/* Get local bases for boundary vertex i, * return num of constrained bases, * and noramlized direction of rotated bases. * */ SURF_BAS * get_surface_bases(GRID *g, DOF_TYPE *u_type) { SIMPLEX *e; DOF *surf_dof = NULL, *norm_lat = NULL, *norm_bot = NULL; BOOLEAN *rotated = NULL; INT nrot = 0; surf_dof = phgDofNew(g, u_type, DDim, "Surf bases", DofNoAction); //norm_lat = phgDofNew(g, u_type, Dim, "Norm lateral", DofNoAction); //norm_bot = phgDofNew(g, u_type, Dim, "Norm Bottom", DofNoAction); //DOF *coord = phgDofNew(g, u_type, Dim, "coord", func_xyz_); DOF *avg_n = phgDofNew(g, DOF_P2, 3, "avg n", DofNoAction); get_avg_n(g, avg_n); rotated = phgCalloc(DofGetDataCount(surf_dof) / (DDim), sizeof(*rotated)); SURF_BAS *surf_bas; surf_bas = phgCalloc(1, sizeof(*surf_bas)); surf_bas->type = u_type; //surf_bas->dof = phgDofNew(g, u_type, DDim, "Surf bases", DofNoAction);//surf_dof; //surf_bas->dof = surf_dof; surf_bas->rotated = rotated; phgDofSetDataByValue(surf_dof, 0.); //phgDofSetDataByValue(surf_bas->dof, 0.); //phgDofSetDataByValue(norm_lat, -99.); //phgDofSetDataByValue(norm_bot, -99.); ForAllElements(g, e) { int s, ii, i, m, dof_i; int N = surf_dof->type->nbas; //int N = surf_bas->dof->type->nbas; FLOAT *avg_n_v; FLOAT normal[Dim]; int v[3]; FLOAT norm; FLOAT norm_value_lat[N][Dim]; FLOAT norm_value_bot[N][Dim]; FLOAT bas_value[N][DDim], H[Dim][Dim], c[Dim], bxyz[Dim][Dim] = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}; phgDofGetElementData(surf_dof, e, &bas_value[0][0]); //phgDofGetElementData(surf_bas->dof, e, &bas_value[0][0]); for (s = 0; s < NFace; s++) { int nbas_face = NbasFace(surf_dof); //int nbas_face = NbasFace(surf_bas->dof); INT id; SHORT ibas_face[nbas_face]; //FLOAT *normal = phgGeomGetFaceOutNormal(g, e, s); //if (!((e->bound_type[s] & BC_BOTTOM) && !(e->bound_type[s] & BC_ISHELF))) if (!(e->bound_type[s] & BC_BOTTOM)) continue; phgDofGetBasesOnFace(surf_dof, e, s, ibas_face); //phgDofGetBasesOnFace(surf_bas->dof, e, s, ibas_face); for (ii = 0; ii < nbas_face; ii++) { i = ibas_face[ii]; dof_i = phgDofMapE2D(avg_n, e, i*Dim); avg_n_v = DofData(avg_n); normal[0] = avg_n_v[dof_i + 0]; normal[1] = avg_n_v[dof_i + 1]; normal[2] = avg_n_v[dof_i + 2]; /* i means the base function number in the element */ /* Use Gram–Schmidt process to get orthogonal bases, * one constrains */ id = phgDofMapE2D(surf_dof, e, i * (DDim)) / (DDim); //id = phgDofMapE2D(surf_bas->dof, e, i * (DDim)) / (DDim); rotated[id] = TRUE; nrot++; BTYPE elem_btype = phgDofGetElementBoundaryType(surf_dof, e, i*DDim); //BTYPE elem_btype = phgDofGetElementBoundaryType(surf_bas->dof, e, i*DDim); /* fisrt basis */ memcpy(H[0], normal, Dim * sizeof(FLOAT)); /* second basis */ for (m = 0; m < Dim; m++) if (fabs(c[0] = INNER_PRODUCT(H[0], bxyz[m])) < 0.9) break; assert(m < Dim); H[1][0] = bxyz[m][0] - c[0] * H[0][0]; H[1][1] = bxyz[m][1] - c[0] * H[0][1]; H[1][2] = bxyz[m][2] - c[0] * H[0][2]; norm = sqrt(INNER_PRODUCT(H[1], H[1])); assert(norm > 1e-10); H[1][0] /= norm; H[1][1] /= norm; H[1][2] /= norm; H[1][0] = 0; H[1][1] = 1; H[1][2] = 0; /* third basis */ for (m++; m < Dim; m++) if (fabs(c[0] = INNER_PRODUCT(H[0], bxyz[m])) < 0.9) break; assert(m < Dim); //c[1] = INNER_PRODUCT(H[1], bxyz[m]); c[1] = H[1][0]*(bxyz[m][0] - c[0] * H[0][0])+H[1][1]*(bxyz[m][1] - c[0] * H[0][1]) + H[1][2]*(bxyz[m][2] - c[0] * H[0][2]); H[2][0] = bxyz[m][0] - c[0] * H[0][0] - c[1] * H[1][0]; H[2][1] = bxyz[m][1] - c[0] * H[0][1] - c[1] * H[1][1]; H[2][2] = bxyz[m][2] - c[0] * H[0][2] - c[1] * H[1][2]; H[2][0] = H[0][1]*H[1][2] - H[0][2]*H[1][1]; H[2][1] = H[0][2]*H[1][0] - H[0][0]*H[1][2]; H[2][2] = H[0][0]*H[1][1] - H[0][1]*H[1][0]; norm = sqrt(INNER_PRODUCT(H[2], H[2])); assert(norm > 1e-10); H[2][0] /= norm; H[2][1] /= norm; H[2][2] /= norm; if ((elem_btype & BC_BOTTOM_GRD) && (elem_btype & BC_DIVIDE)) { H[1][0] = 1; H[1][1] = 0; H[1][2] = 0; H[2][0] = (H[0][1]*H[1][2]-H[0][2]*H[1][1]); H[2][1] = -(H[0][0]*H[1][2]-H[0][2]*H[1][0]); H[2][2] = (H[0][0]*H[1][1]-H[0][1]*H[1][0]); } #if 0 # warning check use only: xyz coord ---------------------------- memcpy(bas_value[i], bxyz[0], DDim*sizeof(FLOAT)); #else memcpy(bas_value[i], H[0], DDim*sizeof(FLOAT)); /* bas_value is contains all bas values of all nodes in the element. * For the nodes at the boundaries, bas value is real number, otherwise * bas value is just 0 */ #endif } /* end bas */ } /* end face */ phgDofSetElementData(surf_dof, e, &bas_value[0][0]); //phgDofSetElementData(surf_bas->dof, e, &bas_value[0][0]); } /* end elem */
/**************************************************************** * 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); }
/* 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); }
void phgNSBuildPc(NSSolver *ns) { GRID *g = ns->g; SIMPLEX *e; FLOAT *dt = ns->dt; int i, j, q, s, k, l; FLOAT Theta = _nsp->Theta, nu = _nsp->nu, Thet1, nu0 = 0; DOF *tmp_u1 = phgDofNew(g, _nsp->utype, Dim, "tmp u1", func_u); int viscosity_type = ns->viscosity_type; LTYPE ltype = ns->ltype; #if STEADY_STATE assert(fabs(Theta - 1) < 1e-12); Thet1 = 0; Unused(Thet1); Unused(dt); #else Thet1 = 1 - Theta; #endif /* STEADY_STATE */ ForAllElements(g, e) { int M = ns->u[1]->type->nbas; /* num of bases of Velocity */ int N = ns->p[1]->type->nbas; /* num of bases of Pressure */ int order = 2 * DofTypeOrder(ns->p[1], e) + DofTypeOrder(ns->u[1], e) - 1; /* highest order term (u \nabla p, psi) */ FLOAT Ap[N][N], Fp[N][N], Qp[N][N], bufp[N], rhs1 = 1; FLOAT F[M*Dim][M*Dim], B[N][M*Dim], Bt[M*Dim][N]; INT Ip[N]; QUAD *quad; FLOAT vol, det; const FLOAT *w, *p, *vw, *gu, *vTe; quad = phgQuadGetQuad3D(order); vw = phgQuadGetDofValues(e, ns->wind, quad); /* value wind */ gu = phgQuadGetDofValues(e, ns->gradu[1], quad); /* grad u^{n+1} */ if (ns_params->noniter_temp) vTe = phgQuadGetDofValues(e, ns->T[1], quad); /* value temp */ else vTe = phgQuadGetDofValues(e, ns->T[0], quad); /* value temp */ vol = 0; Bzero(Ap); Bzero(Fp); Bzero(Qp); Bzero(F); Bzero(Bt); Bzero(B); Bzero(bufp); p = quad->points; w = quad->weights; for (q = 0; q < quad->npoints; q++) { phgGeomGetCurvedJacobianAtLambda(g, e, p, &det); vol = fabs(det / 6.); for (i = 0; i < N; i++) { const FLOAT *gi = phgQuadGetBasisValues(e, ns->p[1], i, quad) + q; /* phi_i */ const FLOAT *ggi = phgQuadGetBasisCurvedGradient(e, ns->p[1], i, quad, q); /* grad phi_i */ for (j = 0; j < N; j++) { const FLOAT *gj = phgQuadGetBasisValues(e, ns->p[1], j, quad) + q; /* phi_j */ const FLOAT *ggj = phgQuadGetBasisCurvedGradient(e, ns->p[1], j, quad, q); /* grad phi_i */ nu = get_effective_viscosity(gu, *vTe, 0, viscosity_type); if (i == 0 && j == 0) nu0 += nu; #if ICE_BENCH_TEST || \ ESIMINT_TEST || \ HEINO_TEST || \ TEST_CASE == ICE_EXACT || \ TEST_CASE == ICE_GREEN_LAND Unused(dt); /* Note: B Q^-1 Bt ~ Ap(nu=1), * Fp(nu varies) is very different to Ap */ Ap[i][j] += vol*(*w) * INNER_PRODUCT(ggj, ggi); # if USE_QP_ONLY //Qp[i][j] += vol*(*w) * LEN_SCALING * PRES_SCALING /(nu) * (*gj) * (*gi); Qp[i][j] += vol*(*w) * 1. /(EQU_SCALING * nu) * (*gj) * (*gi); /* if (i < NVert && j < NVert) { */ /* Qp[i][j] += vol*(*w) * LEN_SCALING * PRES_SCALING / (nu) * (*gj) * (*gi); */ /* } else if (i == NVert && j == NVert) { */ /* Qp[i][j] += vol*(*w) * LEN_SCALING * PRES_SCALING / (nu) * (*gj) * (*gi); */ /* } */ # else Qp[i][j] += vol*(*w) * (*gj) * (*gi); # endif Fp[i][j] += vol*(*w) * (EQU_SCALING * nu * INNER_PRODUCT(ggj, ggi) ); #elif STEADY_STATE Ap[i][j] += vol*(*w) * INNER_PRODUCT(ggj, ggi); Qp[i][j] += vol*(*w) * (*gj) * (*gi); Fp[i][j] += vol*(*w) * (nu * INNER_PRODUCT(ggj, ggi) * EQU_SCALING ); #elif TIME_DEP_NON Ap[i][j] += vol*(*w) * INNER_PRODUCT(ggj, ggi); Qp[i][j] += vol*(*w) * (*gj) * (*gi); Fp[i][j] += vol*(*w) * ((*gj) * (*gi) / dt[0] + Theta * (nu * INNER_PRODUCT(ggj, ggi) ) ); #else TIME_DEP_LINEAR_ENTRY; /* Unavailable */ #endif /* STEADY_STATE */ } } vw += Dim; gu += DDim; vTe++; w++; p += Dim+1; } /* Map: Element -> system */ for (i = 0; i < N; i++) Ip[i] = phgMapE2L(_pcd->matFp->cmap, 0, e, i); /* * PCD boundary setup I: * Automaticly decide inflow boundary condition using wind direction. * * NOT active. * */ if (FALSE && !_nsp->pin_node) { for (i = 0; i < N; i++) { BOOLEAN flag_inflow = FALSE; for (s = 0; s < NFace; s++) { SHORT bases[NbasFace(ns->p[1])]; FLOAT *coord, vw_[3]; const FLOAT *lam, *normal; if (!(e->bound_type[s] & BDRY_MASK)) //if (!(e->bound_type[s] & INFLOW)) continue; /* boundary face */ phgDofGetBasesOnFace(ns->p[1], e, s, bases); for (j = 0; j < NbasFace(ns->p[1]); j++) if (i == bases[j]) { normal = phgGeomGetFaceOutNormal(g, e, s); coord = phgDofGetElementCoordinates(ns->p[1], e, i); lam = phgGeomXYZ2Lambda(g, e, coord[0], coord[1], coord[2]); phgDofEval(tmp_u1, e, lam, vw_); if (INNER_PRODUCT(vw_, normal) > 1e-8) flag_inflow = TRUE; } } if (flag_inflow) { Bzero(bufp); bufp[i] = 1.0; phgMatAddEntries(_pcd->matAp, 1, Ip + i, N, Ip, bufp); phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, bufp); //phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, bufp); phgVecAddEntries(_pcd->rhsScale, 0, 1, Ip + i, &rhs1); } else { /* interior node Or Neumann */ phgMatAddEntries(_pcd->matAp, 1, Ip + i, N, Ip, Ap[i]); phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, Fp[i]); //phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, Qp[i]); } phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, Qp[i]); } } /* * PCD boundary setup II: * Enclose flow: use pinnode boundary. * * Qp is pinned, this is different to open flow. * * */ else if (_nsp->pin_node) { for (i = 0; i < N; i++) { if (phgDofDirichletBC(_pcd->pbc, e, i, NULL, bufp, NULL, DOF_PROJ_NONE)) { #if PIN_AT_ROOT if (g->rank != 0) phgError(1, "Pinned node only on rank 0!\n"); if (e->verts[i] != ns->pinned_node_id) phgError(1, "pinned node [%d] & [%d] doesn't coincide when build pc!\n", e->verts[i], ns->pinned_node_id); #else if (GlobalVertex(g, e->verts[i]) != ns->pinned_node_id) phgError(1, "pinned node [%d] & [%d] doesn't coincide when build pc!\n", e->verts[i], ns->pinned_node_id); #endif /* PIN_AT_ROOT */ phgMatAddEntries(_pcd->matAp, 1, Ip + i, N, Ip, bufp); phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, bufp); phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, bufp); phgVecAddEntries(_pcd->rhsScale, 0, 1, Ip + i, &rhs1); } else { /* interior node Or Neumann */ phgMatAddEntries(_pcd->matAp, 1, Ip + i, N, Ip, Ap[i]); phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, Fp[i]); phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, Qp[i]); } } } /* * PCD boundary setup III: * Open flow: there could be varies kinds of combination on seting up * boundary conditon, but Inflow:Robin & Outflow:scaled Dirich is * prefered. See Ref[2]. * * */ else { for (i = 0; i < N; i++) { /*****************/ /* Inflow */ /*****************/ #warning PCD B.C.: Step 2.1. build mat, all neumann, add dirich entries if (FALSE && phgDofDirichletBC(_pcd->dof_inflow, e, i, NULL, bufp, NULL, DOF_PROJ_NONE)) { phgMatAddEntries(_pcd->matAp, 1, Ip + i, N, Ip, bufp); phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, bufp); phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, bufp); phgVecAddEntries(_pcd->rhsScale, 0, 1, Ip + i, &rhs1); } else if (FALSE && phgDofDirichletBC(_pcd->dof_outflow, e, i, NULL, bufp, NULL, DOF_PROJ_NONE) && !(phgDofGetElementBoundaryType(ns->p[1], e, i) & INFLOW) ) { ERROR_MSG("Fp, Qp"); nu = get_effective_viscosity(NULL, 0, 0, viscosity_type); phgMatAddEntries(_pcd->matAp, 1, Ip + i, N, Ip, bufp); bufp[i] *= EQU_SCALING * nu; phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, bufp); phgVecAddEntries(_pcd->rhsScale, 0, 1, Ip + i, &rhs1); //phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, bufp); } else if (FALSE && phgDofDirichletBC(_pcd->pbc, e, i, NULL, bufp, NULL, DOF_PROJ_NONE)) { phgMatAddEntries(_pcd->matAp, 1, Ip + i, N, Ip, bufp); phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, bufp); phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, bufp); phgVecAddEntries(_pcd->rhsScale, 0, 1, Ip + i, &rhs1); } else if (FALSE) { /* interior node Or Neumann */ ERROR_MSG("Fp, Qp"); phgMatAddEntries(_pcd->matAp, 1, Ip + i, N, Ip, Ap[i]); phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, Fp[i]); //phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, Qp[i]); } /******************/ /* No bdry */ /******************/ //phgMatAddEntries(_pcd->matFp, 1, Ip + i, N, Ip, Fp[i]); phgMatAddEntries(_pcd->matQp, 1, Ip + i, N, Ip, Qp[i]); } } if (0) { /* Special term <[[p_i]], [[p_j]]> */ int face; nu0 /= quad->npoints; for (face = 0; face < NFace; face++) { FLOAT area = phgGeomGetFaceArea(g, e, face); //FLOAT value = {area, -area}; FLOAT values[2] = {vol * 1. /(EQU_SCALING * nu0), -vol * 1. /(EQU_SCALING * nu0)}; SIMPLEX *e_neigh; phgMatAddEntries(_pcd->matQp, 1, Ip+NVert, 1, Ip+NVert, values); if ((e_neigh = GetNeighbour(e, face)) != NULL) { INT Ip_neigh = phgMapE2L(_pcd->matFp->cmap, 0, e_neigh, NVert); phgMatAddEntries(_pcd->matQp, 1, Ip+NVert, 1, &Ip_neigh, values + 1); } } } } /* end element */