sparse BuildAdvection(const DataStructure& Domain, double velocity) {
int Npts = Domain.GetNpts();
sparse Advection(Npts,Npts,3*Npts);
int nnz = 0;
if(velocity > .0)
for(int i = 0; i < Npts; i++) {
Advection.Val(nnz) = - 1.0 / hx - 1.0 / hy;
Advection.Row(nnz) = i;
Advection.Col(nnz) = i;
nnz++;
if(Domain(Domain[i],Domain(i)+1) != -4) {
Advection.Val(nnz) = 1.0 / hx;
Advection.Row(nnz) = i;
Advection.Col(nnz) = Domain(Domain[i],Domain(i)+1);
nnz++;
}
else {
Advection.Val(nnz) = 1.0 / hx;
Advection.Row(nnz) = i;
Advection.Col(nnz) = i;
nnz++;
}
if(Domain(Domain[i] + 1,Domain(i)) != -3) {
Advection.Val(nnz) = 1.0/hy;
Advection.Row(nnz) = i;
Advection.Col(nnz) = Domain(Domain[i]+1,Domain(i));
nnz++;
}
else {
Advection.Val(nnz) = 1.0/hy;
Advection.Row(nnz) = i;
Advection.Col(nnz) = i;
nnz++;
}
}
else
for(int i = 0; i < Npts; i++) {
Advection.Val(nnz) = 1.0 / hx + 1.0 / hy;
Advection.Row(nnz) = i;
Advection.Col(nnz) = i;
nnz++;
if(Domain(Domain[i],Domain(i) - 1) != -2) {
Advection.Val(nnz) = - 1.0 / hx;
Advection.Row(nnz) = i;
Advection.Col(nnz) = Domain(Domain[i],Domain(i)-1);
nnz++;
}
else {
Advection.Val(nnz) = - 1.0 / hx;
Advection.Row(nnz) = i;
Advection.Col(nnz) = i;
nnz++;
}
if(Domain(Domain[i]-1,Domain(i)) != -1) {
Advection.Val(nnz) = - 1.0/hy;
Advection.Row(nnz) = i;
Advection.Col(nnz) = Domain(Domain[i]-1,Domain(i));
nnz++;
}
else {
Advection.Val(nnz) = - 1.0/hy;
Advection.Row(nnz) = i;
Advection.Col(nnz) = i;
nnz++;
}
}
Advection.CreateSparse();
return Advection;
}
sparse AssembleAdvection(DataStructure& Data, double velocity, char* BCType) {
/* Dirichlet BC is implemented inefficiently here */
int Nverts = Data.GetNverts(), nnz = 0, NNZMAX = 0, nBC = 0, uBC;
bool DirichletIsTrue = false;
if(!strcmp(BCType,"Dirichlet"))
DirichletIsTrue = true;
for(int i = 0; i < Data.GetNverts(); i++)
NNZMAX += Data.GetNeigh(i,0);
sparse Advection(Nverts,Nverts,2*NNZMAX);
ifstream file;
if(DirichletIsTrue) {
file.open("Dirichlet.dat");
file >> nBC >> uBC;
}
vector BoundPts(nBC);
if(DirichletIsTrue)
for(int i = 0; i < nBC; i++)
file >> BoundPts(i);
file.close();
for(int i = 0; i < Nverts; i++) {
int n = Data.GetNeigh(i,0);
double Area_C = .0;
for(int k = 1; k <= n; k++)
Area_C += Data.GetArea(Data.GetNeigh(i,k));
Area_C *= 1.0/3.0;
for(int j = 1; j <= n; j++) {
double x[3], y[3]; vector nodes(3);
for(int k = 0; k < 3; k++)
nodes(k) = Data.GetTris(Data.GetNeigh(i,j),k);
int index1 = find(nodes,i), index2 = 1, index3 = 2;
if(index1 == 1) {
index2 = 2;
index3 = 0;
}
if(index1 == 2) {
index2 = 0;
index3 = 1;
}
x[0] = Data.GetVerts(nodes(index1),0);
y[0] = Data.GetVerts(nodes(index1),1);
x[1] = Data.GetVerts(nodes(index2),0);
y[1] = Data.GetVerts(nodes(index2),1);
x[2] = Data.GetVerts(nodes(index3),0);
y[2] = Data.GetVerts(nodes(index3),1);
bool IsBoundary1 = CheckBC(nodes(index1),BoundPts),
IsBoundary2 = CheckBC(nodes(index2),BoundPts),
IsBoundary3 = CheckBC(nodes(index3),BoundPts);
double delta_x1 = x[2]/3.0 - x[1]/6.0 - x[0]/6.0,
delta_y1 = y[2]/3.0 - y[1]/6.0 - y[0]/6.0,
delta_x2 = x[2]/6.0 - x[1]/3.0 + x[0]/6.0,
delta_y2 = y[2]/6.0 - y[1]/3.0 + y[0]/6.0;
double qf1 = velocity * (delta_y1 - delta_x1),
qf2 = velocity * (delta_y2 - delta_x2);
if(qf1 > 0) {
Advection.Row(nnz) = i;
Advection.Col(nnz) = Data.GetTris(Data.GetNeigh(i,j),index1);
if(IsBoundary1)
Advection.Val(nnz) = .0;
else
Advection.Val(nnz) = - qf1 / Area_C;
nnz++;
}
else {
Advection.Row(nnz) = i;
Advection.Col(nnz) = Data.GetTris(Data.GetNeigh(i,j),index2);
if(IsBoundary2)
Advection.Val(nnz) = .0;
else
Advection.Val(nnz) = - qf1 / Area_C;
nnz++;
}
if(qf2 > 0) {
Advection.Row(nnz) = i;
Advection.Col(nnz) = Data.GetTris(Data.GetNeigh(i,j),index1);
if(IsBoundary1)
Advection.Val(nnz) = .0;
else
Advection.Val(nnz) = - qf2 / Area_C;
nnz++;
}
else {
Advection.Row(nnz) = i;
Advection.Col(nnz) = Data.GetTris(Data.GetNeigh(i,j),index3);
if(IsBoundary3)
Advection.Val(nnz) = .0;
else
Advection.Val(nnz) = - qf2 / Area_C;
nnz++;
}
}
}
Advection.CreateSparse();
return Advection;
}
void MappingExtrapolate::v_CalcNeumannPressureBCs(
const Array<OneD, const Array<OneD, NekDouble> > &fields,
const Array<OneD, const Array<OneD, NekDouble> > &N,
NekDouble kinvis)
{
if (m_mapping->HasConstantJacobian() && !m_implicitViscous)
{
Extrapolate::v_CalcNeumannPressureBCs( fields, N, kinvis);
}
else
{
int physTot = m_fields[0]->GetTotPoints();
int nvel = m_fields.num_elements()-1;
Array<OneD, NekDouble> Pvals;
StdRegions::StdExpansionSharedPtr Pbc;
StdRegions::StdExpansionSharedPtr elmt;
Array<OneD, Array<OneD, const NekDouble> > Velocity(m_bnd_dim);
Array<OneD, Array<OneD, const NekDouble> > Advection(m_bnd_dim);
// Get transformation Jacobian
Array<OneD, NekDouble> Jac(physTot,0.0);
m_mapping->GetJacobian(Jac);
// Declare variables
Array<OneD, Array<OneD, NekDouble> > BndValues(m_bnd_dim);
Array<OneD, Array<OneD, NekDouble> > Q(m_bnd_dim);
Array<OneD, Array<OneD, NekDouble> > Q_field(nvel);
Array<OneD, Array<OneD, NekDouble> > fields_new(nvel);
Array<OneD, Array<OneD, NekDouble> > N_new(m_bnd_dim);
// Temporary variables
Array<OneD, NekDouble> tmp(physTot,0.0);
Array<OneD, NekDouble> tmp2(physTot,0.0);
for(int i = 0; i < m_bnd_dim; i++)
{
BndValues[i] = Array<OneD, NekDouble> (m_pressureBCsMaxPts,0.0);
Q[i] = Array<OneD, NekDouble> (m_pressureBCsElmtMaxPts,0.0);
N_new[i] = Array<OneD, NekDouble> (physTot,0.0);
}
for(int i = 0; i < nvel; i++)
{
Q_field[i] = Array<OneD, NekDouble> (physTot,0.0);
fields_new[i] = Array<OneD, NekDouble> (physTot,0.0);
}
// Multiply convective terms by Jacobian
for(int i = 0; i < m_bnd_dim; i++)
{
if (m_fields[0]->GetWaveSpace())
{
m_fields[0]->HomogeneousBwdTrans(N[i],N_new[i]);
}
else
{
Vmath::Vcopy(physTot, N[i], 1, N_new[i], 1);
}
Vmath::Vmul(physTot, Jac, 1, N_new[i], 1, N_new[i], 1);
if (m_fields[0]->GetWaveSpace())
{
m_fields[0]->HomogeneousFwdTrans(N_new[i],N_new[i]);
}
}
// Get velocity in physical space
for(int i = 0; i < nvel; i++)
{
if (m_fields[0]->GetWaveSpace())
{
m_fields[0]->HomogeneousBwdTrans(fields[i],fields_new[i]);
}
else
{
Vmath::Vcopy(physTot, fields[i], 1, fields_new[i], 1);
}
}
// Calculate appropriate form of the CurlCurl operator
m_mapping->CurlCurlField(fields_new, Q_field, m_implicitViscous);
// If viscous terms are treated explicitly,
// add grad(U/J \dot grad J) to CurlCurl
if ( !m_implicitViscous)
{
m_mapping->DotGradJacobian(fields_new, tmp);
Vmath::Vdiv(physTot, tmp, 1, Jac, 1, tmp, 1);
bool wavespace = m_fields[0]->GetWaveSpace();
m_fields[0]->SetWaveSpace(false);
for(int i = 0; i < m_bnd_dim; i++)
{
m_fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[i],
tmp, tmp2);
Vmath::Vadd(physTot, Q_field[i], 1, tmp2, 1, Q_field[i], 1);
}
m_fields[0]->SetWaveSpace(wavespace);
}
// Multiply by Jacobian and convert to wavespace (if necessary)
for(int i = 0; i < m_bnd_dim; i++)
{
Vmath::Vmul(physTot, Jac, 1, fields_new[i], 1, fields_new[i], 1);
Vmath::Vmul(physTot, Jac, 1, Q_field[i] , 1, Q_field[i] , 1);
if (m_fields[0]->GetWaveSpace())
{
m_fields[0]->HomogeneousFwdTrans(fields_new[i],fields_new[i]);
m_fields[0]->HomogeneousFwdTrans(Q_field[i],Q_field[i]);
}
}
for(int j = 0 ; j < m_HBCdata.num_elements() ; j++)
{
/// Casting the boundary expansion to the specific case
Pbc = boost::dynamic_pointer_cast<StdRegions::StdExpansion>
(m_PBndExp[m_HBCdata[j].m_bndryID]
->GetExp(m_HBCdata[j].m_bndElmtID));
/// Picking up the element where the HOPBc is located
elmt = m_pressure->GetExp(m_HBCdata[j].m_globalElmtID);
/// Assigning
for(int i = 0; i < m_bnd_dim; i++)
{
Velocity[i] = fields_new[i] + m_HBCdata[j].m_physOffset;
Advection[i] = N_new[i] + m_HBCdata[j].m_physOffset;
Q[i] = Q_field[i] + m_HBCdata[j].m_physOffset;
}
// Mounting advection component into the high-order condition
for(int i = 0; i < m_bnd_dim; i++)
{
MountHOPBCs(m_HBCdata[j].m_ptsInElmt,kinvis,Q[i],Advection[i]);
}
Pvals = m_pressureHBCs[0] + m_HBCdata[j].m_coeffOffset;
// Getting values on the edge and filling the pressure boundary
// expansion and the acceleration term. Multiplication by the
// normal is required
switch(m_pressure->GetExpType())
{
case MultiRegions::e2D:
case MultiRegions::e3DH1D:
{
elmt->GetEdgePhysVals(m_HBCdata[j].m_elmtTraceID, Pbc,
Q[0], BndValues[0]);
elmt->GetEdgePhysVals(m_HBCdata[j].m_elmtTraceID, Pbc,
Q[1], BndValues[1]);
// InnerProduct
Pbc->NormVectorIProductWRTBase(BndValues[0], BndValues[1],
Pvals);
}
break;
case MultiRegions::e3DH2D:
{
if(m_HBCdata[j].m_elmtTraceID == 0)
{
(m_PBndExp[m_HBCdata[j].m_bndryID]->UpdateCoeffs()
+ m_PBndExp[m_HBCdata[j].m_bndryID]
->GetCoeff_Offset(
m_HBCdata[j].m_bndElmtID))[0]
= -1.0*Q[0][0];
}
else if (m_HBCdata[j].m_elmtTraceID == 1)
{
(m_PBndExp[m_HBCdata[j].m_bndryID]->UpdateCoeffs()
+ m_PBndExp[m_HBCdata[j].m_bndryID]
->GetCoeff_Offset(
m_HBCdata[j].m_bndElmtID))[0]
= Q[0][m_HBCdata[j].m_ptsInElmt-1];
}
else
{
ASSERTL0(false,
"In the 3D homogeneous 2D approach BCs edge "
"ID can be just 0 or 1 ");
}
}
break;
case MultiRegions::e3D:
{
elmt->GetFacePhysVals(m_HBCdata[j].m_elmtTraceID, Pbc,
Q[0], BndValues[0]);
elmt->GetFacePhysVals(m_HBCdata[j].m_elmtTraceID, Pbc,
Q[1], BndValues[1]);
elmt->GetFacePhysVals(m_HBCdata[j].m_elmtTraceID, Pbc,
Q[2], BndValues[2]);
Pbc->NormVectorIProductWRTBase(BndValues[0], BndValues[1],
BndValues[2], Pvals);
}
break;
default:
ASSERTL0(0,"Dimension not supported");
break;
}
}
}
// If pressure terms are treated implicitly, we need to multiply
// by the relaxation parameter, and zero the correction term
if (m_implicitPressure)
{
Vmath::Smul(m_pressureHBCs[0].num_elements(), m_pressureRelaxation,
m_pressureHBCs[0], 1,
m_pressureHBCs[0], 1);
}
m_bcCorrection = Array<OneD, NekDouble> (m_pressureHBCs[0].num_elements(), 0.0);
}