static void
build_linear_system(SOLVER *solver, DOF *u_h, DOF *f_h)
{
int i, j;
GRID *g = u_h->g;
ELEMENT *e;
assert(u_h->dim == 1);
ForAllElements(g, e) {
int N = DofGetNBas(u_h, e); /* number of bases in the element */
FLOAT A[N][N], rhs[N], buffer[N];
INT I[N];
/* compute \int \grad\phi_j \cdot \grad\phi_i making use of symmetry */
for (i = 0; i < N; i++) {
I[i] = phgSolverMapE2L(solver, 0, e, i);
for (j = 0; j <= i; j++) {
A[j][i] = A[i][j] =
/* stiffness */
phgQuadGradBasDotGradBas(e, u_h, j, u_h, i, QUAD_DEFAULT) +
/* mass */
a * phgQuadBasDotBas(e, u_h, j, u_h, i, QUAD_DEFAULT);
}
}
/* loop on basis functions */
for (i = 0; i < N; i++) {
if (phgDofDirichletBC(u_h, e, i, func_u, buffer, rhs+i,
DOF_PROJ_NONE)) {
phgSolverAddMatrixEntries(solver, 1, I + i, N, I, buffer);
}
else { /* interior node */
/* right hand side = \int f * phi_i */
phgQuadDofTimesBas(e, f_h, u_h, i, QUAD_DEFAULT, rhs + i);
phgSolverAddMatrixEntries(solver, 1, I + i, N, I, A[i]);
}
}
phgSolverAddRHSEntries(solver, N, I, rhs);
}
static void
build_matrices(MAT *ma, MAT *mb, VEC *rhs_vec, DOF *u_h, DOF *f)
/* build stiffness (ma) and mass (mb) matrices */
{
int N = u_h->type->nbas; /* number of element basis functions */
int i, j, k, l;
GRID *g = u_h->g;
ELEMENT *e;
FLOAT A[N][3][N][3], buffer[N], rhs[N][3], d;
static FLOAT *B0 = NULL;
FLOAT B[N][N];
INT I[N][3], J[3][N];
QUAD *quad = phgQuadGetQuad3D((u_h->type->order - 1) * 2);
assert(u_h->type->dim == 1 && u_h->dim == 3);
assert(mb == NULL || u_h->type->invariant);
if (mb != NULL && B0 == NULL && g->nroot > 0) {
/* (\int \phi_j\cdot\phi_i)/vol is independent of element */
FreeAtExit(B0);
B0 = phgAlloc(N * N * sizeof(*B0));
e = g->roots;
d = 1. / phgGeomGetVolume(g, e);
for (i = 0; i < N; i++)
for (j = 0; j <= i; j++)
B0[i * N + j] = B0[i + j * N] = d *
phgQuadBasDotBas(e, u_h, j, u_h, i, QUAD_DEFAULT);
}
ForAllElements(g, e) {
d = phgGeomGetVolume(g, e) * rho;
for (i = 0; i < N; i++) {
for (k = 0; k < 3; k++)
J[k][i] = I[i][k] = phgMapE2L(ma->rmap, 0, e, i * 3 + k);
for (j = 0; j <= i; j++) {
/* the stiffness matrix */
stiffness_matrix(e, u_h, i, j, E, nu, 3 * N, &A[i][0][j][0],
quad);
if (j != i) {
for (k = 0; k < 3; k++)
for (l = 0; l < 3; l++)
A[j][k][i][l] = A[i][l][j][k];
}
/* the mass matrix: \int \phi_i\cdot\phi_j */
if (mb != NULL)
B[j][i] = B[i][j] = B0[i * N + j] * d;
}
}
#if 0
/* print element stiffness matrix */
FLOAT *p = (void *)A;
printf("vol = %0.16lg;\n", phgGeomGetVolume(g, e));
printf("a = [\n");
for (i = 0; i < 3 * N; i++) {
for (j = 0; j < 3 * N; j++) printf("%0.16lg ", p[i * 3 * N + j]); printf("\n");
}
printf("];\n");
printf("b = [\n");
for (i = 0; i < N; i++) for (k = 0; k < 3; k++) {
for (j = 0; j < N; j++) for (l = 0; l < 3; l++)
printf("%0.16lg ", l == k ? B[i][j] : 0.0);
printf("\n");
}
printf("];\n");
exit(0);
#endif
/* loop on basis functions */
for (i = 0; i < N; i++) {
if (phgDofDirichletBC(u_h, e, i, func_g, buffer, rhs[i],
DOF_PROJ_NONE)) {
/* Dirichlet boundary */
for (k = 0; k < 3; k++) {
phgMatAddEntries(ma, 1, I[i] + k, N, J[k], buffer);
if (mb != NULL)
phgMatAddEntries(mb, 1, I[i] + k, N, J[k], buffer);
}
}
else {
/* interior node */
phgMatAddEntries(ma, 3, I[i], 3 * N, I[0], &A[i][0][0][0]);
if (mb == NULL) {
phgQuadDofTimesBas(e, f, u_h, i, QUAD_DEFAULT, rhs[i]);
for (k = 0; k < 3; k++)
rhs[i][k] = -rhs[i][k];
}
else {
for (k = 0; k < 3; k++)
phgMatAddEntries(mb, 1, I[i] + k, N, J[k], B[i]);
}
}
}
if (rhs_vec != NULL)
phgVecAddEntries(rhs_vec, 0, N * 3, I[0], rhs[0]);
}
/* build linear system */
static void
build_mat_vec(DOF *u_w, DOF *dp, DOF *p_nk, DOF *ds, DOF *s_w, DOF *s_w_l, DOF *b_o, DOF *b_o_l, DOF *kro, DOF *dot_kro, DOF *q_o, DOF *b_w, DOF *b_w_l, DOF *krw, DOF *dot_krw, DOF *q_w, DOF *phi, DOF *phi_l, MAP *map_u, MAP *map_p, MAT *A, MAT *B, MAT *TB, MAT *C, VEC *vec_f, VEC *vec_g)
{
GRID *g = u_w->g;
SIMPLEX *e;
FLOAT *p_bo, *p_bw, *p_bol, *p_bwl, *p_kro, *p_dotkro, *p_krw, *p_dotkrw, *p_swl, *p_dp, *p_ds, *p_sw, *p_phi;
INT N = u_w->type->nbas * u_w->dim;
INT M = dp->type->nbas * dp->dim;
INT I[N], J[M];
FLOAT mat_A[N][N], mat_TB[N][M], mat_B[M][N], mat_C[M][M], rhs_f[N], rhs_g[M];
phgVecDisassemble(vec_f);
phgVecDisassemble(vec_g);
int i, j, k;
ForAllElements(g, e) {
p_phi = DofElementData(phi, e->index);
p_bo = DofElementData(b_o, e->index);
p_bol = DofElementData(b_o_l, e->index);
p_bw = DofElementData(b_w, e->index);
p_bwl = DofElementData(b_w_l, e->index);
p_sw = DofElementData(s_w, e->index);
p_swl = DofElementData(s_w_l, e->index);
p_kro = DofElementData(kro, e->index);
p_dotkro = DofElementData(dot_kro, e->index);
p_krw = DofElementData(krw, e->index);
p_dotkrw = DofElementData(dot_krw, e->index);
p_dp = DofElementData(dp, e->index);
p_ds = DofElementData(ds, e->index);
FLOAT T_o = 0, T_w = 0;
T_w = K * p_krw[0] * p_bw[0] / MU_W + K * p_krw[0] * C_W / (MU_W * B0_W) * p_dp[0] + K * p_bw[0] * p_dotkrw[0] / MU_W * p_ds[0];
T_o = K * p_kro[0] * p_bo[0] / MU_O + K * p_kro[0] * C_O / (MU_O * B0_O) * p_dp[0] + K * p_bo[0] * p_dotkro[0] / MU_O * p_ds[0];
for (i = 0; i < N; i++) {
for (j = 0; j < N; j++) {
mat_A[i][j] = stime * phgQuadBasDotBas(e, u_w, i, u_w, j, QUAD_DEFAULT) / T_w;
}
}
for (i = 0; i < N; i++) {
for (j = 0; j < M; j++) {
mat_TB[i][j] = -stime * phgQuadDivBasDotBas(e, u_w, i, dp, j, QUAD_DEFAULT);
}
}
FLOAT wat_sw = 0, oil_sw = 0, wat_cp = 0, oil_cp = 0, beta = 0;
for (i = 0; i < M; i++) {
for (j = 0; j < M; j++) {
wat_sw = p_phi[0] * p_bw[0] * phgQuadBasDotBas(e, ds, i, ds, j, QUAD_DEFAULT);
oil_sw = p_phi[0] * p_bo[0] * phgQuadBasDotBas(e, ds, i, ds, j, QUAD_DEFAULT);
}
}
wat_cp = p_sw[0] * (p_bw[0] * PHI0 * C_R + p_phi[0] * C_W / B0_W);
oil_cp = (1. - p_sw[0]) * (p_bo[0] * PHI0 * C_R + p_phi[0] * C_O / B0_O);
beta = 1. / wat_sw + T_o / (T_w * oil_sw);
FLOAT quad = 0.;
for (i = 0; i < M; i++) {
for (j = 0; j < M; j++) {
quad = phgQuadBasDotBas(e, dp, i, dp, j, QUAD_DEFAULT);
mat_C[i][j] = (wat_cp / wat_sw + oil_cp / oil_sw) * quad / beta;
}
}
/*create oil rhs*/
FLOAT quad_phi = 0., quad_phil = 0., quad_qo = 0, quad_qw = 0;
FLOAT rhs_oil = 0., rhs_wat = 0.;
for (i = 0; i < M; i++) {
phgQuadDofTimesBas(e, q_o, dp, i, QUAD_DEFAULT, &quad_qo);
phgQuadDofTimesBas(e, q_w, dp, i, QUAD_DEFAULT, &quad_qw);
phgQuadDofTimesBas(e, phi, dp, i, QUAD_DEFAULT, &quad_phi);
phgQuadDofTimesBas(e, phi_l, dp, i, QUAD_DEFAULT, &quad_phil);
rhs_oil = -stime * quad_qo + p_bo[0] * (1. - p_sw[0]) * quad_phi - p_bol[0] * (1. - p_swl[0]) * quad_phil;
rhs_wat = -stime * quad_qw + p_bw[0] * p_sw[0] * quad_phi - p_bwl[0] * p_swl[0] * quad_phil;
rhs_g[i] = (rhs_wat / wat_sw + rhs_oil / oil_sw) / beta;
}
for (i = 0; i < N; i++) {
rhs_f[i] = stime * phgQuadDofTimesDivBas(e, p_nk, u_w, i, QUAD_DEFAULT);
}
/* Handle Bdry Conditions*/
for (i = 0; i < N; i++) {
if (phgDofGetElementBoundaryType(u_w, e, i) & (NEUMANN | DIRICHLET)) {
bzero(mat_A[i], N * sizeof(mat_A[i][0]));
bzero(mat_TB[i], M * sizeof(mat_TB[i][0]));
for (j = 0; j < N; j++) {
mat_A[j][i] = 0.;
}
mat_A[i][i] = 1.;
rhs_f[i] = 0.;
}
}
for (i = 0; i < N; i++) {
for (j = 0; j < M; j++) {
mat_B[j][i] = mat_TB[i][j];
}
}
for (i = 0; i < N; i++) {
I[i] = phgMapE2L(map_u, 0, e, i);
}
for (i = 0; i < M; i++) {
J[i] = phgMapE2L(map_p, 0, e, i);
}
phgMatAddEntries(A, N, I, N, I, mat_A[0]);
phgMatAddEntries(TB, N, I, M, J, mat_TB[0]);
phgMatAddEntries(B, M, J, N, I, mat_B[0]);
phgMatAddEntries(C, M, J, M, J, mat_C[0]);
phgVecAddEntries(vec_f, 0, N, I, rhs_f);
phgVecAddEntries(vec_g, 0, M, J, rhs_g);
}
/****************************************************************
* Build RHS which is the residual of the nonlinear system.
***************************************************************/
static void
build_rhs(SOLVER *solver, SOLVER *pc, DOF **dofs, MAT **mats)
{
DOF *u = dofs[0], *p = dofs[1];
DOF *f, *pbc, *gn[3], *gradu, *divu, *lapu, *gradp, *f0;
int M = u->type->nbas; /* num of bases of Velocity */
int i, k, s;
GRID *g = u->g;
ELEMENT *e;
FLOAT bufu[M], resu[M][Dim], tmp[9];
INT Iu[M][Dim];
/* Unpack Dofs */
unpackDof(dofs, 9, &u, &p, &gradu, &divu, &f, &pbc, &gn[0], &gn[1],
&gn[2]);
lapu = phgDofDivergence(gradu, NULL, NULL, NULL);
gradp = phgDofGradient(p, NULL, NULL, NULL);
time -= dt;
f0 = phgDofNew(g, DOF_HB6, 3, "p_n", func_f);
time += dt;
ForAllElements(g, e) {
/* Map: Element -> system */
for (i = 0; i < M; i++)
for (k = 0; k < Dim; k++)
Iu[i][k] = phgMapE2L(solver->rhs->map, 0, e, i * Dim + k);
/* Global Matrix */
bzero(resu, sizeof(resu));
for (i = 0; i < M; i++) {
/* Dirichle Boundary for velocity. */
if (phgDofDirichletBC(u, e, i, func_u, bufu, &resu[i][0],
DOF_PROJ_NONE)) {
/* set velocity at Dirichlet bdry */
}
else { /* interior node or Neumann */
/* (u(t_n), \phi) */
phgQuadDofTimesBas(e, u, u, i, QUAD_DEFAULT, tmp);
for (k = 0; k < Dim; k++)
resu[i][k] = tmp[k];
/* (f, \phi_i) */
phgQuadDofTimesBas(e, f0, u, i, QUAD_DEFAULT, tmp);
for (k = 0; k < Dim; k++)
resu[i][k] += dt * (1 - Theta) * tmp[k];
phgQuadDofTimesBas(e, f, u, i, QUAD_DEFAULT, tmp);
for (k = 0; k < Dim; k++)
resu[i][k] += dt * Theta * tmp[k];
/* -( ((u.\grad) u, \phi) */
phgQuadDofDotGradDofBas(e, u, gradu, i, QUAD_DEFAULT, tmp);
for (k = 0; k < Dim; k++)
resu[i][k] -= dt * (1 - Theta) * tmp[k];
/* +\nu ( lap(u(t_n)), \phi) */
phgQuadDofTimesBas(e, lapu, u, i, QUAD_DEFAULT, tmp);
for (k = 0; k < Dim; k++)
resu[i][k] += (1 - Theta) * dt * nu * tmp[k];
/* -(gradp(t_n), \phi) */
phgQuadDofTimesBas(e, gradp, u, i, QUAD_DEFAULT, tmp);
for (k = 0; k < Dim; k++)
resu[i][k] -= (1 - Theta) * dt * tmp[k];
}
} /* end of Block (1,1), (1,2) */
/* Neumann Bdry */
for (s = 0; s < NFace; s++) {
if (e->bound_type[s] & NEUMANN) {
SHORT bases[NbasFace(u)];
phgDofGetBasesOnFace(u, e, s, bases);
for (i = 0; i < NbasFace(u); i++) {
if (phgDofGetElementBoundaryType(u, e, bases[i] * Dim)
& DIRICHLET) {
/* Dirichlet bas on Neumann face, do nothing */
}
else if (phgDofGetElementBoundaryType(u, e, bases[i] * Dim)
& NEUMANN) {
for (k = 0; k < Dim; k++)
resu[bases[i]][k] += dt * Theta *
phgQuadFaceDofDotBas(e, s, gn[k],
DOF_PROJ_DOT, u,
bases[i], QUAD_DEFAULT);
}
else {
fprintf(stderr, "Warning: unkown bdry!");
}
} /* end of base on face */
} /* end of face neu */
} /* end of all neumann face in element */
/* Global res */
phgSolverAddRHSEntries(solver, M * Dim, Iu[0], &resu[0][0]);
} /* end element */
solver->rhs_updated = FALSE;
phgDofFree(&lapu);
phgDofFree(&gradp);
phgDofFree(&f0);
return;
}
static void
/*build_linear_system*/
build_mat_vec(DOF *dp, DOF *d_so, DOF *d_sw, DOF *dot_muo, DOF *dot_muw, DOF *dot_mug, DOF *dso_kro, DOF *dsw_kro, DOF *dsw_krw, DOF *dso_krg, DOF *dsw_krg, DOF *u_o, DOF *p_h, DOF *p_h_newton, DOF *s_o, DOF *s_o_l, DOF *mu_o, DOF *b_o, DOF *b_o_l, DOF *kro, DOF *dot_bo, DOF *q_o, DOF *s_w, DOF *s_w_l, DOF *mu_w, DOF *b_w, DOF *b_w_l, DOF *krw, DOF *dot_bw, DOF *q_w, DOF *phi, DOF *phi_l, DOF *dot_phi, DOF *Rs, DOF *Rs_l, DOF *dot_Rs, DOF *mu_g, DOF *b_g, DOF *b_g_l, DOF *krg, DOF *dot_bg, DOF *q_g, MAP *map_u, MAP *map_p, MAT *A, MAT *B, MAT *TB, MAT *C, VEC *vec_f, VEC *vec_g)
{
GRID *g = u_o->g;
SIMPLEX *e;
FLOAT *p_so, *p_sol, *p_bo, *p_bol, *p_kro, *p_phi, *p_phil, *p_dotbo, *p_Rs, *p_dotRs, *p_bg, *p_bgl, *p_krg, *p_dotbg, *p_muo, *p_mug, *p_dotphi, *p_Rsl, *p_sw, *p_swl, *p_bw, *p_bwl, *p_krw, *p_dotbw, *p_muw;
FLOAT *p_dotmuo, *p_dotmuw, *p_dotmug, *p_dsokro, *p_dswkro, *p_dswkrw, *p_dsokrg, *p_dswkrg, *p_dp, *p_dso, *p_dsw;
INT N = u_o->type->nbas * u_o->dim;
INT M = dp->type->nbas * dp->dim;
INT I[N], J[M];
FLOAT mat_A[N][N], mat_TB[N][M], mat_B[M][N], mat_C[M][M], rhs_f[N], rhs_g[M];
phgVecDisassemble(vec_f);
phgVecDisassemble(vec_g);
int i, j, k;
ForAllElements(g, e){
p_so = DofElementData(s_o, e->index);
p_sol = DofElementData(s_o_l, e->index);
p_bo = DofElementData(b_o, e->index);
p_bol = DofElementData(b_o_l, e->index);
p_kro = DofElementData(kro, e->index);
p_phi = DofElementData(phi, e->index);
p_phil = DofElementData(phi_l, e->index);
p_dotphi = DofElementData(dot_phi, e->index);
p_dotbo = DofElementData(dot_bo, e->index);
p_Rs = DofElementData(Rs, e->index);
p_Rsl = DofElementData(Rs_l, e->index);
p_dotRs = DofElementData(dot_Rs, e->index);
p_bg = DofElementData(b_g, e->index);
p_bgl = DofElementData(b_g_l, e->index);
p_krg= DofElementData(krg, e->index);
p_dotbg = DofElementData(dot_bg, e->index);
p_muo = DofElementData(mu_o, e->index);
p_muw = DofElementData(mu_w, e->index);
p_mug = DofElementData(mu_g, e->index);
p_sw = DofElementData(s_w, e->index);
p_swl = DofElementData(s_w_l, e->index);
p_bw = DofElementData(b_w, e->index);
p_bwl = DofElementData(b_w_l, e->index);
p_krw = DofElementData(krw, e->index);
p_dotbw = DofElementData(dot_bw, e->index);
/* Add Dofs For SS */
p_dp = DofElementData(dp, e->index);
p_dso = DofElementData(d_so, e->index);
p_dsw = DofElementData(d_sw, e->index);
p_dotmuo = DofElementData(dot_muo, e->index);
p_dotmuw = DofElementData(dot_muw, e->index);
p_dotmug = DofElementData(dot_mug, e->index);
p_dsokro = DofElementData(dso_kro, e->index);
p_dswkro = DofElementData(dsw_kro, e->index);
p_dswkrw = DofElementData(dsw_krw, e->index);
p_dsokrg = DofElementData(dso_krg, e->index);
p_dswkrg = DofElementData(dsw_krg, e->index);
/*Create inverse matrix*/
FLOAT oil_so = 0., wat_sw = 0., gas_so = 0., gas_sw = 0.;
for (i = 0; i < M; i++){
for (j = 0; j < M; j++){
oil_so = p_phi[0] * p_bo[0] * phgQuadBasDotBas(e, d_so, i, d_so, j, QUAD_DEFAULT);
wat_sw = p_phi[0] * p_bw[0] * phgQuadBasDotBas(e, d_sw, i, d_sw, j, QUAD_DEFAULT);
gas_so = p_phi[0] * (p_bg[0] - p_Rs[0] * p_bo[0]) * phgQuadBasDotBas(e, d_so, i, d_so, j, QUAD_DEFAULT);
gas_sw = p_phi[0] * p_bg[0] * phgQuadBasDotBas(e, d_sw, i, d_sw, j, QUAD_DEFAULT);
}
}
#if SS
FLOAT alpha_o = 0., alpha_w = 0., alpha_g = 0.;
alpha_o = K * p_kro[0] * p_bo[0] * p_muo[0] + K * p_kro[0] * (p_bo[0] * p_dotmuo[0] + p_dotbo[0] * p_muo[0]) * p_dp[0] \
+ K * p_bo[0] * p_muo[0] * (p_dsokro[0] * p_dso[0] + p_dswkro[0] * p_dsw[0]);
alpha_w = K * p_krw[0] * p_bw[0] * p_muw[0] + K * p_krw[0] * (p_bw[0] * p_dotmuw[0] + p_dotbw[0] * p_muw[0]) * p_dp[0] \
+ K * p_bw[0] * p_muw[0] * p_dswkrw[0] * p_dsw[0];
alpha_g = K * p_krg[0] * p_bg[0] * p_mug[0] + K * p_krg[0] * (p_bg[0] * p_dotmug[0] + p_dotbg[0] * p_mug[0]) * p_dp[0] \
+ K * p_bg[0] * p_mug[0] * (p_dsokrg[0] * p_dso[0] + p_dswkrg[0] * p_dsw[0]);
for (i = 0; i < N; i++){
for (j = 0; j < N; j++){
mat_A[i][j] = stime * phgQuadBasDotBas(e, u_o, i, u_o, j, QUAD_DEFAULT) / alpha_o;
}
}
FLOAT beta = 0;
beta = gas_so / oil_so + gas_sw * alpha_w / (wat_sw * alpha_o) + (p_Rs[0] + alpha_g / alpha_o);
#endif
#if IMPES
FLOAT T_o = 0, T_w = 0, T_g = 0;
T_o = K * p_kro[0] * p_bo[0] * p_muo[0];
T_w = K * p_krw[0] * p_bw[0] * p_muw[0];
T_g = K * p_krg[0] * p_bg[0] * p_mug[0];
for (i = 0; i < N; i++){
for (j = 0; j < N; j++){
mat_A[i][j] = stime * phgQuadBasDotBas(e, u_o, i, u_o, j, QUAD_DEFAULT) / T_o;
}
}
FLOAT beta = 0;
beta = gas_so / oil_so + gas_sw * T_w / (wat_sw * T_o) + (p_Rs[0] + T_g / T_o);
#endif
for (i = 0; i < N; i++){
for (j = 0; j < M; j++){
mat_TB[i][j] = -stime * phgQuadDivBasDotBas(e, u_o, i, dp, j, QUAD_DEFAULT);
}
}
FLOAT quad = 0., oil_cp = 0., wat_cp = 0., gas_cp = 0.;
oil_cp = p_so[0] * (p_bo[0] * p_dotphi[0] + p_phi[0] * p_dotbo[0]);
wat_cp = p_sw[0] * (p_bw[0] * p_dotphi[0] + p_phi[0] * p_dotbw[0]);
gas_cp = p_so[0] * p_phi[0] * p_bo[0] * p_dotRs[0] + p_Rs[0] * oil_cp + (1. - p_so[0] - p_sw[0]) * (p_phi[0] * p_dotbg[0] + p_bg[0] * p_dotphi[0]);
for (i = 0; i < M; i++){
for (j = 0; j < M; j++){
quad = phgQuadBasDotBas(e, dp, i, dp, j, QUAD_DEFAULT);
mat_C[i][j] = (gas_so * oil_cp / oil_so + gas_sw * wat_cp / wat_sw + gas_cp) * quad / beta;
}
}
/*Create rhs*/
FLOAT quad_qo = 0;
FLOAT quad_qw = 0.;
FLOAT quad_qg = 0.;
FLOAT quad_phi = 0, quad_phil = 0;
FLOAT rhs_oil = 0, rhs_wat = 0., rhs_gas = 0;
for (i = 0; i < M; i++){
phgQuadDofTimesBas(e, q_o, dp, i, QUAD_DEFAULT, &quad_qo);
phgQuadDofTimesBas(e, q_w, dp, i, QUAD_DEFAULT, &quad_qw);
phgQuadDofTimesBas(e, q_g, dp, i, QUAD_DEFAULT, &quad_qg);
phgQuadDofTimesBas(e, phi, dp, i, QUAD_DEFAULT, &quad_phi);
phgQuadDofTimesBas(e, phi_l, dp, i, QUAD_DEFAULT, &quad_phil);
rhs_oil = -stime * quad_qo + p_so[0] * p_bo[0] * quad_phi - p_sol[0] * p_bol[0] * quad_phil;
rhs_wat = -stime * quad_qw + p_sw[0] * p_bw[0] * quad_phi - p_swl[0] * p_bwl[0] * quad_phil;
rhs_gas = -stime * quad_qg + (p_bg[0] * (1. - p_so[0] - p_sw[0]) + p_Rs[0] * p_so[0] * p_bo[0]) * quad_phi \
- (p_Rsl[0] * p_bol[0] * p_sol[0] + p_bgl[0] * (1. - p_sol[0] - p_swl[0])) * quad_phil;
rhs_g[i] = (gas_so * rhs_oil / oil_so + gas_sw * rhs_wat / wat_sw + rhs_gas) / beta;
}
for (i = 0; i < N; i++){
rhs_f[i] = stime * phgQuadDofTimesDivBas(e, p_h, u_o, i, QUAD_DEFAULT);
}
/* Handle Bdry Conditions */
for (i = 0; i < N; i++){
if (phgDofGetElementBoundaryType(u_o, e, i) & (NEUMANN | DIRICHLET)){
bzero(mat_A[i], N *sizeof(mat_A[i][0]));
bzero(mat_TB[i], M *sizeof(mat_TB[i][0]));
for (j = 0; j < N; j++){
mat_A[j][i] = 0.0;
}
mat_A[i][i] = 1.0;
rhs_f[i] = 0.;
}
}
for (i = 0; i < N; i++){
for (j = 0; j < M; j++){
mat_B[j][i] = mat_TB[i][j];
}
}
for (i = 0; i < N; i++){
I[i] = phgMapE2L(map_u, 0, e, i);
}
for (i = 0; i < M; i++){
J[i] = phgMapE2L(map_p, 0, e, i);
}
phgMatAddEntries(A, N, I, N, I, mat_A[0]);
phgMatAddEntries(TB, N, I, M, J, mat_TB[0]);
phgMatAddEntries(B, M, J, N, I, mat_B[0]);
phgMatAddEntries(C, M, J, M, J, mat_C[0]);
phgVecAddEntries(vec_f, 0, N, I, rhs_f);
phgVecAddEntries(vec_g, 0, M, J, rhs_g);
}
