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fractionalStepGrid.cpp
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fractionalStepGrid.cpp
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#include "fractionalStepGrid.hpp"
FractionalStepGrid::FractionalStepGrid(vector<std::tuple<double, double, double>> points, vector<Boundary> boundaries,
GridProperties properties, Eigen::VectorXd source) : Grid(points, boundaries, properties, source){
u = new Eigen::VectorXd(laplaceMatSize_);
u_old = new Eigen::VectorXd(laplaceMatSize_);
v = new Eigen::VectorXd(laplaceMatSize_);
v_old = new Eigen::VectorXd(laplaceMatSize_);
u_hat = new Eigen::VectorXd(laplaceMatSize_);
v_hat = new Eigen::VectorXd(laplaceMatSize_);
u_old->setZero();
v_old->setZero();
u->setZero();
v->setZero();
u_hat->setZero();
v_hat->setZero();
}
FractionalStepGrid::~FractionalStepGrid() {
delete u_hat;
delete v_hat;
delete u;
delete v;
delete u_old;
delete v_old;
}
void FractionalStepGrid::prescribe_soln() {
double x, y;
double re = rho / mu;
lambda = 0.5 * re - std::sqrt(0.25*re*re + 4*EIGEN_PI*EIGEN_PI);
for (int i = 0; i < laplaceMatSize_; i++) {
x = std::get<0>(points_[i]);
y = std::get<1>(points_[i]);
u->coeffRef(i) = 1 - std::exp(lambda * x) * std::cos(2 * EIGEN_PI * y);
v->coeffRef(i) = lambda / (2 * EIGEN_PI) * std::exp(lambda * x) * std::sin(2 * EIGEN_PI * y);
u_old->coeffRef(i) = 1 - std::exp(lambda * x) * std::cos(2 * EIGEN_PI * y);
v_old->coeffRef(i) = lambda / (2 * EIGEN_PI) * std::exp(lambda * x) * std::sin(2 * EIGEN_PI * y);
values_->coeffRef(i) = 0.5 * std::exp(2 * lambda * x);
}
values_->coeffRef(laplaceMatSize_) = 0;
}
void FractionalStepGrid::set_uv_bound() {
double x, y,nx,ny;
double re = rho / mu;
if (flowType.compare("couette") == 0) {
for (size_t i = 0; i < boundaries_.size(); i++) {
for (size_t j = 0; j < (boundaries_[i].bcPoints).size(); j++) {
//cout << i << " " << j << " " << u->rows() << endl;
x = std::get<0>(points_[boundaries_[i].bcPoints.at(j)]);
y = std::get<1>(points_[boundaries_[i].bcPoints.at(j)]);
nx = std::get<0>(normalVecs_[boundaries_[i].bcPoints.at(j)]);
ny = std::get<1>(normalVecs_[boundaries_[i].bcPoints.at(j)]);
if (std::abs(std::pow(x,2) + std::pow(y,2) - 1) < 1e-6 ) {
u->coeffRef(boundaries_[i].bcPoints.at(j)) = 0;
v->coeffRef(boundaries_[i].bcPoints.at(j)) = 0;
u_old->coeffRef(boundaries_[i].bcPoints.at(j)) = 0;
v_old->coeffRef(boundaries_[i].bcPoints.at(j)) = 0;
}
if (std::abs(std::pow(x,2) + std::pow(y,2) - 0.25) < 1e-6 ) {
u->coeffRef(boundaries_[i].bcPoints.at(j)) = -ny;
v->coeffRef(boundaries_[i].bcPoints.at(j)) = nx;
u_old->coeffRef(boundaries_[i].bcPoints.at(j)) = -ny;
v_old->coeffRef(boundaries_[i].bcPoints.at(j)) = nx;
}
/*if(j==0){
cout<<v->coeffRef(boundaries_[0].bcPoints.at(0))<<endl;
cout<<v->coeffRef(boundaries_[1].bcPoints.at(0))<<endl;
}
*/
}
}
//cout<<v->coeffRef(boundaries_[0].bcPoints.at(0))<<endl;
//cout<<v->coeffRef(boundaries_[1].bcPoints.at(1))<<endl;
}
}
void FractionalStepGrid::build_derivX_mat() {
vector<Eigen::Triplet<double>> tripletList;
for (int i = 0; i < laplaceMatSize_; i++) {
std::pair <Eigen::VectorXd, vector<int>> weights = derivx_weights(i);
for (size_t j = 0; j < weights.second.size(); j++) {
tripletList.push_back(Eigen::Triplet<double>(i, weights.second[j], weights.first(j)));
}
}
derivXMat_ = new Eigen::SparseMatrix<double, Eigen::RowMajor>(laplaceMatSize_, laplaceMatSize_);
derivXMat_->setFromTriplets(tripletList.begin(), tripletList.end());
derivXMat_->makeCompressed();
}
void FractionalStepGrid::build_derivY_mat() {
vector<Eigen::Triplet<double>> tripletList;
vector<Eigen::Triplet<double>> boundaryList;
for (int i = 0; i < laplaceMatSize_; i++) {
std::pair <Eigen::VectorXd, vector<int>> weights = derivy_weights(i);
for (size_t j = 0; j < weights.second.size(); j++) {
tripletList.push_back(Eigen::Triplet<double>(i, weights.second[j], weights.first(j)));
}
}
derivYMat_ = new Eigen::SparseMatrix<double, Eigen::RowMajor>(laplaceMatSize_, laplaceMatSize_);
derivYMat_->setFromTriplets(tripletList.begin(), tripletList.end());
derivYMat_->makeCompressed();
}
void FractionalStepGrid::build_uv_laplace_mat() {
vector<Eigen::Triplet<double>> tripletList;
vector<Eigen::Triplet<double>> boundaryList;
for (int i = 0; i < laplaceMatSize_; i++) {
std::pair <Eigen::VectorXd, vector<int>> weights = laplaceWeights(i);
for (size_t j = 0; j < weights.second.size(); j++) {
tripletList.push_back(Eigen::Triplet<double>(i, weights.second[j], weights.first(j)));
}
}
uvLaplaceMat_ = new Eigen::SparseMatrix<double, Eigen::RowMajor>(laplaceMatSize_, laplaceMatSize_);
uvLaplaceMat_->setFromTriplets(tripletList.begin(), tripletList.end());
uvLaplaceMat_->makeCompressed();
}
void FractionalStepGrid::calc_u_hat() {
Eigen::VectorXd u_x, u_y, del2_u, p_x;
u_x = *derivXMat_ * *u;
u_y = *derivYMat_ * *u;
del2_u = *uvLaplaceMat_ * *u;
for (int i = 0; i < laplaceMatSize_; i++) {
u_hat->coeffRef(i) = u->coeff(i) + dt * (-(u->coeff(i) * u_x.coeff(i) + v->coeff(i) * u_y.coeff(i)) + mu / rho * del2_u.coeff(i));
}
}
void FractionalStepGrid::calc_v_hat() {
Eigen::VectorXd v_x, v_y, del2_v, p_y;
v_x = *derivXMat_ * *v;
v_y = *derivYMat_ * *v;
del2_v = *uvLaplaceMat_ * *v;
for (int i = 0; i < laplaceMatSize_; i++) {
v_hat->coeffRef(i) = v->coeff(i) +dt * (-(u->coeff(i) * v_x.coeff(i) + v->coeff(i) * v_y.coeff(i)) + mu / rho * del2_v.coeff(i));
}
}
void FractionalStepGrid::set_ppe_source() {
//cout << laplaceMatSize_ << " " << source_.rows() << endl;
source_.head(laplaceMatSize_) = rho/dt*(*derivXMat_ * *u_hat + *derivYMat_ * *v_hat); //interior
//boundary
double dpdx, dpdy, nx, ny;
int currPoint;
for (size_t i = 0; i < boundaries_.size(); i++) {
for (size_t j = 0; j < (boundaries_[i].bcPoints).size(); j++) {
currPoint = boundaries_[i].bcPoints[j];
dpdx = -rho / dt * (u->coeff(currPoint) - u_hat->coeff(currPoint));
dpdy = -rho / dt * (v->coeff(currPoint) - v_hat->coeff(currPoint));
//cout << dpdx << " " << dpdy << endl;
nx = std::get<0>(normalVecs_[currPoint]);
ny = std::get<1>(normalVecs_[currPoint]);
source_(currPoint) = nx * dpdx + ny * dpdy;
//cout << source_(i) << endl;
}
}
}
void FractionalStepGrid::correct_u() {
*u = *u_hat - dt / rho * (*derivXMat_ * values_->head(laplaceMatSize_));
}
void FractionalStepGrid::correct_v() {
*v = *v_hat - dt / rho * (*derivYMat_ * values_->head(laplaceMatSize_));
}
double FractionalStepGrid::fs_residual() {
return (*u - *u_hat).lpNorm<1>()/laplaceMatSize_;
}
double FractionalStepGrid::delu() {
return (*u - *u_old).lpNorm<1>()/laplaceMatSize_;
}