /*           tmp=dsqrt(tg(1)**2+tg(2)**2) */
    2433: /*           tg=tg/tmp */
    2434:         bn[0] = 0.;
    2435:         bn[1] = 0.;
    2436:         bn[2] = 1.;
    2437:     }
    2438:     rl = ul[0];
    2439:     rr = ur[0];
    2440:     uxl = 0.;
    2441:     uxr = 0.;
    2442:     utl = 0.;
    2443:     utr = 0.;
    2444:     ubl = 0.;
    2445:     ubr = 0.;
    2446:     i__1 = *ndim;
    2447:     for (k = 1; k <= i__1; ++k) {
    2448:         uxl += ul[k] * nn[k-1];
    2449:         uxr += ur[k] * nn[k-1];
    2450:         utl += ul[k] * tg[k - 1];
    2451:         utr += ur[k] * tg[k - 1];
    2452:         ubl += ul[k] * bn[k - 1];
    2453:         ubr += ur[k] * bn[k - 1];
    2454:     }
    2455:     uxl /= rl;
    2456:     uxr /= rr;
    2457:     utl /= rl;
    2458:     utr /= rr;
    2459:     ubl /= rl;
    2460:     ubr /= rr;

    2462:     gaml = *gamma;
    2463:     gamr = *gamma;
    2464: /* Computing 2nd power */
    2465:     d__1 = uxl;
    2466: /* Computing 2nd power */
    2467:     d__2 = utl;
    2468: /* Computing 2nd power */
    2469:     d__3 = ubl;
    2470:     pl = (*gamma - 1.) * (ul[*ndim + 1] - rl * .5 * (d__1 * d__1 + d__2 * d__2 + d__3 * d__3));
    2471: /* Computing 2nd power */
    2472:     d__1 = uxr;
    2473: /* Computing 2nd power */
    2474:     d__2 = utr;
    2475: /* Computing 2nd power */
    2476:     d__3 = ubr;
    2477:     pr = (*gamma - 1.) * (ur[*ndim + 1] - rr * .5 * (d__1 * d__1 + d__2 * d__2 + d__3 * d__3));
    2478:     rho1l = rl;
    2479:     rho1r = rr;

    2481:     iwave = riemannsolver(&xcen, &xp, &dtt, &rl, &uxl, &pl, &utl, &ubl, &gaml, &
    2482:                           rho1l, &rr, &uxr, &pr, &utr, &ubr, &gamr, &rho1r, &rhom, &unm, &
    2483:                           pm, &utm, &ubm, &gamm, &rho1m);

    2485:     flux[0] = rhom * unm;
    2486:     fn = rhom * unm * unm + pm;
    2487:     ft = rhom * unm * utm;
    2488: /*           flux(2)=fn*nn(1)+ft*nn(2) */
    2489: /*           flux(3)=fn*tg(1)+ft*tg(2) */
    2490:     flux[1] = fn * nn[0] + ft * tg[0];
    2491:     flux[2] = fn * nn[1] + ft * tg[1];
    2492: /*           flux(2)=rhom*unm*(unm)+pm */
    2493: /*           flux(3)=rhom*(unm)*utm */
    2494:     if (*ndim == 3) {
    2495:         flux[3] = rhom * unm * ubm;
    2496:     }
    2497:     flux[*ndim + 1] = (rhom * .5 * (unm * unm + utm * utm + ubm * ubm) + gamm / (gamm - 1.) * pm) * unm;
    2498:     return iwave;
    2499: } /* godunovflux_ */

    2501: /* Subroutine to set up the initial conditions for the */
    2502: /* Shock Interface interaction or linear wave (Ravi Samtaney,Mark Adams). */
    2503: /* ----------------------------------------------------------------------- */
    2504: int projecteqstate(PetscReal wc[], const PetscReal ueq[], PetscReal lv[][3])
    2505: {
    2506:   int j,k;
    2507: /*      Wc=matmul(lv,Ueq) 3 vars */
    2508:   for (k = 0; k < 3; ++k) {
    2509:     wc[k] = 0.;
    2510:     for (j = 0; j < 3; ++j) {
    2511:       wc[k] += lv[k][j]*ueq[j];
    2512:     }
    2513:   }
    2514:   return 0;
    2515: }
    2516: /* ----------------------------------------------------------------------- */
    2517: int projecttoprim(PetscReal v[], const PetscReal wc[], PetscReal rv[][3])
    2518: {
    2519:   int k,j;
    2520:   /*      V=matmul(rv,WC) 3 vars */
    2521:   for (k = 0; k < 3; ++k) {
    2522:     v[k] = 0.;
    2523:     for (j = 0; j < 3; ++j) {
    2524:       v[k] += rv[k][j]*wc[j];
    2525:     }
    2526:   }
    2527:   return 0;
    2528: }
    2529: /* ---------------------------------------------------------------------- */
    2530: int eigenvectors(PetscReal rv[][3], PetscReal lv[][3], const PetscReal ueq[], PetscReal gamma)
    2531: {
    2532:   int j,k;
    2533:   PetscReal rho,csnd,p0;
    2534:   /* PetscScalar u; */

    2536:   for (k = 0; k < 3; ++k) for (j = 0; j < 3; ++j) { lv[k][j] = 0.; rv[k][j] = 0.; }
    2537:   rho = ueq[0];
    2538:   /* u = ueq[1]; */
    2539:   p0 = ueq[2];
    2540:   csnd = PetscSqrtReal(gamma * p0 / rho);
    2541:   lv[0][1] = rho * .5;
    2542:   lv[0][2] = -.5 / csnd;
    2543:   lv[1][0] = csnd;
    2544:   lv[1][2] = -1. / csnd;
    2545:   lv[2][1] = rho * .5;
    2546:   lv[2][2] = .5 / csnd;
    2547:   rv[0][0] = -1. / csnd;
    2548:   rv[1][0] = 1. / rho;
    2549:   rv[2][0] = -csnd;
    2550:   rv[0][1] = 1. / csnd;
    2551:   rv[0][2] = 1. / csnd;
    2552:   rv[1][2] = 1. / rho;
    2553:   rv[2][2] = csnd;
    2554:   return 0;
    2555: }

    2557: int initLinearWave(EulerNode *ux, const PetscReal gamma, const PetscReal coord[], const PetscReal Lx)
    2558: {
    2559:   PetscReal p0,u0,wcp[3],wc[3];
    2560:   PetscReal lv[3][3];
    2561:   PetscReal vp[3];
    2562:   PetscReal rv[3][3];
    2563:   PetscReal eps, ueq[3], rho0, twopi;

    2565:   /* Function Body */
    2566:   twopi = 2.*PETSC_PI;
    2567:   eps = 1e-4; /* perturbation */
    2568:   rho0 = 1e3;   /* density of water */
    2569:   p0 = 101325.; /* init pressure of 1 atm (?) */
    2570:   u0 = 0.;
    2571:   ueq[0] = rho0;
    2572:   ueq[1] = u0;
    2573:   ueq[2] = p0;
    2574:   /* Project initial state to characteristic variables */
    2575:   eigenvectors(rv, lv, ueq, gamma);
    2576:   projecteqstate(wc, ueq, lv);
    2577:   wcp[0] = wc[0];
    2578:   wcp[1] = wc[1];
    2579:   wcp[2] = wc[2] + eps * PetscCosReal(coord[0] * 2. * twopi / Lx);
    2580:   projecttoprim(vp, wcp, rv);
    2581:   ux->r = vp[0]; /* density */
    2582:   ux->ru[0] = vp[0] * vp[1]; /* x momentum */
    2583:   ux->ru[1] = 0.;
    2584: #if defined DIM > 2
    2585:   if (dim>2) ux->ru[2] = 0.;
    2586: #endif
    2587:   /* E = rho * e + rho * v^2/2 = p/(gam-1) + rho*v^2/2 */
    2588:   ux->E = vp[2]/(gamma - 1.) + 0.5*vp[0]*vp[1]*vp[1];
    2589:   return 0;
    2590: }

    2592: /*TEST

    2594:   # 2D Advection 0-10
    2595:   test:
    2596:     suffix: 0
    2597:     requires: exodusii
    2598:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo

    2600:   test:
    2601:     suffix: 1
    2602:     requires: exodusii
    2603:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo

    2605:   test:
    2606:     suffix: 2
    2607:     requires: exodusii
    2608:     nsize: 2
    2609:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo

    2611:   test:
    2612:     suffix: 3
    2613:     requires: exodusii
    2614:     nsize: 2
    2615:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo

    2617:   test:
    2618:     suffix: 4
    2619:     requires: exodusii
    2620:     nsize: 8
    2621:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad.exo

    2623:   test:
    2624:     suffix: 5
    2625:     requires: exodusii
    2626:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo -ts_type rosw -ts_adapt_reject_safety 1

    2628:   test:
    2629:     suffix: 6
    2630:     requires: exodusii
    2631:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/squaremotor-30.exo -ufv_split_faces

    2633:   test:
    2634:     suffix: 7
    2635:     requires: exodusii
    2636:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 1

    2638:   test:
    2639:     suffix: 8
    2640:     requires: exodusii
    2641:     nsize: 2
    2642:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 1

    2644:   test:
    2645:     suffix: 9
    2646:     requires: exodusii
    2647:     nsize: 8
    2648:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 1

    2650:   test:
    2651:     suffix: 10
    2652:     requires: exodusii
    2653:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad.exo

    2655:   # 2D Shallow water
    2656:   test:
    2657:     suffix: sw_0
    2658:     requires: exodusii
    2659:     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

    2661:   test:
    2662:     suffix: sw_hll
    2663:     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

    2665:   # 2D Advection: p4est
    2666:   test:
    2667:     suffix: p4est_advec_2d
    2668:     requires: p4est
    2669:     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

    2671:   # Advection in a box
    2672:   test:
    2673:     suffix: adv_2d_quad_0
    2674:     args: -ufv_vtk_interval 0 -dm_refine 3 -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3

    2676:   test:
    2677:     suffix: adv_2d_quad_1
    2678:     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
    2679:     timeoutfactor: 3

    2681:   test:
    2682:     suffix: adv_2d_quad_p4est_0
    2683:     requires: p4est
    2684:     args: -ufv_vtk_interval 0 -dm_refine 5 -dm_type p4est -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3

    2686:   test:
    2687:     suffix: adv_2d_quad_p4est_1
    2688:     requires: p4est
    2689:     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
    2690:     timeoutfactor: 3

    2692:   test:
    2693:     suffix: adv_2d_quad_p4est_adapt_0
    2694:     requires: p4est !__float128 #broken for quad precision
    2695:     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
    2696:     timeoutfactor: 3

    2698:   test:
    2699:     suffix: adv_2d_tri_0
    2700:     requires: triangle
    2701:     TODO: how did this ever get in main when there is no support for this
    2702:     args: -ufv_vtk_interval 0 -simplex -dm_refine 3 -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3

    2704:   test:
    2705:     suffix: adv_2d_tri_1
    2706:     requires: triangle
    2707:     TODO: how did this ever get in main when there is no support for this
    2708:     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

    2710:   test:
    2711:     suffix: adv_0
    2712:     requires: exodusii
    2713:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/blockcylinder-50.exo -bc_inflow 100,101,200 -bc_outflow 201

    2715:   test:
    2716:     suffix: shock_0
    2717:     requires: p4est !single !complex
    2718:     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
    2719:     timeoutfactor: 3

    2721:   # Test GLVis visualization of PetscFV fields
    2722:   test:
    2723:     suffix: glvis_adv_2d_tet
    2724:     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

    2726:   test:
    2727:     suffix: glvis_adv_2d_quad
    2728:     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

    2730:   test:
    2731:     suffix: tut_1
    2732:     requires: exodusii
    2733:     nsize: 1
    2734:     args: -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo

    2736:   test:
    2737:     suffix: tut_2
    2738:     requires: exodusii
    2739:     nsize: 1
    2740:     args: -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo -ts_type rosw

    2742:   test:
    2743:     suffix: tut_3
    2744:     requires: exodusii
    2745:     nsize: 4
    2746:     args: -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/annulus-20.exo -monitor Error -advect_sol_type bump -petscfv_type leastsquares -petsclimiter_type sin

    2748:   test:
    2749:     suffix: tut_4
    2750:     requires: exodusii
    2751:     nsize: 4
    2752:     args: -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/annulus-20.exo -physics sw -monitor Height,Energy -petscfv_type leastsquares -petsclimiter_type minmod

    2754: TEST*/