int
main(int argc, char *argv[])
{
const char *fn = "cube.dat";
ELEMENT *e;
GRID *g;
DOF *u;
int i, n;
/* Test initialize MPI before phgInit */
MPI_Init(&argc, &argv);
phgInit(&argc, &argv);
g = phgNewGrid(-1);
if (argc > 1)
fn = argv[1];
if (!phgImport(g, fn, FALSE))
phgError(1, "can't read file \"%s\".\n", fn);
phgRefineAllElements(g, 0);
u = phgDofNew(g, DOF_DEFAULT, 1, "u", DofNoAction);
n = u->type->nbas;
ForAllElements(g, e) {
FLOAT xyz[3];
const FLOAT *c;
for (i = 0; i < n; i++) {
c = phgDofGetElementCoordinates(u, e, i);
phgDofGetElementBasisInfo_(u, e, i, NULL, NULL, NULL, xyz, NULL);
assert(!memcmp(c, xyz, sizeof(xyz)));
}
}
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 */
