Actual source code: ex33.c
petsc-3.4.2 2013-07-02

      1: static char help[] = "Multiphase flow in a porous medium in 1d.\n\n";
      2: #include <petscdmda.h>
      3: #include <petscsnes.h>

      5: typedef struct {
      6:   DM        cda;
      7:   Vec       uold;
      8:   Vec       Kappa;
      9:   PetscReal phi;
     10:   PetscReal kappaWet;
     11:   PetscReal kappaNoWet;
     12:   PetscReal dt;
     13:   /* Boundary conditions */
     14:   PetscReal sl, vl, pl;
     15: } AppCtx;

     17: typedef struct {
     18:   PetscScalar s; /* The saturation on each cell */
     19:   PetscScalar v; /* The velocity on each face */
     20:   PetscScalar p; /* The pressure on each cell */
     21: } Field;

     25: /*
     26:    FormPermeability - Forms permeability field.

     28:    Input Parameters:
     29:    user - user-defined application context

     31:    Output Parameter:
     32:    Kappa - vector
     33:  */
     34: PetscErrorCode FormPermeability(DM da, Vec Kappa, AppCtx *user)
     35: {
     36:   DM             cda;
     37:   Vec            c;
     38:   PetscScalar    *K;
     39:   PetscScalar    *coords;
     40:   PetscInt       xs, xm, i;

     44:   DMGetCoordinateDM(da, &cda);
     45:   DMGetCoordinates(da, &c);
     46:   DMDAGetCorners(da, &xs,NULL,NULL, &xm,NULL,NULL);
     47:   DMDAVecGetArray(da, Kappa, &K);
     48:   DMDAVecGetArray(cda, c, &coords);
     49:   for (i = xs; i < xs+xm; ++i) {
     50: #if 1
     51:     K[i] = 1.0;
     52: #else
     53:     /* Notch */
     54:     if (i == (xs+xm)/2) K[i] = 0.00000001;
     55:     else K[i] = 1.0;
     56: #endif
     57:   }
     58:   DMDAVecRestoreArray(da, Kappa, &K);
     59:   DMDAVecRestoreArray(cda, c, &coords);
     60:   return(0);
     61: }

     65: /*
     66:    FormFunctionLocal - Evaluates nonlinear residual, F(x) on local process patch
     67: */
     68: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info, Field *u, Field *f, AppCtx *user)
     69: {
     70:   Vec            L;
     71:   PetscReal      phi        = user->phi;
     72:   PetscReal      dt         = user->dt;
     73:   PetscReal      dx         = 1.0/(PetscReal)(info->mx-1);
     74:   PetscReal      alpha      = 2.0;
     75:   PetscReal      beta       = 2.0;
     76:   PetscReal      kappaWet   = user->kappaWet;
     77:   PetscReal      kappaNoWet = user->kappaNoWet;
     78:   Field          *uold;
     79:   PetscScalar    *Kappa;
     80:   PetscInt       i;

     84:   DMGetGlobalVector(user->cda, &L);

     86:   DMDAVecGetArray(info->da, user->uold,  &uold);
     87:   DMDAVecGetArray(user->cda, user->Kappa, &Kappa);
     88:   /* Compute residual over the locally owned part of the grid */
     89:   for (i = info->xs; i < info->xs+info->xm; ++i) {
     90:     if (i == 0) {
     91:       f[i].s = u[i].s - user->sl;
     92:       f[i].v = u[i].v - user->vl;
     93:       f[i].p = u[i].p - user->pl;
     94:     } else {
     95:       PetscScalar K          = 2*dx/(dx/Kappa[i] + dx/Kappa[i-1]);
     96:       PetscReal   lambdaWet  = kappaWet*pow(u[i].s, alpha);
     97:       PetscReal   lambda     = lambdaWet + kappaNoWet*pow(1-u[i].s, beta);
     98:       PetscReal   lambdaWetL = kappaWet*pow(u[i-1].s, alpha);
     99:       PetscReal   lambdaL    = lambdaWetL + kappaNoWet*pow(1-u[i-1].s, beta);

    101:       f[i].s = phi*(u[i].s - uold[i].s) + (dt/dx)*((lambdaWet/lambda)*u[i].v - (lambdaWetL/lambdaL)*u[i-1].v);

    103:       f[i].v = u[i].v + K*lambda*(u[i].p - u[i-1].p)/dx;

    105:       /*pxx     = (2.0*u[i].p - u[i-1].p - u[i+1].p)/dx;*/
    106:       f[i].p = u[i].v - u[i-1].v;
    107:     }
    108:   }
    109:   DMDAVecRestoreArray(info->da, user->uold, &uold);
    110:   DMDAVecRestoreArray(user->cda, user->Kappa, &Kappa);
    111:   /* PetscLogFlops(11.0*info->ym*info->xm); */

    113:   DMRestoreGlobalVector(user->cda, &L);
    114:   return(0);
    115: }

    119: int main(int argc, char **argv)
    120: {
    121:   SNES           snes;   /* nonlinear solver */
    122:   DM             da;     /* grid */
    123:   Vec            u;      /* solution vector */
    124:   AppCtx         user;   /* user-defined work context */
    125:   PetscReal      t;      /* time */
    127:   PetscInt       n;

    129:   PetscInitialize(&argc, &argv, NULL, help);
    130:   /* Create solver */
    131:   SNESCreate(PETSC_COMM_WORLD, &snes);
    132:   /* Create mesh */
    133:   DMDACreate1d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,-4,3,1,NULL,&da);
    134:   DMSetApplicationContext(da, &user);
    135:   SNESSetDM(snes, da);
    136:   /* Create coefficient */
    137:   DMDACreate1d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,-4,1,1,NULL,&user.cda);
    138:   DMDASetUniformCoordinates(user.cda, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);
    139:   DMGetGlobalVector(user.cda, &user.Kappa);
    140:   FormPermeability(user.cda, user.Kappa, &user);
    141:   /* Setup Problem */
    142:   DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,&user);
    143:   DMGetGlobalVector(da, &u);
    144:   DMGetGlobalVector(da, &user.uold);

    146:   user.sl  = 1.0;
    147:   user.vl  = 0.1;
    148:   user.pl  = 1.0;
    149:   user.phi = 1.0;

    151:   user.kappaWet   = 1.0;
    152:   user.kappaNoWet = 0.3;

    154:   /* Time Loop */
    155:   user.dt = 0.1;
    156:   for (n = 0; n < 100; ++n, t += user.dt) {
    157:     PetscPrintf(PETSC_COMM_WORLD, "Starting time %g\n", t);
    158:     VecView(u, PETSC_VIEWER_DRAW_WORLD);
    159:     /* Solve */
    160:     SNESSetFromOptions(snes);
    161:     SNESSolve(snes, NULL, u);
    162:     /* Update */
    163:     VecCopy(u, user.uold);

    165:     VecView(u, PETSC_VIEWER_DRAW_WORLD);
    166:   }
    167:   /* Cleanup */
    168:   DMRestoreGlobalVector(da, &u);
    169:   DMRestoreGlobalVector(da, &user.uold);
    170:   DMRestoreGlobalVector(user.cda, &user.Kappa);
    171:   DMDestroy(&user.cda);
    172:   DMDestroy(&da);
    173:   SNESDestroy(&snes);
    174:   PetscFinalize();
    175:   return 0;
    176: }