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: }