/****************************************************************
* Build RHS which is the residual of the nonlinear system.
***************************************************************/
void
phgNSBuildSolverURHS(NSSolver *ns)
{
GRID *g = ns->g;
SIMPLEX *e;
SOLVER *solver_u = ns->solver_u;
int i, k, l, q, s;
FLOAT *dt = ns->dt;
BOOLEAN tstep_minus = (ns->u[-1] != NULL);
VEC *vec_rhs = phgMapCreateVec(solver_u->rhs->map, 1);
FLOAT Theta = _nsp->Theta, nu = _nsp->nu, Thet1;
int viscosity_type = ns->viscosity_type;
SURF_BAS *surf_bas = ns->surf_bas;
DOF *surf_dof = surf_bas->dof;
BOOLEAN *rotated = surf_bas->rotated;
const FLOAT *Trans = DofData(surf_dof);
#if STEADY_STATE
assert(fabs(Theta - 1) < 1e-12);
Thet1 = 0; Unused(Thet1);
Unused(dt);
#else
Thet1 = 1 - Theta;
Unused(dt);
#endif /* STEADY_STATE */
phgPrintf(" DB_mask: [");
for (k = 0; k < Dim; k++)
phgPrintf("%d ", ns->u[1]->DB_masks[k]);
phgPrintf("] ");
nu_max = -1e10;
nu_min = +1e10;
phgVecDisassemble(vec_rhs);
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 = DofTypeOrder(ns->u[1], e) * 3 - 1; /* Note:
* quad order is really high here,
* highest order term (u \nabla u, phi) */
FLOAT bufu[M], bufp[N], rhsu[M][Dim], rhsp[N];
INT Iu[M][Dim], Ip[N];
QUAD *quad;
FLOAT vol, area, det;
const FLOAT *w, *p, *normal,
**vu, *vu_queue[3],
*vf[2], *gu[2], *vp[2], *vw, *vT;
FLOAT *vf_cache[2];
vu = vu_queue + 1;
quad = phgQuadGetQuad3D(order);
vu[0] = phgQuadGetDofValues(e, ns->u[0], quad); /* u^{n} */
vp[0] = phgQuadGetDofValues(e, ns->p[0], quad); /* p^{n} */
gu[0] = phgQuadGetDofValues(e, ns->gradu[0], quad); /* grad u^{n} */
vw = phgQuadGetDofValues(e, ns->wind, quad); /* wind */
vT = phgQuadGetDofValues(e, ns->T[1], quad); /* T^{n} */
if (tstep_minus) {
vu[-1] = phgQuadGetDofValues(e, ns->u[-1], quad); /* u^{n-1} */
} else {
vu[-1] = vu[0];
}
#if STEADY_STATE || TIME_DEP_NON
vu[1] = phgQuadGetDofValues(e, ns->u[1], quad); /* u^{n+1} */
gu[1] = phgQuadGetDofValues(e, ns->gradu[1], quad); /* grad u^{n} */
vp[1] = phgQuadGetDofValues(e, ns->p[1], quad); /* p^{n+1} */
#else
TIME_DEP_LINEAR_ENTRY; /* Unavailable */
#endif /* STEADY_STATE || TIME_DEP_NON */
Unused(l);
Unused(vf); Unused(vf_cache);
if (!_nsp->no_extern_source) {
/* cache f values */
for (l = 0; l < 2; l++) {
const FLOAT *cache;
size_t cache_size;
setFuncTime(ns->time[l]); /* set static time in ins-test.c */
/* cache f */
cache_size = Dim * quad->npoints * sizeof(FLOAT);
cache = phgQuadGetFuncValues(g, e, Dim, func_f, quad);
vf[l] = vf_cache[l] = phgAlloc(cache_size);
memcpy(vf_cache[l], cache, cache_size);
phgQuadGetFuncValues(NULL, NULL, 0, NULL, NULL); /* clear cache */
}
}
/* Global Matrix */
Bzero(rhsu); Bzero(rhsp);
p = quad->points;
w = quad->weights;
for (q = 0; q < quad->npoints; q++) {
phgGeomGetCurvedJacobianAtLambda(g, e, p, &det);
vol = fabs(det / 6.);
/* rhs u */
for (i = 0; i < M; i++) {
/* interior node or Neumann */
const FLOAT *gi_u = phgQuadGetBasisValues(e, ns->u[1], i, quad) + q; /* phi_i */
const FLOAT *ggi_u = phgQuadGetBasisCurvedGradient(e, ns->u[1], i, quad, q); /* grad phi_i */
for (k = 0; k < Dim; k++) {
#if ICE_BENCH_TEST
nu = get_effective_viscosity(gu[1], 0, 0, viscosity_type);
FLOAT eu[DDim];
MAT3_SYM(gu[1], eu);
rhsu[i][k] += vol*(*w) * EQU_SCALING * (- nu * INNER_PRODUCT(eu+k*Dim, ggi_u)
+ (*vp[1]) * *(ggi_u+k) * LEN_SCALING * PRES_SCALING
); /* left */
if (k == Z_DIR) {
const FLOAT rho = RHO_ICE;
const FLOAT grav = GRAVITY;
const FLOAT a = SEC_PER_YEAR;
const FLOAT f = rho*grav * EQU_SCALING * LEN_SCALING2;
Unused(a);
rhsu[i][k] += vol*(*w) * (-f * (*gi_u)
); /* right */
}
#elif ESIMINT_TEST || \
HEINO_TEST || \
TEST_CASE == ICE_GREEN_LAND
nu = get_effective_viscosity(gu[1], *vT, 0, viscosity_type);
FLOAT eu[DDim];
MAT3_SYM(gu[1], eu);
rhsu[i][k] += vol*(*w) * EQU_SCALING * (- nu * INNER_PRODUCT(eu+k*Dim, ggi_u)
+ (*vp[1]) * *(ggi_u+k) * LEN_SCALING * PRES_SCALING
); /* left */
if (k == Z_DIR) {
const FLOAT rho = RHO_ICE;
const FLOAT grav = GRAVITY;
const FLOAT a = SEC_PER_YEAR;
const FLOAT f = rho*grav * EQU_SCALING * LEN_SCALING2;
Unused(a);
rhsu[i][k] += vol*(*w) * (-f * (*gi_u)
); /* right */
}
#elif STEADY_STATE
rhsu[i][k] += vol*(*w) * (- nu * INNER_PRODUCT(gu[1]+k*Dim, ggi_u)
+ (*vp[1]) * *(ggi_u+k)
); /* left */
if (!_nsp->no_extern_source)
rhsu[i][k] += vol*(*w) * (*(vf[1]+k) * (*gi_u)
); /* right */
#elif TIME_DEP_NON
rhsu[i][k] -= vol*(*w) * ((vu[1][k] - vu[0][k]) * (*gi_u) / dt[0]
+ Theta * (nu * INNER_PRODUCT(gu[1]+k*Dim, ggi_u)
)
- (*vp[1]) * *(ggi_u+k)
+ Thet1 * (nu * INNER_PRODUCT(gu[0]+k*Dim, ggi_u)
)
); /* left */
if (!_nsp->no_extern_source)
rhsu[i][k] += vol*(*w) * (Theta * *(vf[1]+k) * (*gi_u)
+ Thet1 * *(vf[0]+k) * (*gi_u)
); /* right */
#else
TIME_DEP_LINEAR_ENTRY; /* Unavailable */
#endif /* STEADY_STATE */
}
}
/* rhs p */
for (i = 0; i < N; i++) {
const FLOAT *gi_p = phgQuadGetBasisValues(e, ns->p[1], i, quad) + q; /* psi_i */
FLOAT divu1 = gu[1][0] + gu[1][4] + gu[1][8];
//FLOAT divu0 = gu[0][0] + gu[0][4] + gu[0][8];
rhsp[i] += vol*(*w) * (divu1 * (*gi_p)
);
}
if (tstep_minus)
vu[-1] += Dim;
#if STEADY_STATE || TIME_DEP_NON
vu[1] += Dim;
gu[1] += Dim*Dim;
vp[1]++;
#else
TIME_DEP_LINEAR; /* Unavailable */
#endif /* STEADY_STATE || TIME_DEP_NON */
vu[0] += Dim;
gu[0] += Dim * Dim;
vp[0]++;
vw += Dim;
if (!_nsp->no_extern_source) {
vf[0] += Dim; vf[1] += Dim;
}
vT++;
w++; p += Dim + 1;
}
if (!_nsp->no_extern_source) {
phgFree(vf_cache[0]);
phgFree(vf_cache[1]);
}
normal = NULL; Unused(normal);
area = 0; Unused(area);
if (!_nsp->enclosed_flow) {
/* slip boundary */
for (s = 0; s < NFace; s++) {
if (e->bound_type[s] & INFLOW) {
int v0, v1, v2;
int nbas_face = NbasFace(ns->u[1]);
SHORT bases[nbas_face];
FLOAT lambda[Dim + 1], x,y,z, beta;
order = DofTypeOrder(ns->u[1], e) * 3 - 1;
phgDofGetBasesOnFace(ns->u[1], e, s, bases);
v0 = GetFaceVertex(s, 0);
v1 = GetFaceVertex(s, 1);
v2 = GetFaceVertex(s, 2);
lambda[s] = 0.;
area = phgGeomGetFaceArea(g, e, s);
normal = phgGeomGetFaceOutNormal(g, e, s);
quad = phgQuadGetQuad2D(order);
p = quad->points;
w = quad->weights;
for (q = 0; q < quad->npoints; q++) {
FLOAT vu[Dim];
lambda[v0] = *(p++);
lambda[v1] = *(p++);
lambda[v2] = *(p++);
phgGeomLambda2XYZ(g, e, lambda, &x, &y, &z);
func_beta(x, y, z, &beta);
phgDofEval(ns->u[1], e, lambda, vu);
for (i = 0; i < nbas_face; i++) {
int ii = bases[i];
FLOAT gi_u =
*ns->u[1]->type->BasFuncs(ns->u[1], e, ii, ii + 1, lambda);
for (k = 0; k < Dim; k++) {
#if STEADY_STATE
rhus[ii][k] += 0.;
#elif TIME_DEP_NON
# if USE_SLIDING_BC
abort();
rhsu[ii][k] += SIGN_FRICTION * area*(*w) * beta * vu[k] * (gi_u)
* EQU_SCALING * LEN_SCALING;
# else
Unused(gi_u);
# endif
#else
TIME_DEP_LINEAR_ENTRY; /* Unavailable */
#endif /* STEADY_STATE */
}
} /* end of bas_i */
w++;
} /* end of quad point */
} /* end of face outflow */
} /* end of all outflow face in element */
} /* end out flow boundary */
#if USE_SLIDING_BC
/* Rotate bases */
for (i = 0; i < M; i++) {
INT id = phgDofMapE2D(surf_dof, e, i * (Dim*Dim)) / (Dim*Dim);
if (!rotated[id])
continue;
const FLOAT *trans = Trans + id*(Dim*Dim);
trans_left(&rhsu[i][0], 1, 1, trans);
}
#else
Unused(Trans);
Unused(rotated);
#endif
/* Map: Element -> system */
for (i = 0; i < M; i++)
for (k = 0; k < Dim; k++)
Iu[i][k] = phgMapE2L(solver_u->rhs->map, 0, e, i * Dim + k);
for (i = 0; i < N; i++)
Ip[i] = phgMapE2L(solver_u->rhs->map, 1, e, i);
/* set velocity dirichlet bdry */
FLOAT tmp[Dim];
for (i = 0; i < M; i++)
for (k = 0; k < Dim; k++)
if (phgDofDirichletBC_(ns->u[1], e, i*Dim+k, NULL, bufu, tmp,
DOF_PROJ_NONE)) {
rhsu[i][k] = 0.;
}
#if STEADY_STATE || TIME_DEP_NON
/* set pressure dirichlet bdry for pinned point */
for (i = 0; i < N; i++)
if (phgDofDirichletBC(ns->p[1], e, i, NULL, bufp, &rhsp[i],
DOF_PROJ_NONE)) {
if (!_nsp->enclosed_flow)
phgError(1, "No dirichlet bc for Unenclosed flow!\n");
if (_nsp->pin_node) {
# if PIN_AT_ROOT
if (g->rank != 0)
phgError(1, "Pinned node only on rank 0!\n");
if (g, e->verts[i] != ns->pinned_node_id)
phgError(1, "Build rhs: pinned node e:%d, bas:%d, [%d] and [%d] "
"doesn't coincide when build RHS!\n",
e->index, i, e->verts[i], ns->pinned_node_id);
# else
if (GlobalVertex(g, e->verts[i]) != ns->pinned_node_id)
phgError(1, "Build rhs: pinned node e:%d, bas:%d, [%d] and [%d] "
"doesn't coincide when build RHS!\n",
e->index, i, e->verts[i], ns->pinned_node_id);
# endif /* PIN_AT_ROOT */
}
}
#else
TIME_DEP_LINEAR; /* Unavailable */
#endif /* STEADY_STATE || TIME_DEP_NON */
/* Global res */
phgVecAddEntries(vec_rhs, 0, M * Dim, Iu[0], &rhsu[0][0]);
phgVecAddEntries(vec_rhs, 0, N, Ip, rhsp);
} /* end element */
/****************************************************************
* 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;
}
/* 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 */
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 */
