void arrayops() {
double nx = 10;
double ny = 10;
double nt = 100;
double c = 1;
double dx = 2/(nx-1);
double dy = 2/(ny-1);
double sigma = .2;
double dt = sigma*dx;
Eigen::ArrayXd x; // Array containing our x values
x.setLinSpaced(nx,0,2);
Eigen::ArrayXd y; // Array containing our x values
y.setLinSpaced(ny,0,2);
Eigen::ArrayXXd u;
u.setOnes(ny,nx);
Eigen::ArrayXXd un;
un.setOnes(ny,nx);
u.block(.5/dy,.5/dx,(1/dy+1)-.5/dy,(1/dx+1)-.5/dx) = Eigen::ArrayXXd::Constant((1/dy+1)-.5/dy,(1/dx+1)-.5/dx,2);
int count;
for(int i=0;i<nt;i++) {
un << u;
u.block(1,1,ny-1,nx-1) = un.block(1,1,ny-1,nx-1)-(c*dt/dx*(un.block(1,1,ny-1,nx-1)-un.block(0,1,ny-1,nx-1)))-(c*dt/dy*(un.block(1,1,ny-1,nx-1)-un.block(1,0,ny-1,nx-1)));
}
std::cout << u << std::endl;
}
void nonlin2d() {
double nx = 101;
double ny = 101;
double nt = 80;
double c = 1;
double dx = 2/(nx-1);
double dy = 2/(ny-1);
double sigma = .2;
double dt = sigma*dx;
// Make an output folder
std::string dir = "step6/";
Eigen::ArrayXd x; // Array containing our x values
x.setLinSpaced(nx,0,2);
Eigen::ArrayXd y; // Array containing our x values
y.setLinSpaced(ny,0,2);
Eigen::ArrayXXd u;
u.setOnes(ny,nx);
Eigen::ArrayXXd v;
v.setOnes(ny,nx);
Eigen::ArrayXXd un;
un.setOnes(ny,nx);
Eigen::ArrayXXd vn;
vn.setOnes(ny,nx);
u.block(.5/dy, .5/dx, 1/dy+1-.5/dy, 1/dx+1-.5/dx) = Eigen::ArrayXXd::Constant(1/dy+1-.5/dy,1/dx+1-.5/dx,2);
v.block(.5/dy, .5/dx, 1/dy+1-.5/dy, 1/dx+1-.5/dx) = Eigen::ArrayXXd::Constant(1/dy+1-.5/dy,1/dx+1-.5/dx,2);
for(int i=0;i<nt+1;i++) {
un << u;
vn << v;
u.block(1,1,ny-1,nx-1) = un.block(1,1,ny-1,nx-1)-(un.block(1,1,ny-1,nx-1)*dt/dx*(un.block(1,1,ny-1,nx-1)-un.block(0,1,ny-1,nx-1)))-(vn.block(1,1,ny-1,nx-1)*dt/dy*(un.block(1,1,ny-1,nx-1)-un.block(1,0,ny-1,nx-1)));
v.block(1,1,ny-1,nx-1) = vn.block(1,1,ny-1,nx-1)-(un.block(1,1,ny-1,nx-1)*dt/dx*(vn.block(1,1,ny-1,nx-1)-vn.block(0,1,ny-1,nx-1)))-(vn.block(1,1,ny-1,nx-1)*dt/dy*(vn.block(1,1,ny-1,nx-1)-vn.block(1,0,ny-1,nx-1)));
u.block(0,0,1,nx-1) = Eigen::ArrayXXd::Constant(1,nx-1,1);
u.block(ny-1,0,1,nx-1) = Eigen::ArrayXXd::Constant(1,nx-1,1);
u.block(0,0,ny-1,1) = Eigen::ArrayXXd::Constant(ny-1,1,1);
u.block(0,nx-1,ny-1,1) = Eigen::ArrayXXd::Constant(ny-1,1,1);
v.block(0,0,1,nx-1) = Eigen::ArrayXXd::Constant(1,nx-1,1);
v.block(ny-1,0,1,nx-1) = Eigen::ArrayXXd::Constant(1,nx-1,1);
v.block(0,0,ny-1,1) = Eigen::ArrayXXd::Constant(ny-1,1,1);
v.block(0,nx-1,ny-1,1) = Eigen::ArrayXXd::Constant(ny-1,1,1);
}
ofstream writexdata((dir + "output.dat").c_str(), ios::out | ios::trunc);
writexdata << u << endl;
writexdata.close();
}
void laplace2d() {
double nx = 31;
double ny = 31;
double c = 1;
double dx = 2/(nx-1);
double dy = 2/(ny-1);
double linorm_target = .01;
double linorm = 1;
// Make an output folder
std::string dir = "step9/";
Eigen::ArrayXd x; // Array containing our x values
x.setLinSpaced(nx,0,2); // Array is linearly spaced values from 0 to 2
Eigen::ArrayXd y; // Array containing our x values
y.setLinSpaced(ny,0,1);
// Arrays containing our calculated values
Eigen::ArrayXXd p;
Eigen::ArrayXXd pn;
// Initial Conditions
p.setZero(ny,nx);
pn.setZero(ny,nx);
//Set Boundary Conditions
p.block(0,0,ny,1) = Eigen::ArrayXXd::Constant(ny,1,0);
p.block(0,nx-1,ny,1) = y.block(0,0,ny,1);
p.block(0,0,1,nx) = p.block(1,0,1,nx);
p.block(ny-1,0,1,nx) = p.block(ny-2,0,1,nx);
while(linorm>linorm_target)
{
pn << p;
p.block(1,1,ny-2,nx-2) = (pow(dy,2)*(pn.block(2,1,ny-2,nx-2)+pn.block(0,1,ny-2,nx-2))+pow(dx,2)*(pn.block(1,2,ny-2,nx-2)+pn.block(1,0,ny-2,nx-2)))/(2*(pow(dx,2)+pow(dy,2)));
p(0,0) = (pow(dy,2)*(pn(1,0)+pn(ny-1,0))+pow(dx,2)*(pn(0,1)+pn(0,nx-1)))/(2*(pow(dx,2)+pow(dy,2)));
p(ny-1,nx-1) = (pow(dy,2)*(pn(0,nx-1)+pn(ny-2,nx-1))+pow(dx,2)*(pn(ny-1,0)+pn(ny-1,nx-2)))/(2*(pow(dx,2)+pow(dy,2)));
//Set Boundary Conditions
p.block(0,0,ny,1) = Eigen::ArrayXXd::Constant(ny,1,0);
p.block(0,nx-1,ny,1) = y.block(0,0,ny,1);
p.block(0,0,1,nx) = p.block(1,0,1,nx);
p.block(ny-1,0,1,nx) = p.block(ny-2,0,1,nx);
linorm = (p.cwiseAbs()-pn.cwiseAbs()).sum()/(pn.cwiseAbs()).sum();
}
ofstream writexdata((dir + "output.dat").c_str(), ios::out | ios::trunc);
writexdata << p << endl;
writexdata.close();
}