Date: 2021-03-03T22:27:45+00:00

Actual source code: ex33.c
petsc-3.14.5 2021-03-03
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      1: static char help[] = "Multiphase flow in a porous medium in 1d.\n\n";
      2: #include <petscdm.h>
      3: #include <petscdmda.h>
      4: #include <petscsnes.h>

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

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

     24: /*
     25:    FormPermeability - Forms permeability field.

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

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

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

     62: /*
     63:    FormFunctionLocal - Evaluates nonlinear residual, F(x) on local process patch
     64: */
     65: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info, Field *u, Field *f, AppCtx *user)
     66: {
     67:   Vec            L;
     68:   PetscReal      phi        = user->phi;
     69:   PetscReal      dt         = user->dt;
     70:   PetscReal      dx         = 1.0/(PetscReal)(info->mx-1);
     71:   PetscReal      alpha      = 2.0;
     72:   PetscReal      beta       = 2.0;
     73:   PetscReal      kappaWet   = user->kappaWet;
     74:   PetscReal      kappaNoWet = user->kappaNoWet;
     75:   Field          *uold;
     76:   PetscScalar    *Kappa;
     77:   PetscInt       i;

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

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

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

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

    102:       /*pxx     = (2.0*u[i].p - u[i-1].p - u[i+1].p)/dx;*/
    103:       f[i].p = u[i].v - u[i-1].v;
    104:     }
    105:   }
    106:   DMDAVecRestoreArray(info->da, user->uold, &uold);
    107:   DMDAVecRestoreArray(user->cda, user->Kappa, &Kappa);
    108:   /* PetscLogFlops(11.0*info->ym*info->xm); */

    110:   DMRestoreGlobalVector(user->cda, &L);
    111:   return(0);
    112: }

    114: int main(int argc, char **argv)
    115: {
    116:   SNES           snes;   /* nonlinear solver */
    117:   DM             da;     /* grid */
    118:   Vec            u;      /* solution vector */
    119:   AppCtx         user;   /* user-defined work context */
    120:   PetscReal      t = 0.0;/* time */
    122:   PetscInt       n;

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

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

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

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

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

    177: /*TEST

    179:   test:
    180:     suffix: 0
    181:     requires: !single
    182:     args: -snes_converged_reason -snes_monitor_short

    184: TEST*/