Actual source code: ex11.c
petsc-3.13.6 2020-09-29
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      1: static char help[] = "Second Order TVD Finite Volume Example.\n";

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

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

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

     46: static PetscFunctionList PhysicsList;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    414: #if defined(PETSC_USE_COMPLEX)
    415:   uLreal.swnode.h = 0; uRreal.swnode.h = 0;
    416:   for (i = 0; i < 1+dim; i++) uLreal.vals[i] = PetscRealPart(xL[i]);
    417:   for (i = 0; i < 1+dim; i++) uRreal.vals[i] = PetscRealPart(xR[i]);
    418: #endif
    419:   if (uL->h < 0 || uR->h < 0) {for (i=0; i<1+dim; i++) flux[i] = zero/zero; return;} /* SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Reconstructed thickness is negative"); */
    420:   nn[0] = n[0];
    421:   nn[1] = n[1];
    422:   Normalize2Real(nn);
    423:   SWFlux(phys,nn,uL,&(fL.swnode));
    424:   SWFlux(phys,nn,uR,&(fR.swnode));
    425:   cL    = PetscSqrtReal(sw->gravity*uL->h);
    426:   cR    = PetscSqrtReal(sw->gravity*uR->h); /* gravity wave speed */
    427:   speed = PetscMax(PetscAbsReal(Dot2Real(uL->uh,nn)/uL->h) + cL,PetscAbsReal(Dot2Real(uR->uh,nn)/uR->h) + cR);
    428:   for (i=0; i<1+dim; i++) flux[i] = (0.5*(fL.vals[i] + fR.vals[i]) + 0.5*speed*(xL[i] - xR[i])) * Norm2Real(n);
    429: }

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

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

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

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

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

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

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

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

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

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

    500:   return(0);
    501: }

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

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

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

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

    550:   if (eu->type==EULER_IV_SHOCK || eu->type==EULER_SS_SHOCK) {
    551:     /******************* Euler Density Shock ********************/
    552:     /* On initial-value and self-similar solutions of the compressible Euler equations */
    553:     /* Ravi Samtaney and D. I. Pullin */
    554:     /* Phys. Fluids 8, 2650 (1996); http://dx.doi.org/10.1063/1.869050 */
    555:     /* initial conditions 1: left of shock, 0: left of discontinuity 2: right of discontinuity,  */
    556:     p0 = 1.;
    557:     if (x[0] < 0.0 + x[1]*eu->pars[EULER_PAR_ITANA]) {
    558:       if (x[0] < mod->bounds[0]*0.5) { /* left of shock (1) */
    559:         PetscReal amach,rho,press,gas1,p1;
    560:         amach = eu->pars[EULER_PAR_AMACH];
    561:         rho = 1.;
    562:         press = p0;
    563:         p1 = press*(1.0+2.0*gamma/(gamma+1.0)*(amach*amach-1.0));
    564:         gas1 = (gamma-1.0)/(gamma+1.0);
    565:         uu->r = rho*(p1/press+gas1)/(gas1*p1/press+1.0);
    566:         uu->ru[0]   = ((uu->r - rho)*PetscSqrtReal(gamma*press/rho)*amach);
    567:         uu->E = p1/(gamma-1.0) + .5/uu->r*uu->ru[0]*uu->ru[0];
    568:       }
    569:       else { /* left of discontinuity (0) */
    570:         uu->r = 1.; /* rho = 1 */
    571:         uu->E = p0/(gamma-1.0);
    572:       }
    573:     }
    574:     else { /* right of discontinuity (2) */
    575:       uu->r = eu->pars[EULER_PAR_RHOR];
    576:       uu->E = p0/(gamma-1.0);
    577:     }
    578:   }
    579:   else if (eu->type==EULER_SHOCK_TUBE) {
    580:     /* For (x<x0) set (rho,u,p)=(8,0,10) and for (x>x0) set (rho,u,p)=(1,0,1). Choose x0 to the midpoint of the domain in the x-direction. */
    581:     if (x[0] < 0.0 ) {
    582:       uu->r = 8.;
    583:       uu->E = 10./(gamma-1.);
    584:     }
    585:     else {
    586:       uu->r = 1.;
    587:       uu->E = 1./(gamma-1.);
    588:     }
    589:   }
    590:   else if (eu->type==EULER_LINEAR_WAVE) {
    591:     initLinearWave( uu, gamma, x, mod->bounds[1] - mod->bounds[0]);
    592:   }
    593:   else SETERRQ1(mod->comm,PETSC_ERR_SUP,"Unknown type %d",eu->type);

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

    600:   return(0);
    601: }

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

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

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

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

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

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

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

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

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

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

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

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

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

    811:   return(0);
    812: }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    1043:     DMGetLabelName(dm, l, &lname);
    1044:     PetscStrcmp(lname, "depth", &isDepth);
    1045:     if (isDepth) continue;
    1046:     PetscStrcmp(lname, "dim", &isDim);
    1047:     if (isDim) continue;
    1048:     DMCreateLabel(sdm, lname);
    1049:     DMGetLabelIdIS(dm, lname, &idIS);
    1050:     ISGetLocalSize(idIS, &numFS);
    1051:     ISGetIndices(idIS, &ids);
    1052:     for (fs = 0; fs < numFS; ++fs) {
    1053:       IS             pointIS;
    1054:       const PetscInt *points;
    1055:       PetscInt       numPoints;

    1057:       DMGetStratumIS(dm, lname, ids[fs], &pointIS);
    1058:       ISGetLocalSize(pointIS, &numPoints);
    1059:       ISGetIndices(pointIS, &points);
    1060:       for (p = 0; p < numPoints; ++p) {
    1061:         PetscInt newpoint = points[p];

    1063:         DMSetLabelValue(sdm, lname, newpoint, ids[fs]);
    1064:       }
    1065:       ISRestoreIndices(pointIS, &points);
    1066:       ISDestroy(&pointIS);
    1067:     }
    1068:     ISRestoreIndices(idIS, &ids);
    1069:     ISDestroy(&idIS);
    1070:   }
    1071:   {
    1072:     /* Convert pointSF */
    1073:     const PetscSFNode *remotePoints;
    1074:     PetscSFNode       *gremotePoints;
    1075:     const PetscInt    *localPoints;
    1076:     PetscInt          *glocalPoints,*newLocation,*newRemoteLocation;
    1077:     PetscInt          numRoots, numLeaves;
    1078:     PetscMPIInt       size;

    1080:     MPI_Comm_size(PetscObjectComm((PetscObject)dm), &size);
    1081:     DMGetPointSF(dm, &sfPoint);
    1082:     DMGetPointSF(sdm, &gsfPoint);
    1083:     DMPlexGetChart(dm,&pStart,&pEnd);
    1084:     PetscSFGetGraph(sfPoint, &numRoots, &numLeaves, &localPoints, &remotePoints);
    1085:     if (numRoots >= 0) {
    1086:       PetscMalloc2(numRoots,&newLocation,pEnd-pStart,&newRemoteLocation);
    1087:       for (l=0; l<numRoots; l++) newLocation[l] = l; /* + (l >= cEnd ? numGhostCells : 0); */
    1088:       PetscSFBcastBegin(sfPoint, MPIU_INT, newLocation, newRemoteLocation);
    1089:       PetscSFBcastEnd(sfPoint, MPIU_INT, newLocation, newRemoteLocation);
    1090:       PetscMalloc1(numLeaves,    &glocalPoints);
    1091:       PetscMalloc1(numLeaves, &gremotePoints);
    1092:       for (l = 0; l < numLeaves; ++l) {
    1093:         glocalPoints[l]        = localPoints[l]; /* localPoints[l] >= cEnd ? localPoints[l] + numGhostCells : localPoints[l]; */
    1094:         gremotePoints[l].rank  = remotePoints[l].rank;
    1095:         gremotePoints[l].index = newRemoteLocation[localPoints[l]];
    1096:       }
    1097:       PetscFree2(newLocation,newRemoteLocation);
    1098:       PetscSFSetGraph(gsfPoint, numRoots+numGhostCells, numLeaves, glocalPoints, PETSC_OWN_POINTER, gremotePoints, PETSC_OWN_POINTER);
    1099:     }
    1100:     DMDestroy(dmSplit);
    1101:     *dmSplit = sdm;
    1102:   }
    1103:   return(0);
    1104: }

    1106: PetscErrorCode CreatePartitionVec(DM dm, DM *dmCell, Vec *partition)
    1107: {
    1108:   PetscSF        sfPoint;
    1109:   PetscSection   coordSection;
    1110:   Vec            coordinates;
    1111:   PetscSection   sectionCell;
    1112:   PetscScalar    *part;
    1113:   PetscInt       cStart, cEnd, c;
    1114:   PetscMPIInt    rank;

    1118:   DMGetCoordinateSection(dm, &coordSection);
    1119:   DMGetCoordinatesLocal(dm, &coordinates);
    1120:   DMClone(dm, dmCell);
    1121:   DMGetPointSF(dm, &sfPoint);
    1122:   DMSetPointSF(*dmCell, sfPoint);
    1123:   DMSetCoordinateSection(*dmCell, PETSC_DETERMINE, coordSection);
    1124:   DMSetCoordinatesLocal(*dmCell, coordinates);
    1125:   MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);
    1126:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionCell);
    1127:   DMPlexGetHeightStratum(*dmCell, 0, &cStart, &cEnd);
    1128:   PetscSectionSetChart(sectionCell, cStart, cEnd);
    1129:   for (c = cStart; c < cEnd; ++c) {
    1130:     PetscSectionSetDof(sectionCell, c, 1);
    1131:   }
    1132:   PetscSectionSetUp(sectionCell);
    1133:   DMSetLocalSection(*dmCell, sectionCell);
    1134:   PetscSectionDestroy(&sectionCell);
    1135:   DMCreateLocalVector(*dmCell, partition);
    1136:   PetscObjectSetName((PetscObject)*partition, "partition");
    1137:   VecGetArray(*partition, &part);
    1138:   for (c = cStart; c < cEnd; ++c) {
    1139:     PetscScalar *p;

    1141:     DMPlexPointLocalRef(*dmCell, c, part, &p);
    1142:     p[0] = rank;
    1143:   }
    1144:   VecRestoreArray(*partition, &part);
    1145:   return(0);
    1146: }

    1148: PetscErrorCode CreateMassMatrix(DM dm, Vec *massMatrix, User user)
    1149: {
    1150:   DM                dmMass, dmFace, dmCell, dmCoord;
    1151:   PetscSection      coordSection;
    1152:   Vec               coordinates, facegeom, cellgeom;
    1153:   PetscSection      sectionMass;
    1154:   PetscScalar       *m;
    1155:   const PetscScalar *fgeom, *cgeom, *coords;
    1156:   PetscInt          vStart, vEnd, v;
    1157:   PetscErrorCode    ierr;

    1160:   DMGetCoordinateSection(dm, &coordSection);
    1161:   DMGetCoordinatesLocal(dm, &coordinates);
    1162:   DMClone(dm, &dmMass);
    1163:   DMSetCoordinateSection(dmMass, PETSC_DETERMINE, coordSection);
    1164:   DMSetCoordinatesLocal(dmMass, coordinates);
    1165:   PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionMass);
    1166:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
    1167:   PetscSectionSetChart(sectionMass, vStart, vEnd);
    1168:   for (v = vStart; v < vEnd; ++v) {
    1169:     PetscInt numFaces;

    1171:     DMPlexGetSupportSize(dmMass, v, &numFaces);
    1172:     PetscSectionSetDof(sectionMass, v, numFaces*numFaces);
    1173:   }
    1174:   PetscSectionSetUp(sectionMass);
    1175:   DMSetLocalSection(dmMass, sectionMass);
    1176:   PetscSectionDestroy(&sectionMass);
    1177:   DMGetLocalVector(dmMass, massMatrix);
    1178:   VecGetArray(*massMatrix, &m);
    1179:   DMPlexTSGetGeometryFVM(dm, &facegeom, &cellgeom, NULL);
    1180:   VecGetDM(facegeom, &dmFace);
    1181:   VecGetArrayRead(facegeom, &fgeom);
    1182:   VecGetDM(cellgeom, &dmCell);
    1183:   VecGetArrayRead(cellgeom, &cgeom);
    1184:   DMGetCoordinateDM(dm, &dmCoord);
    1185:   VecGetArrayRead(coordinates, &coords);
    1186:   for (v = vStart; v < vEnd; ++v) {
    1187:     const PetscInt        *faces;
    1188:     PetscFVFaceGeom       *fgA, *fgB, *cg;
    1189:     PetscScalar           *vertex;
    1190:     PetscInt               numFaces, sides[2], f, g;

    1192:     DMPlexPointLocalRead(dmCoord, v, coords, &vertex);
    1193:     DMPlexGetSupportSize(dmMass, v, &numFaces);
    1194:     DMPlexGetSupport(dmMass, v, &faces);
    1195:     for (f = 0; f < numFaces; ++f) {
    1196:       sides[0] = faces[f];
    1197:       DMPlexPointLocalRead(dmFace, faces[f], fgeom, &fgA);
    1198:       for (g = 0; g < numFaces; ++g) {
    1199:         const PetscInt *cells = NULL;
    1200:         PetscReal      area   = 0.0;
    1201:         PetscInt       numCells;

    1203:         sides[1] = faces[g];
    1204:         DMPlexPointLocalRead(dmFace, faces[g], fgeom, &fgB);
    1205:         DMPlexGetJoin(dmMass, 2, sides, &numCells, &cells);
    1206:         if (numCells != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Invalid join for faces");
    1207:         DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cg);
    1208:         area += PetscAbsScalar((vertex[0] - cg->centroid[0])*(fgA->centroid[1] - cg->centroid[1]) - (vertex[1] - cg->centroid[1])*(fgA->centroid[0] - cg->centroid[0]));
    1209:         area += PetscAbsScalar((vertex[0] - cg->centroid[0])*(fgB->centroid[1] - cg->centroid[1]) - (vertex[1] - cg->centroid[1])*(fgB->centroid[0] - cg->centroid[0]));
    1210:         m[f*numFaces+g] = Dot2Real(fgA->normal, fgB->normal)*area*0.5;
    1211:         DMPlexRestoreJoin(dmMass, 2, sides, &numCells, &cells);
    1212:       }
    1213:     }
    1214:   }
    1215:   VecRestoreArrayRead(facegeom, &fgeom);
    1216:   VecRestoreArrayRead(cellgeom, &cgeom);
    1217:   VecRestoreArrayRead(coordinates, &coords);
    1218:   VecRestoreArray(*massMatrix, &m);
    1219:   DMDestroy(&dmMass);
    1220:   return(0);
    1221: }

    1223: /* Behavior will be different for multi-physics or when using non-default boundary conditions */
    1224: static PetscErrorCode ModelSolutionSetDefault(Model mod,SolutionFunction func,void *ctx)
    1225: {
    1227:   mod->solution    = func;
    1228:   mod->solutionctx = ctx;
    1229:   return(0);
    1230: }

    1232: static PetscErrorCode ModelFunctionalRegister(Model mod,const char *name,PetscInt *offset,FunctionalFunction func,void *ctx)
    1233: {
    1235:   FunctionalLink link,*ptr;
    1236:   PetscInt       lastoffset = -1;

    1239:   for (ptr=&mod->functionalRegistry; *ptr; ptr = &(*ptr)->next) lastoffset = (*ptr)->offset;
    1240:   PetscNew(&link);
    1241:   PetscStrallocpy(name,&link->name);
    1242:   link->offset = lastoffset + 1;
    1243:   link->func   = func;
    1244:   link->ctx    = ctx;
    1245:   link->next   = NULL;
    1246:   *ptr         = link;
    1247:   *offset      = link->offset;
    1248:   return(0);
    1249: }

    1251: static PetscErrorCode ModelFunctionalSetFromOptions(Model mod,PetscOptionItems *PetscOptionsObject)
    1252: {
    1254:   PetscInt       i,j;
    1255:   FunctionalLink link;
    1256:   char           *names[256];

    1259:   mod->numMonitored = ALEN(names);
    1260:   PetscOptionsStringArray("-monitor","list of functionals to monitor","",names,&mod->numMonitored,NULL);
    1261:   /* Create list of functionals that will be computed somehow */
    1262:   PetscMalloc1(mod->numMonitored,&mod->functionalMonitored);
    1263:   /* Create index of calls that we will have to make to compute these functionals (over-allocation in general). */
    1264:   PetscMalloc1(mod->numMonitored,&mod->functionalCall);
    1265:   mod->numCall = 0;
    1266:   for (i=0; i<mod->numMonitored; i++) {
    1267:     for (link=mod->functionalRegistry; link; link=link->next) {
    1268:       PetscBool match;
    1269:       PetscStrcasecmp(names[i],link->name,&match);
    1270:       if (match) break;
    1271:     }
    1272:     if (!link) SETERRQ1(mod->comm,PETSC_ERR_USER,"No known functional '%s'",names[i]);
    1273:     mod->functionalMonitored[i] = link;
    1274:     for (j=0; j<i; j++) {
    1275:       if (mod->functionalCall[j]->func == link->func && mod->functionalCall[j]->ctx == link->ctx) goto next_name;
    1276:     }
    1277:     mod->functionalCall[mod->numCall++] = link; /* Just points to the first link using the result. There may be more results. */
    1278: next_name:
    1279:     PetscFree(names[i]);
    1280:   }

    1282:   /* Find out the maximum index of any functional computed by a function we will be calling (even if we are not using it) */
    1283:   mod->maxComputed = -1;
    1284:   for (link=mod->functionalRegistry; link; link=link->next) {
    1285:     for (i=0; i<mod->numCall; i++) {
    1286:       FunctionalLink call = mod->functionalCall[i];
    1287:       if (link->func == call->func && link->ctx == call->ctx) {
    1288:         mod->maxComputed = PetscMax(mod->maxComputed,link->offset);
    1289:       }
    1290:     }
    1291:   }
    1292:   return(0);
    1293: }

    1295: static PetscErrorCode FunctionalLinkDestroy(FunctionalLink *link)
    1296: {
    1298:   FunctionalLink l,next;

    1301:   if (!link) return(0);
    1302:   l     = *link;
    1303:   *link = NULL;
    1304:   for (; l; l=next) {
    1305:     next = l->next;
    1306:     PetscFree(l->name);
    1307:     PetscFree(l);
    1308:   }
    1309:   return(0);
    1310: }

    1312: /* put the solution callback into a functional callback */
    1313: static PetscErrorCode SolutionFunctional(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *modctx)
    1314: {
    1315:   Model          mod;
    1318:   mod  = (Model) modctx;
    1319:   (*mod->solution)(mod, time, x, u, mod->solutionctx);
    1320:   return(0);
    1321: }

    1323: PetscErrorCode SetInitialCondition(DM dm, Vec X, User user)
    1324: {
    1325:   PetscErrorCode     (*func[1]) (PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
    1326:   void               *ctx[1];
    1327:   Model              mod = user->model;
    1328:   PetscErrorCode     ierr;

    1331:   func[0] = SolutionFunctional;
    1332:   ctx[0]  = (void *) mod;
    1333:   DMProjectFunction(dm,0.0,func,ctx,INSERT_ALL_VALUES,X);
    1334:   return(0);
    1335: }

    1337: static PetscErrorCode OutputVTK(DM dm, const char *filename, PetscViewer *viewer)
    1338: {

    1342:   PetscViewerCreate(PetscObjectComm((PetscObject)dm), viewer);
    1343:   PetscViewerSetType(*viewer, PETSCVIEWERVTK);
    1344:   PetscViewerFileSetName(*viewer, filename);
    1345:   return(0);
    1346: }

    1348: static PetscErrorCode MonitorVTK(TS ts,PetscInt stepnum,PetscReal time,Vec X,void *ctx)
    1349: {
    1350:   User           user = (User)ctx;
    1351:   DM             dm;
    1352:   Vec            cellgeom;
    1353:   PetscViewer    viewer;
    1354:   char           filename[PETSC_MAX_PATH_LEN],*ftable = NULL;
    1355:   PetscReal      xnorm;

    1359:   PetscObjectSetName((PetscObject) X, "u");
    1360:   VecGetDM(X,&dm);
    1361:   DMPlexTSGetGeometryFVM(dm, NULL, &cellgeom, NULL);
    1362:   VecNorm(X,NORM_INFINITY,&xnorm);

    1364:   if (stepnum >= 0) {
    1365:     stepnum += user->monitorStepOffset;
    1366:   }
    1367:   if (stepnum >= 0) {           /* No summary for final time */
    1368:     Model             mod = user->model;
    1369:     PetscInt          c,cStart,cEnd,fcount,i;
    1370:     size_t            ftableused,ftablealloc;
    1371:     const PetscScalar *cgeom,*x;
    1372:     DM                dmCell;
    1373:     DMLabel           vtkLabel;
    1374:     PetscReal         *fmin,*fmax,*fintegral,*ftmp;
    1375:     fcount = mod->maxComputed+1;
    1376:     PetscMalloc4(fcount,&fmin,fcount,&fmax,fcount,&fintegral,fcount,&ftmp);
    1377:     for (i=0; i<fcount; i++) {
    1378:       fmin[i]      = PETSC_MAX_REAL;
    1379:       fmax[i]      = PETSC_MIN_REAL;
    1380:       fintegral[i] = 0;
    1381:     }
    1382:     VecGetDM(cellgeom,&dmCell);
    1383:     DMPlexGetSimplexOrBoxCells(dmCell,0,&cStart,&cEnd);
    1384:     VecGetArrayRead(cellgeom,&cgeom);
    1385:     VecGetArrayRead(X,&x);
    1386:     DMGetLabel(dm,"vtk",&vtkLabel);
    1387:     for (c = cStart; c < cEnd; ++c) {
    1388:       PetscFVCellGeom       *cg;
    1389:       const PetscScalar     *cx    = NULL;
    1390:       PetscInt              vtkVal = 0;

    1392:       /* not that these two routines as currently implemented work for any dm with a
    1393:        * localSection/globalSection */
    1394:       DMPlexPointLocalRead(dmCell,c,cgeom,&cg);
    1395:       DMPlexPointGlobalRead(dm,c,x,&cx);
    1396:       if (vtkLabel) {DMLabelGetValue(vtkLabel,c,&vtkVal);}
    1397:       if (!vtkVal || !cx) continue;        /* ghost, or not a global cell */
    1398:       for (i=0; i<mod->numCall; i++) {
    1399:         FunctionalLink flink = mod->functionalCall[i];
    1400:         (*flink->func)(mod,time,cg->centroid,cx,ftmp,flink->ctx);
    1401:       }
    1402:       for (i=0; i<fcount; i++) {
    1403:         fmin[i]       = PetscMin(fmin[i],ftmp[i]);
    1404:         fmax[i]       = PetscMax(fmax[i],ftmp[i]);
    1405:         fintegral[i] += cg->volume * ftmp[i];
    1406:       }
    1407:     }
    1408:     VecRestoreArrayRead(cellgeom,&cgeom);
    1409:     VecRestoreArrayRead(X,&x);
    1410:     MPI_Allreduce(MPI_IN_PLACE,fmin,fcount,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)ts));
    1411:     MPI_Allreduce(MPI_IN_PLACE,fmax,fcount,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
    1412:     MPI_Allreduce(MPI_IN_PLACE,fintegral,fcount,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));

    1414:     ftablealloc = fcount * 100;
    1415:     ftableused  = 0;
    1416:     PetscMalloc1(ftablealloc,&ftable);
    1417:     for (i=0; i<mod->numMonitored; i++) {
    1418:       size_t         countused;
    1419:       char           buffer[256],*p;
    1420:       FunctionalLink flink = mod->functionalMonitored[i];
    1421:       PetscInt       id    = flink->offset;
    1422:       if (i % 3) {
    1423:         PetscArraycpy(buffer,"  ",2);
    1424:         p    = buffer + 2;
    1425:       } else if (i) {
    1426:         char newline[] = "\n";
    1427:         PetscMemcpy(buffer,newline,sizeof(newline)-1);
    1428:         p    = buffer + sizeof(newline) - 1;
    1429:       } else {
    1430:         p = buffer;
    1431:       }
    1432:       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]);
    1433:       countused--;
    1434:       countused += p - buffer;
    1435:       if (countused > ftablealloc-ftableused-1) { /* reallocate */
    1436:         char *ftablenew;
    1437:         ftablealloc = 2*ftablealloc + countused;
    1438:         PetscMalloc(ftablealloc,&ftablenew);
    1439:         PetscArraycpy(ftablenew,ftable,ftableused);
    1440:         PetscFree(ftable);
    1441:         ftable = ftablenew;
    1442:       }
    1443:       PetscArraycpy(ftable+ftableused,buffer,countused);
    1444:       ftableused += countused;
    1445:       ftable[ftableused] = 0;
    1446:     }
    1447:     PetscFree4(fmin,fmax,fintegral,ftmp);

    1449:     PetscPrintf(PetscObjectComm((PetscObject)ts),"% 3D  time %8.4g  |x| %8.4g  %s\n",stepnum,(double)time,(double)xnorm,ftable ? ftable : "");
    1450:     PetscFree(ftable);
    1451:   }
    1452:   if (user->vtkInterval < 1) return(0);
    1453:   if ((stepnum == -1) ^ (stepnum % user->vtkInterval == 0)) {
    1454:     if (stepnum == -1) {        /* Final time is not multiple of normal time interval, write it anyway */
    1455:       TSGetStepNumber(ts,&stepnum);
    1456:     }
    1457:     PetscSNPrintf(filename,sizeof filename,"%s-%03D.vtu",user->outputBasename,stepnum);
    1458:     OutputVTK(dm,filename,&viewer);
    1459:     VecView(X,viewer);
    1460:     PetscViewerDestroy(&viewer);
    1461:   }
    1462:   return(0);
    1463: }

    1465: static PetscErrorCode initializeTS(DM dm, User user, TS *ts)
    1466: {

    1470:   TSCreate(PetscObjectComm((PetscObject)dm), ts);
    1471:   TSSetType(*ts, TSSSP);
    1472:   TSSetDM(*ts, dm);
    1473:   if (user->vtkmon) {
    1474:     TSMonitorSet(*ts,MonitorVTK,user,NULL);
    1475:   }
    1476:   DMTSSetBoundaryLocal(dm, DMPlexTSComputeBoundary, user);
    1477:   DMTSSetRHSFunctionLocal(dm, DMPlexTSComputeRHSFunctionFVM, user);
    1478:   TSSetMaxTime(*ts,2.0);
    1479:   TSSetExactFinalTime(*ts,TS_EXACTFINALTIME_STEPOVER);
    1480:   return(0);
    1481: }

    1483: static PetscErrorCode adaptToleranceFVM(PetscFV fvm, TS ts, Vec sol, VecTagger refineTag, VecTagger coarsenTag, User user, TS *tsNew, Vec *solNew)
    1484: {
    1485:   DM                dm, gradDM, plex, cellDM, adaptedDM = NULL;
    1486:   Vec               cellGeom, faceGeom;
    1487:   PetscBool         isForest, computeGradient;
    1488:   Vec               grad, locGrad, locX, errVec;
    1489:   PetscInt          cStart, cEnd, c, dim, nRefine, nCoarsen;
    1490:   PetscReal         minMaxInd[2] = {PETSC_MAX_REAL, PETSC_MIN_REAL}, minMaxIndGlobal[2], minInd, maxInd, time;
    1491:   PetscScalar       *errArray;
    1492:   const PetscScalar *pointVals;
    1493:   const PetscScalar *pointGrads;
    1494:   const PetscScalar *pointGeom;
    1495:   DMLabel           adaptLabel = NULL;
    1496:   IS                refineIS, coarsenIS;
    1497:   PetscErrorCode    ierr;

    1500:   TSGetTime(ts,&time);
    1501:   VecGetDM(sol, &dm);
    1502:   DMGetDimension(dm,&dim);
    1503:   PetscFVGetComputeGradients(fvm,&computeGradient);
    1504:   PetscFVSetComputeGradients(fvm,PETSC_TRUE);
    1505:   DMIsForest(dm, &isForest);
    1506:   DMConvert(dm, DMPLEX, &plex);
    1507:   DMPlexGetDataFVM(plex, fvm, &cellGeom, &faceGeom, &gradDM);
    1508:   DMCreateLocalVector(plex,&locX);
    1509:   DMPlexInsertBoundaryValues(plex, PETSC_TRUE, locX, 0.0, faceGeom, cellGeom, NULL);
    1510:   DMGlobalToLocalBegin(plex, sol, INSERT_VALUES, locX);
    1511:   DMGlobalToLocalEnd  (plex, sol, INSERT_VALUES, locX);
    1512:   DMCreateGlobalVector(gradDM, &grad);
    1513:   DMPlexReconstructGradientsFVM(plex, locX, grad);
    1514:   DMCreateLocalVector(gradDM, &locGrad);
    1515:   DMGlobalToLocalBegin(gradDM, grad, INSERT_VALUES, locGrad);
    1516:   DMGlobalToLocalEnd(gradDM, grad, INSERT_VALUES, locGrad);
    1517:   VecDestroy(&grad);
    1518:   DMPlexGetSimplexOrBoxCells(plex,0,&cStart,&cEnd);
    1519:   VecGetArrayRead(locGrad,&pointGrads);
    1520:   VecGetArrayRead(cellGeom,&pointGeom);
    1521:   VecGetArrayRead(locX,&pointVals);
    1522:   VecGetDM(cellGeom,&cellDM);
    1523:   DMLabelCreate(PETSC_COMM_SELF,"adapt",&adaptLabel);
    1524:   VecCreateMPI(PetscObjectComm((PetscObject)plex),cEnd-cStart,PETSC_DETERMINE,&errVec);
    1525:   VecSetUp(errVec);
    1526:   VecGetArray(errVec,&errArray);
    1527:   for (c = cStart; c < cEnd; c++) {
    1528:     PetscReal             errInd = 0.;
    1529:     PetscScalar           *pointGrad;
    1530:     PetscScalar           *pointVal;
    1531:     PetscFVCellGeom       *cg;

    1533:     DMPlexPointLocalRead(gradDM,c,pointGrads,&pointGrad);
    1534:     DMPlexPointLocalRead(cellDM,c,pointGeom,&cg);
    1535:     DMPlexPointLocalRead(plex,c,pointVals,&pointVal);

    1537:     (user->model->errorIndicator)(dim,cg->volume,user->model->physics->dof,pointVal,pointGrad,&errInd,user->model->errorCtx);
    1538:     errArray[c-cStart] = errInd;
    1539:     minMaxInd[0] = PetscMin(minMaxInd[0],errInd);
    1540:     minMaxInd[1] = PetscMax(minMaxInd[1],errInd);
    1541:   }
    1542:   VecRestoreArray(errVec,&errArray);
    1543:   VecRestoreArrayRead(locX,&pointVals);
    1544:   VecRestoreArrayRead(cellGeom,&pointGeom);
    1545:   VecRestoreArrayRead(locGrad,&pointGrads);
    1546:   VecDestroy(&locGrad);
    1547:   VecDestroy(&locX);
    1548:   DMDestroy(&plex);

    1550:   VecTaggerComputeIS(refineTag,errVec,&refineIS);
    1551:   VecTaggerComputeIS(coarsenTag,errVec,&coarsenIS);
    1552:   ISGetSize(refineIS,&nRefine);
    1553:   ISGetSize(coarsenIS,&nCoarsen);
    1554:   if (nRefine) {DMLabelSetStratumIS(adaptLabel,DM_ADAPT_REFINE,refineIS);}
    1555:   if (nCoarsen) {DMLabelSetStratumIS(adaptLabel,DM_ADAPT_COARSEN,coarsenIS);}
    1556:   ISDestroy(&coarsenIS);
    1557:   ISDestroy(&refineIS);
    1558:   VecDestroy(&errVec);

    1560:   PetscFVSetComputeGradients(fvm,computeGradient);
    1561:   minMaxInd[1] = -minMaxInd[1];
    1562:   MPI_Allreduce(minMaxInd,minMaxIndGlobal,2,MPIU_REAL,MPI_MIN,PetscObjectComm((PetscObject)dm));
    1563:   minInd = minMaxIndGlobal[0];
    1564:   maxInd = -minMaxIndGlobal[1];
    1565:   PetscInfo2(ts, "error indicator range (%E, %E)\n", minInd, maxInd);
    1566:   if (nRefine || nCoarsen) { /* at least one cell is over the refinement threshold */
    1567:     DMAdaptLabel(dm,adaptLabel,&adaptedDM);
    1568:   }
    1569:   DMLabelDestroy(&adaptLabel);
    1570:   if (adaptedDM) {
    1571:     PetscInfo2(ts, "Adapted mesh, marking %D cells for refinement, and %D cells for coarsening\n", nRefine, nCoarsen);
    1572:     if (tsNew) {initializeTS(adaptedDM, user, tsNew);}
    1573:     if (solNew) {
    1574:       DMCreateGlobalVector(adaptedDM, solNew);
    1575:       PetscObjectSetName((PetscObject) *solNew, "solution");
    1576:       DMForestTransferVec(dm, sol, adaptedDM, *solNew, PETSC_TRUE, time);
    1577:     }
    1578:     if (isForest) {DMForestSetAdaptivityForest(adaptedDM,NULL);} /* clear internal references to the previous dm */
    1579:     DMDestroy(&adaptedDM);
    1580:   } else {
    1581:     if (tsNew)  *tsNew  = NULL;
    1582:     if (solNew) *solNew = NULL;
    1583:   }
    1584:   return(0);
    1585: }

    1587: int main(int argc, char **argv)
    1588: {
    1589:   MPI_Comm          comm;
    1590:   PetscDS           prob;
    1591:   PetscFV           fvm;
    1592:   PetscLimiter      limiter = NULL, noneLimiter = NULL;
    1593:   User              user;
    1594:   Model             mod;
    1595:   Physics           phys;
    1596:   DM                dm;
    1597:   PetscReal         ftime, cfl, dt, minRadius;
    1598:   PetscInt          dim, nsteps;
    1599:   TS                ts;
    1600:   TSConvergedReason reason;
    1601:   Vec               X;
    1602:   PetscViewer       viewer;
    1603:   PetscBool         simplex = PETSC_FALSE, vtkCellGeom, splitFaces, useAMR;
    1604:   PetscInt          overlap, adaptInterval;
    1605:   char              filename[PETSC_MAX_PATH_LEN] = "";
    1606:   char              physname[256]  = "advect";
    1607:   VecTagger         refineTag = NULL, coarsenTag = NULL;
    1608:   PetscErrorCode    ierr;

    1610:   PetscInitialize(&argc, &argv, (char*) 0, help);if (ierr) return ierr;
    1611:   comm = PETSC_COMM_WORLD;

    1613:   PetscNew(&user);
    1614:   PetscNew(&user->model);
    1615:   PetscNew(&user->model->physics);
    1616:   mod           = user->model;
    1617:   phys          = mod->physics;
    1618:   mod->comm     = comm;
    1619:   useAMR        = PETSC_FALSE;
    1620:   adaptInterval = 1;

    1622:   /* Register physical models to be available on the command line */
    1623:   PetscFunctionListAdd(&PhysicsList,"advect"          ,PhysicsCreate_Advect);
    1624:   PetscFunctionListAdd(&PhysicsList,"sw"              ,PhysicsCreate_SW);
    1625:   PetscFunctionListAdd(&PhysicsList,"euler"           ,PhysicsCreate_Euler);

    1627:   PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Mesh Options","");
    1628:   {
    1629:     cfl  = 0.9 * 4; /* default SSPRKS2 with s=5 stages is stable for CFL number s-1 */
    1630:     PetscOptionsReal("-ufv_cfl","CFL number per step","",cfl,&cfl,NULL);
    1631:     PetscOptionsString("-f","Exodus.II filename to read","",filename,filename,sizeof(filename),NULL);
    1632:     PetscOptionsBool("-simplex","Flag to use a simplex mesh","",simplex,&simplex,NULL);
    1633:     splitFaces = PETSC_FALSE;
    1634:     PetscOptionsBool("-ufv_split_faces","Split faces between cell sets","",splitFaces,&splitFaces,NULL);
    1635:     overlap = 1;
    1636:     PetscOptionsInt("-ufv_mesh_overlap","Number of cells to overlap partitions","",overlap,&overlap,NULL);
    1637:     user->vtkInterval = 1;
    1638:     PetscOptionsInt("-ufv_vtk_interval","VTK output interval (0 to disable)","",user->vtkInterval,&user->vtkInterval,NULL);
    1639:     user->vtkmon = PETSC_TRUE;
    1640:     PetscOptionsBool("-ufv_vtk_monitor","Use VTKMonitor routine","",user->vtkmon,&user->vtkmon,NULL);
    1641:     vtkCellGeom = PETSC_FALSE;
    1642:     PetscStrcpy(user->outputBasename, "ex11");
    1643:     PetscOptionsString("-ufv_vtk_basename","VTK output basename","",user->outputBasename,user->outputBasename,PETSC_MAX_PATH_LEN,NULL);
    1644:     PetscOptionsBool("-ufv_vtk_cellgeom","Write cell geometry (for debugging)","",vtkCellGeom,&vtkCellGeom,NULL);
    1645:     PetscOptionsBool("-ufv_use_amr","use local adaptive mesh refinement","",useAMR,&useAMR,NULL);
    1646:     PetscOptionsInt("-ufv_adapt_interval","time steps between AMR","",adaptInterval,&adaptInterval,NULL);
    1647:   }
    1648:   PetscOptionsEnd();

    1650:   if (useAMR) {
    1651:     VecTaggerBox refineBox, coarsenBox;

    1653:     refineBox.min  = refineBox.max  = PETSC_MAX_REAL;
    1654:     coarsenBox.min = coarsenBox.max = PETSC_MIN_REAL;

    1656:     VecTaggerCreate(comm,&refineTag);
    1657:     PetscObjectSetOptionsPrefix((PetscObject)refineTag,"refine_");
    1658:     VecTaggerSetType(refineTag,VECTAGGERABSOLUTE);
    1659:     VecTaggerAbsoluteSetBox(refineTag,&refineBox);
    1660:     VecTaggerSetFromOptions(refineTag);
    1661:     VecTaggerSetUp(refineTag);
    1662:     PetscObjectViewFromOptions((PetscObject)refineTag,NULL,"-tag_view");

    1664:     VecTaggerCreate(comm,&coarsenTag);
    1665:     PetscObjectSetOptionsPrefix((PetscObject)coarsenTag,"coarsen_");
    1666:     VecTaggerSetType(coarsenTag,VECTAGGERABSOLUTE);
    1667:     VecTaggerAbsoluteSetBox(coarsenTag,&coarsenBox);
    1668:     VecTaggerSetFromOptions(coarsenTag);
    1669:     VecTaggerSetUp(coarsenTag);
    1670:     PetscObjectViewFromOptions((PetscObject)coarsenTag,NULL,"-tag_view");
    1671:   }

    1673:   PetscOptionsBegin(comm,NULL,"Unstructured Finite Volume Physics Options","");
    1674:   {
    1675:     PetscErrorCode (*physcreate)(Model,Physics,PetscOptionItems*);
    1676:     PetscOptionsFList("-physics","Physics module to solve","",PhysicsList,physname,physname,sizeof physname,NULL);
    1677:     PetscFunctionListFind(PhysicsList,physname,&physcreate);
    1678:     PetscMemzero(phys,sizeof(struct _n_Physics));
    1679:     (*physcreate)(mod,phys,PetscOptionsObject);
    1680:     /* Count number of fields and dofs */
    1681:     for (phys->nfields=0,phys->dof=0; phys->field_desc[phys->nfields].name; phys->nfields++) phys->dof += phys->field_desc[phys->nfields].dof;
    1682:     if (phys->dof <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set dof",physname);
    1683:     ModelFunctionalSetFromOptions(mod,PetscOptionsObject);
    1684:   }
    1685:   PetscOptionsEnd();

    1687:   /* Create mesh */
    1688:   {
    1689:     size_t len,i;
    1690:     for (i = 0; i < DIM; i++) { mod->bounds[2*i] = 0.; mod->bounds[2*i+1] = 1.;};
    1691:     PetscStrlen(filename,&len);
    1692:     dim = DIM;
    1693:     if (!len) { /* a null name means just do a hex box */
    1694:       PetscInt cells[3] = {1, 1, 1}; /* coarse mesh is one cell; refine from there */
    1695:       PetscBool flg1, flg2, skew = PETSC_FALSE;
    1696:       PetscInt nret1 = DIM;
    1697:       PetscInt nret2 = 2*DIM;
    1698:       PetscOptionsBegin(comm,NULL,"Rectangular mesh options","");
    1699:       PetscOptionsIntArray("-grid_size","number of cells in each direction","",cells,&nret1,&flg1);
    1700:       PetscOptionsRealArray("-grid_bounds","bounds of the mesh in each direction (i.e., x_min,x_max,y_min,y_max","",mod->bounds,&nret2,&flg2);
    1701:       PetscOptionsBool("-grid_skew_60","Skew grid for 60 degree shock mesh","",skew,&skew,NULL);
    1702:       PetscOptionsEnd();
    1703:       if (flg1) {
    1704:         dim = nret1;
    1705:         if (dim != DIM) SETERRQ1(comm,PETSC_ERR_ARG_SIZ,"Dim wrong size %D in -grid_size",dim);
    1706:       }
    1707:       DMPlexCreateBoxMesh(comm, dim, simplex, cells, NULL, NULL, mod->bcs, PETSC_TRUE, &dm);
    1708:       if (flg2) {
    1709:         PetscInt dimEmbed, i;
    1710:         PetscInt nCoords;
    1711:         PetscScalar *coords;
    1712:         Vec coordinates;

    1714:         DMGetCoordinatesLocal(dm,&coordinates);
    1715:         DMGetCoordinateDim(dm,&dimEmbed);
    1716:         VecGetLocalSize(coordinates,&nCoords);
    1717:         if (nCoords % dimEmbed) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Coordinate vector the wrong size");
    1718:         VecGetArray(coordinates,&coords);
    1719:         for (i = 0; i < nCoords; i += dimEmbed) {
    1720:           PetscInt j;

    1722:           PetscScalar *coord = &coords[i];
    1723:           for (j = 0; j < dimEmbed; j++) {
    1724:             coord[j] = mod->bounds[2 * j] + coord[j] * (mod->bounds[2 * j + 1] - mod->bounds[2 * j]);
    1725:             if (dim==2 && cells[1]==1 && j==0 && skew) {
    1726:               if (cells[0]==2 && i==8) {
    1727:                 coord[j] = .57735026918963; /* hack to get 60 deg skewed mesh */
    1728:               }
    1729:               else if (cells[0]==3) {
    1730:                 if(i==2 || i==10) coord[j] = mod->bounds[1]/4.;
    1731:                 else if (i==4) coord[j] = mod->bounds[1]/2.;
    1732:                 else if (i==12) coord[j] = 1.57735026918963*mod->bounds[1]/2.;
    1733:               }
    1734:             }
    1735:           }
    1736:         }
    1737:         VecRestoreArray(coordinates,&coords);
    1738:         DMSetCoordinatesLocal(dm,coordinates);
    1739:       }
    1740:     } else {
    1741:       DMPlexCreateFromFile(comm, filename, PETSC_TRUE, &dm);
    1742:     }
    1743:   }
    1744:   DMViewFromOptions(dm, NULL, "-orig_dm_view");
    1745:   DMGetDimension(dm, &dim);

    1747:   /* set up BCs, functions, tags */
    1748:   DMCreateLabel(dm, "Face Sets");

    1750:   mod->errorIndicator = ErrorIndicator_Simple;

    1752:   {
    1753:     DM dmDist;

    1755:     DMSetBasicAdjacency(dm, PETSC_TRUE, PETSC_FALSE);
    1756:     DMPlexDistribute(dm, overlap, NULL, &dmDist);
    1757:     if (dmDist) {
    1758:       DMDestroy(&dm);
    1759:       dm   = dmDist;
    1760:     }
    1761:   }

    1763:   DMSetFromOptions(dm);

    1765:   {
    1766:     DM gdm;

    1768:     DMPlexConstructGhostCells(dm, NULL, NULL, &gdm);
    1769:     DMDestroy(&dm);
    1770:     dm   = gdm;
    1771:     DMViewFromOptions(dm, NULL, "-dm_view");
    1772:   }
    1773:   if (splitFaces) {ConstructCellBoundary(dm, user);}
    1774:   SplitFaces(&dm, "split faces", user);

    1776:   PetscFVCreate(comm, &fvm);
    1777:   PetscFVSetFromOptions(fvm);
    1778:   PetscFVSetNumComponents(fvm, phys->dof);
    1779:   PetscFVSetSpatialDimension(fvm, dim);
    1780:   PetscObjectSetName((PetscObject) fvm,"");
    1781:   {
    1782:     PetscInt f, dof;
    1783:     for (f=0,dof=0; f < phys->nfields; f++) {
    1784:       PetscInt newDof = phys->field_desc[f].dof;

    1786:       if (newDof == 1) {
    1787:         PetscFVSetComponentName(fvm,dof,phys->field_desc[f].name);
    1788:       }
    1789:       else {
    1790:         PetscInt j;

    1792:         for (j = 0; j < newDof; j++) {
    1793:           char     compName[256]  = "Unknown";

    1795:           PetscSNPrintf(compName,sizeof(compName),"%s_%d",phys->field_desc[f].name,j);
    1796:           PetscFVSetComponentName(fvm,dof+j,compName);
    1797:         }
    1798:       }
    1799:       dof += newDof;
    1800:     }
    1801:   }
    1802:   /* FV is now structured with one field having all physics as components */
    1803:   DMAddField(dm, NULL, (PetscObject) fvm);
    1804:   DMCreateDS(dm);
    1805:   DMGetDS(dm, &prob);
    1806:   PetscDSSetRiemannSolver(prob, 0, user->model->physics->riemann);
    1807:   PetscDSSetContext(prob, 0, user->model->physics);
    1808:   (*mod->setupbc)(prob,phys);
    1809:   PetscDSSetFromOptions(prob);
    1810:   {
    1811:     char      convType[256];
    1812:     PetscBool flg;

    1814:     PetscOptionsBegin(comm, "", "Mesh conversion options", "DMPLEX");
    1815:     PetscOptionsFList("-dm_type","Convert DMPlex to another format","ex12",DMList,DMPLEX,convType,256,&flg);
    1816:     PetscOptionsEnd();
    1817:     if (flg) {
    1818:       DM dmConv;

    1820:       DMConvert(dm,convType,&dmConv);
    1821:       if (dmConv) {
    1822:         DMViewFromOptions(dmConv, NULL, "-dm_conv_view");
    1823:         DMDestroy(&dm);
    1824:         dm   = dmConv;
    1825:         DMSetFromOptions(dm);
    1826:       }
    1827:     }
    1828:   }

    1830:   initializeTS(dm, user, &ts);

    1832:   DMCreateGlobalVector(dm, &X);
    1833:   PetscObjectSetName((PetscObject) X, "solution");
    1834:   SetInitialCondition(dm, X, user);
    1835:   if (useAMR) {
    1836:     PetscInt adaptIter;

    1838:     /* use no limiting when reconstructing gradients for adaptivity */
    1839:     PetscFVGetLimiter(fvm, &limiter);
    1840:     PetscObjectReference((PetscObject) limiter);
    1841:     PetscLimiterCreate(PetscObjectComm((PetscObject) fvm), &noneLimiter);
    1842:     PetscLimiterSetType(noneLimiter, PETSCLIMITERNONE);

    1844:     PetscFVSetLimiter(fvm, noneLimiter);
    1845:     for (adaptIter = 0; ; ++adaptIter) {
    1846:       PetscLogDouble bytes;
    1847:       TS             tsNew = NULL;

    1849:       PetscMemoryGetCurrentUsage(&bytes);
    1850:       PetscInfo2(ts, "refinement loop %D: memory used %g\n", adaptIter, bytes);
    1851:       DMViewFromOptions(dm, NULL, "-initial_dm_view");
    1852:       VecViewFromOptions(X, NULL, "-initial_vec_view");
    1853: #if 0
    1854:       if (viewInitial) {
    1855:         PetscViewer viewer;
    1856:         char        buf[256];
    1857:         PetscBool   isHDF5, isVTK;

    1859:         PetscViewerCreate(comm,&viewer);
    1860:         PetscViewerSetType(viewer,PETSCVIEWERVTK);
    1861:         PetscViewerSetOptionsPrefix(viewer,"initial_");
    1862:         PetscViewerSetFromOptions(viewer);
    1863:         PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERHDF5,&isHDF5);
    1864:         PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERVTK,&isVTK);
    1865:         if (isHDF5) {
    1866:           PetscSNPrintf(buf, 256, "ex11-initial-%d.h5", adaptIter);
    1867:         } else if (isVTK) {
    1868:           PetscSNPrintf(buf, 256, "ex11-initial-%d.vtu", adaptIter);
    1869:           PetscViewerPushFormat(viewer,PETSC_VIEWER_VTK_VTU);
    1870:         }
    1871:         PetscViewerFileSetMode(viewer,FILE_MODE_WRITE);
    1872:         PetscViewerFileSetName(viewer,buf);
    1873:         if (isHDF5) {
    1874:           DMView(dm,viewer);
    1875:           PetscViewerFileSetMode(viewer,FILE_MODE_UPDATE);
    1876:         }
    1877:         VecView(X,viewer);
    1878:         PetscViewerDestroy(&viewer);
    1879:       }
    1880: #endif

    1882:       adaptToleranceFVM(fvm, ts, X, refineTag, coarsenTag, user, &tsNew, NULL);
    1883:       if (!tsNew) {
    1884:         break;
    1885:       } else {
    1886:         DMDestroy(&dm);
    1887:         VecDestroy(&X);
    1888:         TSDestroy(&ts);
    1889:         ts   = tsNew;
    1890:         TSGetDM(ts,&dm);
    1891:         PetscObjectReference((PetscObject)dm);
    1892:         DMCreateGlobalVector(dm,&X);
    1893:         PetscObjectSetName((PetscObject) X, "solution");
    1894:         SetInitialCondition(dm, X, user);
    1895:       }
    1896:     }
    1897:     /* restore original limiter */
    1898:     PetscFVSetLimiter(fvm, limiter);
    1899:   }

    1901:   if (vtkCellGeom) {
    1902:     DM  dmCell;
    1903:     Vec cellgeom, partition;

    1905:     DMPlexTSGetGeometryFVM(dm, NULL, &cellgeom, NULL);
    1906:     OutputVTK(dm, "ex11-cellgeom.vtk", &viewer);
    1907:     VecView(cellgeom, viewer);
    1908:     PetscViewerDestroy(&viewer);
    1909:     CreatePartitionVec(dm, &dmCell, &partition);
    1910:     OutputVTK(dmCell, "ex11-partition.vtk", &viewer);
    1911:     VecView(partition, viewer);
    1912:     PetscViewerDestroy(&viewer);
    1913:     VecDestroy(&partition);
    1914:     DMDestroy(&dmCell);
    1915:   }

    1917:   /* collect max maxspeed from all processes -- todo */
    1918:   DMPlexTSGetGeometryFVM(dm, NULL, NULL, &minRadius);
    1919:   MPI_Allreduce(&phys->maxspeed,&mod->maxspeed,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
    1920:   if (mod->maxspeed <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set maxspeed",physname);
    1921:   dt   = cfl * minRadius / mod->maxspeed;
    1922:   TSSetTimeStep(ts,dt);
    1923:   TSSetFromOptions(ts);
    1924:   if (!useAMR) {
    1925:     TSSolve(ts,X);
    1926:     TSGetSolveTime(ts,&ftime);
    1927:     TSGetStepNumber(ts,&nsteps);
    1928:   } else {
    1929:     PetscReal finalTime;
    1930:     PetscInt  adaptIter;
    1931:     TS        tsNew = NULL;
    1932:     Vec       solNew = NULL;

    1934:     TSGetMaxTime(ts,&finalTime);
    1935:     TSSetMaxSteps(ts,adaptInterval);
    1936:     TSSolve(ts,X);
    1937:     TSGetSolveTime(ts,&ftime);
    1938:     TSGetStepNumber(ts,&nsteps);
    1939:     for (adaptIter = 0;ftime < finalTime;adaptIter++) {
    1940:       PetscLogDouble bytes;

    1942:       PetscMemoryGetCurrentUsage(&bytes);
    1943:       PetscInfo2(ts, "AMR time step loop %D: memory used %g\n", adaptIter, bytes);
    1944:       PetscFVSetLimiter(fvm,noneLimiter);
    1945:       adaptToleranceFVM(fvm,ts,X,refineTag,coarsenTag,user,&tsNew,&solNew);
    1946:       PetscFVSetLimiter(fvm,limiter);
    1947:       if (tsNew) {
    1948:         PetscInfo(ts, "AMR used\n");
    1949:         DMDestroy(&dm);
    1950:         VecDestroy(&X);
    1951:         TSDestroy(&ts);
    1952:         ts   = tsNew;
    1953:         X    = solNew;
    1954:         TSSetFromOptions(ts);
    1955:         VecGetDM(X,&dm);
    1956:         PetscObjectReference((PetscObject)dm);
    1957:         DMPlexTSGetGeometryFVM(dm, NULL, NULL, &minRadius);
    1958:         MPI_Allreduce(&phys->maxspeed,&mod->maxspeed,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
    1959:         if (mod->maxspeed <= 0) SETERRQ1(comm,PETSC_ERR_ARG_WRONGSTATE,"Physics '%s' did not set maxspeed",physname);
    1960:         dt   = cfl * minRadius / mod->maxspeed;
    1961:         TSSetStepNumber(ts,nsteps);
    1962:         TSSetTime(ts,ftime);
    1963:         TSSetTimeStep(ts,dt);
    1964:       } else {
    1965:         PetscInfo(ts, "AMR not used\n");
    1966:       }
    1967:       user->monitorStepOffset = nsteps;
    1968:       TSSetMaxSteps(ts,nsteps+adaptInterval);
    1969:       TSSolve(ts,X);
    1970:       TSGetSolveTime(ts,&ftime);
    1971:       TSGetStepNumber(ts,&nsteps);
    1972:     }
    1973:   }
    1974:   TSGetConvergedReason(ts,&reason);
    1975:   PetscPrintf(PETSC_COMM_WORLD,"%s at time %g after %D steps\n",TSConvergedReasons[reason],(double)ftime,nsteps);
    1976:   TSDestroy(&ts);

    1978:   VecTaggerDestroy(&refineTag);
    1979:   VecTaggerDestroy(&coarsenTag);
    1980:   PetscFunctionListDestroy(&PhysicsList);
    1981:   FunctionalLinkDestroy(&user->model->functionalRegistry);
    1982:   PetscFree(user->model->functionalMonitored);
    1983:   PetscFree(user->model->functionalCall);
    1984:   PetscFree(user->model->physics->data);
    1985:   PetscFree(user->model->physics);
    1986:   PetscFree(user->model);
    1987:   PetscFree(user);
    1988:   VecDestroy(&X);
    1989:   PetscLimiterDestroy(&limiter);
    1990:   PetscLimiterDestroy(&noneLimiter);
    1991:   PetscFVDestroy(&fvm);
    1992:   DMDestroy(&dm);
    1993:   PetscFinalize();
    1994:   return ierr;
    1995: }

    1997: /* Godunov fluxs */
    1998: PetscScalar cvmgp_(PetscScalar *a, PetscScalar *b, PetscScalar *test)
    1999: {
    2000:     /* System generated locals */
    2001:     PetscScalar ret_val;

    2003:     if (PetscRealPart(*test) > 0.) {
    2004:         goto L10;
    2005:     }
    2006:     ret_val = *b;
    2007:     return ret_val;
    2008: L10:
    2009:     ret_val = *a;
    2010:     return ret_val;
    2011: } /* cvmgp_ */

    2013: PetscScalar cvmgm_(PetscScalar *a, PetscScalar *b, PetscScalar *test)
    2014: {
    2015:     /* System generated locals */
    2016:     PetscScalar ret_val;

    2018:     if (PetscRealPart(*test) < 0.) {
    2019:         goto L10;
    2020:     }
    2021:     ret_val = *b;
    2022:     return ret_val;
    2023: L10:
    2024:     ret_val = *a;
    2025:     return ret_val;
    2026: } /* cvmgm_ */

    2028: int riem1mdt( PetscScalar *gaml, PetscScalar *gamr, PetscScalar *rl, PetscScalar *pl,
    2029:               PetscScalar *uxl, PetscScalar *rr, PetscScalar *pr,
    2030:               PetscScalar *uxr, PetscScalar *rstarl, PetscScalar *rstarr, PetscScalar *
    2031:               pstar, PetscScalar *ustar)
    2032: {
    2033:     /* Initialized data */

    2035:     static PetscScalar smallp = 1e-8;

    2037:     /* System generated locals */
    2038:     int i__1;
    2039:     PetscScalar d__1, d__2;

    2041:     /* Local variables */
    2042:     static int i0;
    2043:     static PetscScalar cl, cr, wl, zl, wr, zr, pst, durl, skpr1, skpr2;
    2044:     static int iwave;
    2045:     static PetscScalar gascl4, gascr4, cstarl, dpstar, cstarr;
    2046:     /* static PetscScalar csqrl, csqrr, gascl1, gascl2, gascl3, gascr1, gascr2, gascr3; */
    2047:     static int iterno;
    2048:     static PetscScalar ustarl, ustarr, rarepr1, rarepr2;

    2052:     /* gascl1 = *gaml - 1.; */
    2053:     /* gascl2 = (*gaml + 1.) * .5; */
    2054:     /* gascl3 = gascl2 / *gaml; */
    2055:     gascl4 = 1. / (*gaml - 1.);

    2057:     /* gascr1 = *gamr - 1.; */
    2058:     /* gascr2 = (*gamr + 1.) * .5; */
    2059:     /* gascr3 = gascr2 / *gamr; */
    2060:     gascr4 = 1. / (*gamr - 1.);
    2061:     iterno = 10;
    2062: /*        find pstar: */
    2063:     cl = PetscSqrtScalar(*gaml * *pl / *rl);
    2064:     cr = PetscSqrtScalar(*gamr * *pr / *rr);
    2065:     wl = *rl * cl;
    2066:     wr = *rr * cr;
    2067:     /* csqrl = wl * wl; */
    2068:     /* csqrr = wr * wr; */
    2069:     *pstar = (wl * *pr + wr * *pl) / (wl + wr);
    2070:     *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
    2071:     pst = *pl / *pr;
    2072:     skpr1 = cr * (pst - 1.) * PetscSqrtScalar(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
    2073:     d__1 = (*gamr - 1.) / (*gamr * 2.);
    2074:     rarepr2 = gascr4 * 2. * cr * (1. - PetscPowScalar(pst, d__1));
    2075:     pst = *pr / *pl;
    2076:     skpr2 = cl * (pst - 1.) * PetscSqrtScalar(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
    2077:     d__1 = (*gaml - 1.) / (*gaml * 2.);
    2078:     rarepr1 = gascl4 * 2. * cl * (1. - PetscPowScalar(pst, d__1));
    2079:     durl = *uxr - *uxl;
    2080:     if (PetscRealPart(*pr) < PetscRealPart(*pl)) {
    2081:         if (PetscRealPart(durl) >= PetscRealPart(rarepr1)) {
    2082:             iwave = 100;
    2083:         } else if (PetscRealPart(durl) <= PetscRealPart(-skpr1)) {
    2084:             iwave = 300;
    2085:         } else {
    2086:             iwave = 400;
    2087:         }
    2088:     } else {
    2089:         if (PetscRealPart(durl) >= PetscRealPart(rarepr2)) {
    2090:             iwave = 100;
    2091:         } else if (PetscRealPart(durl) <= PetscRealPart(-skpr2)) {
    2092:             iwave = 300;
    2093:         } else {
    2094:             iwave = 200;
    2095:         }
    2096:     }
    2097:     if (iwave == 100) {
    2098: /*     1-wave: rarefaction wave, 3-wave: rarefaction wave */
    2099: /*     case (100) */
    2100:         i__1 = iterno;
    2101:         for (i0 = 1; i0 <= i__1; ++i0) {
    2102:             d__1 = *pstar / *pl;
    2103:             d__2 = 1. / *gaml;
    2104:             *rstarl = *rl * PetscPowScalar(d__1, d__2);
    2105:             cstarl = PetscSqrtScalar(*gaml * *pstar / *rstarl);
    2106:             ustarl = *uxl - gascl4 * 2. * (cstarl - cl);
    2107:             zl = *rstarl * cstarl;
    2108:             d__1 = *pstar / *pr;
    2109:             d__2 = 1. / *gamr;
    2110:             *rstarr = *rr * PetscPowScalar(d__1, d__2);
    2111:             cstarr = PetscSqrtScalar(*gamr * *pstar / *rstarr);
    2112:             ustarr = *uxr + gascr4 * 2. * (cstarr - cr);
    2113:             zr = *rstarr * cstarr;
    2114:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
    2115:             *pstar -= dpstar;
    2116:             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
    2117:             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
    2118: #if 0
    2119:         break;
    2120: #endif
    2121:             }
    2122:         }
    2123: /*     1-wave: shock wave, 3-wave: rarefaction wave */
    2124:     } else if (iwave == 200) {
    2125: /*     case (200) */
    2126:         i__1 = iterno;
    2127:         for (i0 = 1; i0 <= i__1; ++i0) {
    2128:             pst = *pstar / *pl;
    2129:             ustarl = *uxl - (pst - 1.) * cl * PetscSqrtScalar(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
    2130:             zl = *pl / cl * PetscSqrtScalar(*gaml * 2. * (*gaml - 1. + (*gaml + 1.) * pst)) * (*gaml - 1. + (*gaml + 1.) * pst) / (*gaml * 3. - 1. + (*gaml + 1.) * pst);
    2131:             d__1 = *pstar / *pr;
    2132:             d__2 = 1. / *gamr;
    2133:             *rstarr = *rr * PetscPowScalar(d__1, d__2);
    2134:             cstarr = PetscSqrtScalar(*gamr * *pstar / *rstarr);
    2135:             zr = *rstarr * cstarr;
    2136:             ustarr = *uxr + gascr4 * 2. * (cstarr - cr);
    2137:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
    2138:             *pstar -= dpstar;
    2139:             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
    2140:             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
    2141: #if 0
    2142:         break;
    2143: #endif
    2144:             }
    2145:         }
    2146: /*     1-wave: shock wave, 3-wave: shock */
    2147:     } else if (iwave == 300) {
    2148: /*     case (300) */
    2149:         i__1 = iterno;
    2150:         for (i0 = 1; i0 <= i__1; ++i0) {
    2151:             pst = *pstar / *pl;
    2152:             ustarl = *uxl - (pst - 1.) * cl * PetscSqrtScalar(2. / (*gaml * (*gaml - 1. + (*gaml + 1.) * pst)));
    2153:             zl = *pl / cl * PetscSqrtScalar(*gaml * 2. * (*gaml - 1. + (*gaml + 1.) * pst)) * (*gaml - 1. + (*gaml + 1.) * pst) / (*gaml * 3. - 1. + (*gaml + 1.) * pst);
    2154:             pst = *pstar / *pr;
    2155:             ustarr = *uxr + (pst - 1.) * cr * PetscSqrtScalar(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
    2156:             zr = *pr / cr * PetscSqrtScalar(*gamr * 2. * (*gamr - 1. + (*gamr + 1.) * pst)) * (*gamr - 1. + (*gamr + 1.) * pst) / (*gamr * 3. - 1. + (*gamr + 1.) * pst);
    2157:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
    2158:             *pstar -= dpstar;
    2159:             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
    2160:             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
    2161: #if 0
    2162:         break;
    2163: #endif
    2164:             }
    2165:         }
    2166: /*     1-wave: rarefaction wave, 3-wave: shock */
    2167:     } else if (iwave == 400) {
    2168: /*     case (400) */
    2169:         i__1 = iterno;
    2170:         for (i0 = 1; i0 <= i__1; ++i0) {
    2171:             d__1 = *pstar / *pl;
    2172:             d__2 = 1. / *gaml;
    2173:             *rstarl = *rl * PetscPowScalar(d__1, d__2);
    2174:             cstarl = PetscSqrtScalar(*gaml * *pstar / *rstarl);
    2175:             ustarl = *uxl - gascl4 * 2. * (cstarl - cl);
    2176:             zl = *rstarl * cstarl;
    2177:             pst = *pstar / *pr;
    2178:             ustarr = *uxr + (pst - 1.) * cr * PetscSqrtScalar(2. / (*gamr * (*gamr - 1. + (*gamr + 1.) * pst)));
    2179:             zr = *pr / cr * PetscSqrtScalar(*gamr * 2. * (*gamr - 1. + (*gamr + 1.) * pst)) * (*gamr - 1. + (*gamr + 1.) * pst) / (*gamr * 3. - 1. + (*gamr + 1.) * pst);
    2180:             dpstar = zl * zr * (ustarr - ustarl) / (zl + zr);
    2181:             *pstar -= dpstar;
    2182:             *pstar = PetscMax(PetscRealPart(*pstar),PetscRealPart(smallp));
    2183:             if (PetscAbsScalar(dpstar) / PetscRealPart(*pstar) <= 1e-8) {
    2184: #if 0
    2185:               break;
    2186: #endif
    2187:             }
    2188:         }
    2189:     }

    2191:     *ustar = (zl * ustarr + zr * ustarl) / (zl + zr);
    2192:     if (PetscRealPart(*pstar) > PetscRealPart(*pl)) {
    2193:         pst = *pstar / *pl;
    2194:         *rstarl = ((*gaml + 1.) * pst + *gaml - 1.) / ((*gaml - 1.) * pst + *
    2195:                 gaml + 1.) * *rl;
    2196:     }
    2197:     if (PetscRealPart(*pstar) > PetscRealPart(*pr)) {
    2198:         pst = *pstar / *pr;
    2199:         *rstarr = ((*gamr + 1.) * pst + *gamr - 1.) / ((*gamr - 1.) * pst + *
    2200:                 gamr + 1.) * *rr;
    2201:     }
    2202:     return iwave;
    2203: }

    2205: PetscScalar sign(PetscScalar x)
    2206: {
    2207:     if(PetscRealPart(x) > 0) return 1.0;
    2208:     if(PetscRealPart(x) < 0) return -1.0;
    2209:     return 0.0;
    2210: }
    2211: /*        Riemann Solver */
    2212: /* -------------------------------------------------------------------- */
    2213: int riemannsolver(PetscScalar *xcen, PetscScalar *xp,
    2214:                    PetscScalar *dtt, PetscScalar *rl, PetscScalar *uxl, PetscScalar *pl,
    2215:                    PetscScalar *utl, PetscScalar *ubl, PetscScalar *gaml, PetscScalar *rho1l,
    2216:                    PetscScalar *rr, PetscScalar *uxr, PetscScalar *pr, PetscScalar *utr,
    2217:                    PetscScalar *ubr, PetscScalar *gamr, PetscScalar *rho1r, PetscScalar *rx,
    2218:                    PetscScalar *uxm, PetscScalar *px, PetscScalar *utx, PetscScalar *ubx,
    2219:                    PetscScalar *gam, PetscScalar *rho1)
    2220: {
    2221:     /* System generated locals */
    2222:     PetscScalar d__1, d__2;

    2224:     /* Local variables */
    2225:     static PetscScalar s, c0, p0, r0, u0, w0, x0, x2, ri, cx, sgn0, wsp0, gasc1, gasc2, gasc3, gasc4;
    2226:     static PetscScalar cstar, pstar, rstar, ustar, xstar, wspst, ushock, streng, rstarl, rstarr, rstars;
    2227:     int iwave;

    2229:     if (*rl == *rr && *pr == *pl && *uxl == *uxr && *gaml == *gamr) {
    2230:         *rx = *rl;
    2231:         *px = *pl;
    2232:         *uxm = *uxl;
    2233:         *gam = *gaml;
    2234:         x2 = *xcen + *uxm * *dtt;

    2236:         if (PetscRealPart(*xp) >= PetscRealPart(x2)) {
    2237:             *utx = *utr;
    2238:             *ubx = *ubr;
    2239:             *rho1 = *rho1r;
    2240:         } else {
    2241:             *utx = *utl;
    2242:             *ubx = *ubl;
    2243:             *rho1 = *rho1l;
    2244:         }
    2245:         return 0;
    2246:     }
    2247:     iwave = riem1mdt(gaml, gamr, rl, pl, uxl, rr, pr, uxr, &rstarl, &rstarr, &pstar, &ustar);

    2249:     x2 = *xcen + ustar * *dtt;
    2250:     d__1 = *xp - x2;
    2251:     sgn0 = sign(d__1);
    2252: /*            x is in 3-wave if sgn0 = 1 */
    2253: /*            x is in 1-wave if sgn0 = -1 */
    2254:     r0 = cvmgm_(rl, rr, &sgn0);
    2255:     p0 = cvmgm_(pl, pr, &sgn0);
    2256:     u0 = cvmgm_(uxl, uxr, &sgn0);
    2257:     *gam = cvmgm_(gaml, gamr, &sgn0);
    2258:     gasc1 = *gam - 1.;
    2259:     gasc2 = (*gam + 1.) * .5;
    2260:     gasc3 = gasc2 / *gam;
    2261:     gasc4 = 1. / (*gam - 1.);
    2262:     c0 = PetscSqrtScalar(*gam * p0 / r0);
    2263:     streng = pstar - p0;
    2264:     w0 = *gam * r0 * p0 * (gasc3 * streng / p0 + 1.);
    2265:     rstars = r0 / (1. - r0 * streng / w0);
    2266:     d__1 = p0 / pstar;
    2267:     d__2 = -1. / *gam;
    2268:     rstarr = r0 * PetscPowScalar(d__1, d__2);
    2269:     rstar = cvmgm_(&rstarr, &rstars, &streng);
    2270:     w0 = PetscSqrtScalar(w0);
    2271:     cstar = PetscSqrtScalar(*gam * pstar / rstar);
    2272:     wsp0 = u0 + sgn0 * c0;
    2273:     wspst = ustar + sgn0 * cstar;
    2274:     ushock = ustar + sgn0 * w0 / rstar;
    2275:     wspst = cvmgp_(&ushock, &wspst, &streng);
    2276:     wsp0 = cvmgp_(&ushock, &wsp0, &streng);
    2277:     x0 = *xcen + wsp0 * *dtt;
    2278:     xstar = *xcen + wspst * *dtt;
    2279: /*           using gas formula to evaluate rarefaction wave */
    2280: /*            ri : reiman invariant */
    2281:     ri = u0 - sgn0 * 2. * gasc4 * c0;
    2282:     cx = sgn0 * .5 * gasc1 / gasc2 * ((*xp - *xcen) / *dtt - ri);
    2283:     *uxm = ri + sgn0 * 2. * gasc4 * cx;
    2284:     s = p0 / PetscPowScalar(r0, *gam);
    2285:     d__1 = cx * cx / (*gam * s);
    2286:     *rx = PetscPowScalar(d__1, gasc4);
    2287:     *px = cx * cx * *rx / *gam;
    2288:     d__1 = sgn0 * (x0 - *xp);
    2289:     *rx = cvmgp_(rx, &r0, &d__1);
    2290:     d__1 = sgn0 * (x0 - *xp);
    2291:     *px = cvmgp_(px, &p0, &d__1);
    2292:     d__1 = sgn0 * (x0 - *xp);
    2293:     *uxm = cvmgp_(uxm, &u0, &d__1);
    2294:     d__1 = sgn0 * (xstar - *xp);
    2295:     *rx = cvmgm_(rx, &rstar, &d__1);
    2296:     d__1 = sgn0 * (xstar - *xp);
    2297:     *px = cvmgm_(px, &pstar, &d__1);
    2298:     d__1 = sgn0 * (xstar - *xp);
    2299:     *uxm = cvmgm_(uxm, &ustar, &d__1);
    2300:     if (PetscRealPart(*xp) >= PetscRealPart(x2)) {
    2301:         *utx = *utr;
    2302:         *ubx = *ubr;
    2303:         *rho1 = *rho1r;
    2304:     } else {
    2305:         *utx = *utl;
    2306:         *ubx = *ubl;
    2307:         *rho1 = *rho1l;
    2308:     }
    2309:     return iwave;
    2310: }
    2311: int godunovflux( const PetscScalar *ul, const PetscScalar *ur,
    2312:                  PetscScalar *flux, const PetscReal *nn, const int *ndim,
    2313:                  const PetscReal *gamma)
    2314: {
    2315:     /* System generated locals */
    2316:   int i__1,iwave;
    2317:     PetscScalar d__1, d__2, d__3;

    2319:     /* Local variables */
    2320:     static int k;
    2321:     static PetscScalar bn[3], fn, ft, tg[3], pl, rl, pm, pr, rr, xp, ubl, ubm,
    2322:             ubr, dtt, unm, tmp, utl, utm, uxl, utr, uxr, gaml, gamm, gamr,
    2323:             xcen, rhom, rho1l, rho1m, rho1r;
    2324:     /* Parameter adjustments */
    2325:     --nn;
    2326:     --flux;
    2327:     --ur;
    2328:     --ul;

    2330:     /* Function Body */
    2331:     xcen = 0.;
    2332:     xp = 0.;
    2333:     i__1 = *ndim;
    2334:     for (k = 1; k <= i__1; ++k) {
    2335:         tg[k - 1] = 0.;
    2336:         bn[k - 1] = 0.;
    2337:     }
    2338:     dtt = 1.;
    2339:     if (*ndim == 3) {
    2340:         if (nn[1] == 0. && nn[2] == 0.) {
    2341:             tg[0] = 1.;
    2342:         } else {
    2343:             tg[0] = -nn[2];
    2344:             tg[1] = nn[1];
    2345:         }
    2346: /*           tmp=dsqrt(tg(1)**2+tg(2)**2) */
    2347: /*           tg=tg/tmp */
    2348:         bn[0] = -nn[3] * tg[1];
    2349:         bn[1] = nn[3] * tg[0];
    2350:         bn[2] = nn[1] * tg[1] - nn[2] * tg[0];
    2351: /* Computing 2nd power */
    2352:         d__1 = bn[0];
    2353: /* Computing 2nd power */
    2354:         d__2 = bn[1];
    2355: /* Computing 2nd power */
    2356:         d__3 = bn[2];
    2357:         tmp = PetscSqrtScalar(d__1 * d__1 + d__2 * d__2 + d__3 * d__3);
    2358:         i__1 = *ndim;
    2359:         for (k = 1; k <= i__1; ++k) {
    2360:             bn[k - 1] /= tmp;
    2361:         }
    2362:     } else if (*ndim == 2) {
    2363:         tg[0] = -nn[2];
    2364:         tg[1] = nn[1];
    2365: /*           tmp=dsqrt(tg(1)**2+tg(2)**2) */
    2366: /*           tg=tg/tmp */
    2367:         bn[0] = 0.;
    2368:         bn[1] = 0.;
    2369:         bn[2] = 1.;
    2370:     }
    2371:     rl = ul[1];
    2372:     rr = ur[1];
    2373:     uxl = 0.;
    2374:     uxr = 0.;
    2375:     utl = 0.;
    2376:     utr = 0.;
    2377:     ubl = 0.;
    2378:     ubr = 0.;
    2379:     i__1 = *ndim;
    2380:     for (k = 1; k <= i__1; ++k) {
    2381:         uxl += ul[k + 1] * nn[k];
    2382:         uxr += ur[k + 1] * nn[k];
    2383:         utl += ul[k + 1] * tg[k - 1];
    2384:         utr += ur[k + 1] * tg[k - 1];
    2385:         ubl += ul[k + 1] * bn[k - 1];
    2386:         ubr += ur[k + 1] * bn[k - 1];
    2387:     }
    2388:     uxl /= rl;
    2389:     uxr /= rr;
    2390:     utl /= rl;
    2391:     utr /= rr;
    2392:     ubl /= rl;
    2393:     ubr /= rr;

    2395:     gaml = *gamma;
    2396:     gamr = *gamma;
    2397: /* Computing 2nd power */
    2398:     d__1 = uxl;
    2399: /* Computing 2nd power */
    2400:     d__2 = utl;
    2401: /* Computing 2nd power */
    2402:     d__3 = ubl;
    2403:     pl = (*gamma - 1.) * (ul[*ndim + 2] - rl * .5 * (d__1 * d__1 + d__2 * d__2 + d__3 * d__3));
    2404: /* Computing 2nd power */
    2405:     d__1 = uxr;
    2406: /* Computing 2nd power */
    2407:     d__2 = utr;
    2408: /* Computing 2nd power */
    2409:     d__3 = ubr;
    2410:     pr = (*gamma - 1.) * (ur[*ndim + 2] - rr * .5 * (d__1 * d__1 + d__2 * d__2 + d__3 * d__3));
    2411:     rho1l = rl;
    2412:     rho1r = rr;

    2414:     iwave = riemannsolver(&xcen, &xp, &dtt, &rl, &uxl, &pl, &utl, &ubl, &gaml, &
    2415:                           rho1l, &rr, &uxr, &pr, &utr, &ubr, &gamr, &rho1r, &rhom, &unm, &
    2416:                           pm, &utm, &ubm, &gamm, &rho1m);

    2418:     flux[1] = rhom * unm;
    2419:     fn = rhom * unm * unm + pm;
    2420:     ft = rhom * unm * utm;
    2421: /*           flux(2)=fn*nn(1)+ft*nn(2) */
    2422: /*           flux(3)=fn*tg(1)+ft*tg(2) */
    2423:     flux[2] = fn * nn[1] + ft * tg[0];
    2424:     flux[3] = fn * nn[2] + ft * tg[1];
    2425: /*           flux(2)=rhom*unm*(unm)+pm */
    2426: /*           flux(3)=rhom*(unm)*utm */
    2427:     if (*ndim == 3) {
    2428:         flux[4] = rhom * unm * ubm;
    2429:     }
    2430:     flux[*ndim + 2] = (rhom * .5 * (unm * unm + utm * utm + ubm * ubm) + gamm / (gamm - 1.) * pm) * unm;
    2431:     return iwave;
    2432: } /* godunovflux_ */

    2434: /* Subroutine to set up the initial conditions for the */
    2435: /* Shock Interface interaction or linear wave (Ravi Samtaney,Mark Adams). */
    2436: /* ----------------------------------------------------------------------- */
    2437: int projecteqstate(PetscReal wc[], const PetscReal ueq[], PetscReal lv[][3])
    2438: {
    2439:   int j,k;
    2440: /*      Wc=matmul(lv,Ueq) 3 vars */
    2441:   for (k = 0; k < 3; ++k) {
    2442:     wc[k] = 0.;
    2443:     for (j = 0; j < 3; ++j) {
    2444:       wc[k] += lv[k][j]*ueq[j];
    2445:     }
    2446:   }
    2447:   return 0;
    2448: }
    2449: /* ----------------------------------------------------------------------- */
    2450: int projecttoprim(PetscReal v[], const PetscReal wc[], PetscReal rv[][3])
    2451: {
    2452:   int k,j;
    2453:   /*      V=matmul(rv,WC) 3 vars */
    2454:   for (k = 0; k < 3; ++k) {
    2455:     v[k] = 0.;
    2456:     for (j = 0; j < 3; ++j) {
    2457:       v[k] += rv[k][j]*wc[j];
    2458:     }
    2459:   }
    2460:   return 0;
    2461: }
    2462: /* ---------------------------------------------------------------------- */
    2463: int eigenvectors(PetscReal rv[][3], PetscReal lv[][3], const PetscReal ueq[], PetscReal gamma)
    2464: {
    2465:   int j,k;
    2466:   PetscReal rho,csnd,p0;
    2467:   /* PetscScalar u; */

    2469:   for (k = 0; k < 3; ++k) for (j = 0; j < 3; ++j) { lv[k][j] = 0.; rv[k][j] = 0.; }
    2470:   rho = ueq[0];
    2471:   /* u = ueq[1]; */
    2472:   p0 = ueq[2];
    2473:   csnd = PetscSqrtReal(gamma * p0 / rho);
    2474:   lv[0][1] = rho * .5;
    2475:   lv[0][2] = -.5 / csnd;
    2476:   lv[1][0] = csnd;
    2477:   lv[1][2] = -1. / csnd;
    2478:   lv[2][1] = rho * .5;
    2479:   lv[2][2] = .5 / csnd;
    2480:   rv[0][0] = -1. / csnd;
    2481:   rv[1][0] = 1. / rho;
    2482:   rv[2][0] = -csnd;
    2483:   rv[0][1] = 1. / csnd;
    2484:   rv[0][2] = 1. / csnd;
    2485:   rv[1][2] = 1. / rho;
    2486:   rv[2][2] = csnd;
    2487:   return 0;
    2488: }

    2490: int initLinearWave(EulerNode *ux, const PetscReal gamma, const PetscReal coord[], const PetscReal Lx)
    2491: {
    2492:   PetscReal p0,u0,wcp[3],wc[3];
    2493:   PetscReal lv[3][3];
    2494:   PetscReal vp[3];
    2495:   PetscReal rv[3][3];
    2496:   PetscReal eps, ueq[3], rho0, twopi;

    2498:   /* Function Body */
    2499:   twopi = 2.*PETSC_PI;
    2500:   eps = 1e-4; /* perturbation */
    2501:   rho0 = 1e3;   /* density of water */
    2502:   p0 = 101325.; /* init pressure of 1 atm (?) */
    2503:   u0 = 0.;
    2504:   ueq[0] = rho0;
    2505:   ueq[1] = u0;
    2506:   ueq[2] = p0;
    2507:   /* Project initial state to characteristic variables */
    2508:   eigenvectors(rv, lv, ueq, gamma);
    2509:   projecteqstate(wc, ueq, lv);
    2510:   wcp[0] = wc[0];
    2511:   wcp[1] = wc[1];
    2512:   wcp[2] = wc[2] + eps * PetscCosReal(coord[0] * 2. * twopi / Lx);
    2513:   projecttoprim(vp, wcp, rv);
    2514:   ux->r = vp[0]; /* density */
    2515:   ux->ru[0] = vp[0] * vp[1]; /* x momentum */
    2516:   ux->ru[1] = 0.;
    2517: #if defined DIM > 2
    2518:   if (dim>2) ux->ru[2] = 0.;
    2519: #endif
    2520:   /* E = rho * e + rho * v^2/2 = p/(gam-1) + rho*v^2/2 */
    2521:   ux->E = vp[2]/(gamma - 1.) + 0.5*vp[0]*vp[1]*vp[1];
    2522:   return 0;
    2523: }

    2525: /*TEST

    2527:   # 2D Advection 0-10
    2528:   test:
    2529:     suffix: 0
    2530:     requires: exodusii
    2531:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo

    2533:   test:
    2534:     suffix: 1
    2535:     requires: exodusii
    2536:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo

    2538:   test:
    2539:     suffix: 2
    2540:     requires: exodusii
    2541:     nsize: 2
    2542:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo

    2544:   test:
    2545:     suffix: 3
    2546:     requires: exodusii
    2547:     nsize: 2
    2548:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo

    2550:   test:
    2551:     suffix: 4
    2552:     requires: exodusii
    2553:     nsize: 8
    2554:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad.exo

    2556:   test:
    2557:     suffix: 5
    2558:     requires: exodusii
    2559:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo -ts_type rosw -ts_adapt_reject_safety 1

    2561:   test:
    2562:     suffix: 6
    2563:     requires: exodusii
    2564:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/squaremotor-30.exo -ufv_split_faces

    2566:   test:
    2567:     suffix: 7
    2568:     requires: exodusii
    2569:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 1

    2571:   test:
    2572:     suffix: 8
    2573:     requires: exodusii
    2574:     nsize: 2
    2575:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 1

    2577:   test:
    2578:     suffix: 9
    2579:     requires: exodusii
    2580:     nsize: 8
    2581:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad-15.exo -dm_refine 1

    2583:   test:
    2584:     suffix: 10
    2585:     requires: exodusii
    2586:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside-quad.exo

    2588:   # 2D Shallow water
    2589:   test:
    2590:     suffix: sw_0
    2591:     requires: exodusii
    2592:     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

    2594:   # 2D Advection: p4est
    2595:   test:
    2596:     suffix: p4est_advec_2d
    2597:     requires: p4est
    2598:     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

    2600:   # Advection in a box
    2601:   test:
    2602:     suffix: adv_2d_quad_0
    2603:     args: -ufv_vtk_interval 0 -dm_refine 3 -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3

    2605:   test:
    2606:     suffix: adv_2d_quad_1
    2607:     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
    2608:     timeoutfactor: 3

    2610:   test:
    2611:     suffix: adv_2d_quad_p4est_0
    2612:     requires: p4est
    2613:     args: -ufv_vtk_interval 0 -dm_refine 5 -dm_type p4est -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3

    2615:   test:
    2616:     suffix: adv_2d_quad_p4est_1
    2617:     requires: p4est
    2618:     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
    2619:     timeoutfactor: 3

    2621:   test:
    2622:     suffix: adv_2d_quad_p4est_adapt_0
    2623:     requires: p4est !__float128 #broken for quad precision
    2624:     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
    2625:     timeoutfactor: 3

    2627:   test:
    2628:     suffix: adv_2d_tri_0
    2629:     requires: triangle
    2630:     TODO: how did this ever get in master when there is no support for this
    2631:     args: -ufv_vtk_interval 0 -simplex -dm_refine 3 -dm_plex_separate_marker -bc_inflow 1,2,4 -bc_outflow 3

    2633:   test:
    2634:     suffix: adv_2d_tri_1
    2635:     requires: triangle
    2636:     TODO: how did this ever get in master when there is no support for this
    2637:     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

    2639:   test:
    2640:     suffix: adv_0
    2641:     requires: exodusii
    2642:     args: -ufv_vtk_interval 0 -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/blockcylinder-50.exo -bc_inflow 100,101,200 -bc_outflow 201

    2644:   test:
    2645:     suffix: shock_0
    2646:     requires: p4est !single !complex
    2647:     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
    2648:     timeoutfactor: 3

    2650:   # Test GLVis visualization of PetscFV fields
    2651:   test:
    2652:     suffix: glvis_adv_2d_tet
    2653:     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

    2655:   test:
    2656:     suffix: glvis_adv_2d_quad
    2657:     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

    2659:   test:
    2660:     suffix: tut_1
    2661:     requires: exodusii
    2662:     nsize: 1
    2663:     args: -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo

    2665:   test:
    2666:     suffix: tut_2
    2667:     requires: exodusii
    2668:     nsize: 1
    2669:     args: -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo -ts_type rosw

    2671:   test:
    2672:     suffix: tut_3
    2673:     requires: exodusii
    2674:     nsize: 4
    2675:     args: -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/annulus-20.exo -monitor Error -advect_sol_type bump -petscfv_type leastsquares -petsclimiter_type sin

    2677:   test:
    2678:     suffix: tut_4
    2679:     requires: exodusii
    2680:     nsize: 4
    2681:     args: -f ${wPETSC_DIR}/share/petsc/datafiles/meshes/annulus-20.exo -physics sw -monitor Height,Energy -petscfv_type leastsquares -petsclimiter_type minmod

    2683: TEST*/