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Copy pathEuler_roe.cpp
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Euler_roe.cpp
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#include "1D_BTCS.h"
using namespace std;
void Euler_roe()
{
int nx = 256;
double dx = 1.0 / nx;
double dt = 0.0001;
double t = 0.2;
int nt = ceil(t / dt);
vector<double> x(nx, 0);
vector<vector<double>> qt(3, vector<double>(nx, 0));//temperory array by RK3 scheme
vector<vector<vector<double>>> q(nt, vector<vector<double>>(3, vector<double>(nx, 0)));//all timesteps
vector<vector<double>> r(3, vector<double>(nx, 0));//general spatial FD
double gamma = 1.4;//specific gas ratio
//Sod's Riemann problem
//left side
double rhoL = 1.0;
double uL = 0.0;
double pL = 1.0;
//right side
double rhoR = 0.125;
double uR = 0.0;
double pR = 0.1;
double rho, u, p, e = 0;
//grid
for (int i = 0; i < nx; i++)
{
x[i] = (i + 0.5) * dx;
}
double xc = 0.5;
for (int i = 0; i < nx; i++)
{
rho = x[i] > 0.5? rhoR:rhoL;
u = x[i] > 0.5? uR : uL;
p = x[i] > 0.5? pR : pL;
e = p / (rho * (gamma - 1.0)) + 0.5 * u * u;
q[0][0][i] = rho;
q[0][1][i] = rho * u;
q[0][2][i] = rho * e;
}
for (int j = 1; j < nt; j++)// one time step
{
rhs_roe(nx, dx, gamma, q[j - 1], r);
for (int i = 0; i < nx; i++)
{
qt[0][i] =q[j - 1][0][i] + dt * r[0][i];
qt[1][i] =q[j - 1][1][i] + dt * r[1][i];
qt[2][i] =q[j - 1][2][i] + dt * r[2][i];
}
rhs_roe(nx, dx, gamma, qt, r);
for (int i = 0; i < nx; i++)
{
qt[0][i] = 0.75 * q[j - 1][0][i] + 0.25 * qt[0][i] + dt / 4.0 * r[0][i];
qt[1][i] = 0.75 * q[j - 1][1][i] + 0.25 * qt[1][i] + dt / 4.0 * r[1][i];
qt[2][i] = 0.75 * q[j - 1][2][i] + 0.25 * qt[2][i] + dt / 4.0 * r[2][i];
}
rhs_roe(nx, dx, gamma, qt, r);
for (int i = 0; i < nx; i++)
{
q[j][0][i] = q[j - 1][0][i] / 3.0 + 2.0 / 3.0 * qt[0][i] + dt * 2.0 / 3.0 * r[0][i];
q[j][1][i] = q[j - 1][1][i] / 3.0 + 2.0 / 3.0 * qt[1][i] + dt * 2.0 / 3.0 * r[1][i];
q[j][2][i] = q[j - 1][2][i] / 3.0 + 2.0 / 3.0 * qt[2][i] + dt * 2.0 / 3.0 * r[2][i];
}
}
ofstream outfile("roe.dat");
if (outfile.is_open())
{
for (int m = 0; m < 3; m++)
{
for (int i = 0; i < nx; i++)
{
outfile << q[nt-1][m][i] << " ";
}
outfile << endl;
}
outfile << endl;
}
else
{
std::cerr << "Error: unable to open file for writing" << std::endl;
}
return;
}
void rhs_roe(int nx, double dx, double gamma, vector<vector<double>> q, vector<vector<double>>& r)
{
//left and right side fluxes at the interface
vector<vector<double>> qL(3, vector<double>(nx + 1, 0));
vector<vector<double>> qR(3, vector<double>(nx + 1, 0));
vector<vector<double>> fL(3, vector<double>(nx + 1, 0));
vector<vector<double>> fR(3, vector<double>(nx + 1, 0));
vector<vector<double>> f(3, vector<double>(nx + 1, 0));
/*double a = 0;
vector<double> alp(nx, 0);
vector<double> alpha(nx, 0);
for (int i = 0; i < nx; i++)
{
double p = (gamma - 1.0) * (q[2][i] - 0.5 * q[1][i] * q[1][i] / q[0][i]);
f[0][i] = q[1][i];
f[1][i] = q[1][i] * q[1][i] / q[0][i] + p;
f[2][i] = q[1][i] * q[2][i] / q[0][i] + p * q[1][i] / q[0][i];
}
for (int i = 0; i < nx; i++)
{
a = sqrt(gamma * ((gamma - 1) * (q[2][i] - 0.5 * q[1][i] * q[1][i] / q[0][i])) / q[0][i]);
alp[i] = abs(q[1][i] / q[0][i]) + a;
}
for (int i = 2; i < nx - 3; i++)
{
alpha[i] = max(alp[i - 2], max(alp[i - 1], max(alp[i], max(alp[i + 1], alp[i + 2]))));
}
alpha[0] = alp[0];
alpha[1] = alp[1];
alpha[nx - 2] = alp[nx - 2];
alpha[nx - 1] = alp[nx - 1];*/
qL = wenoL_roe(nx, q);
qR = wenoR_roe(nx, q);
flux_roe(nx, gamma, qL, fL);
flux_roe(nx, gamma, qR, fR);
roe(nx, gamma, qL, qR, f, fL,fR);
for (int i = 0; i < nx; i++)
{
for (int m = 0; m < 3; m++)
{
r[m][i] = -(f[m][i + 1] - f[m][i]) / dx;
}
}
return;
}
void flux_roe(int nx, double gamma, vector<vector<double>> q, vector<vector<double>>& f)
{
for (int i = 0; i < nx+1; i++)
{
double p = (gamma - 1.0) * (q[2][i] - 0.5 * q[1][i] * q[1][i] / q[0][i]);
f[0][i] = q[1][i];
f[1][i] = q[1][i] * q[1][i] / q[0][i] + p;
f[2][i] = q[1][i] * q[2][i] / q[0][i] + p* q[1][i] / q[0][i];
}
return;
}
void roe(int nx, double gamma, vector<vector<double>> uL, vector<vector<double>> uR, vector<vector<double>>& f, vector<vector<double>> fL, vector<vector<double>> fR)
{
vector<double> dd(3, 0);
vector<double> dF(3, 0);
vector<double> v(3, 0);
double gm = gamma - 1.0;
for (int i = 0; i < nx+1; i++)
{
//Leftand right states :
double rhLL = uL[0][i];
double uuLL = uL[1][i] / rhLL;
double eeLL = uL[2][i] / rhLL;
double ppLL = gm * (eeLL * rhLL - 0.5 * rhLL * (uuLL * uuLL));
double hhLL = eeLL + ppLL / rhLL;
double rhRR = uR[0][i];
double uuRR = uR[1][i] / rhRR;
double eeRR = uR[2][i] / rhRR;
double ppRR = gm * (eeRR * rhRR - 0.5 * rhRR * (uuRR * uuRR));
double hhRR = eeRR + ppRR / rhRR;
double alpha = 1.0 / (sqrt(abs(rhLL)) + sqrt(abs(rhRR)));
double uu = (sqrt(abs(rhLL)) * uuLL + sqrt(abs(rhRR)) * uuRR) * alpha;
double hh = (sqrt(abs(rhLL)) * hhLL + sqrt(abs(rhRR)) * hhRR) * alpha;
double aa = sqrt(abs(gm * (hh - 0.5 * uu * uu)));
double D11 = abs(uu);
double D22 = abs(uu + aa);
double D33 = abs(uu - aa);
double beta = 0.5 / (aa * aa);
double phi2 = 0.5 * gm * uu * uu;
//Right eigenvector matrix
double R11 = 1.0;
double R21 = uu;
double R31 = phi2/gm;
double R12 = beta;
double R22 = beta * (uu + aa);
double R32 = beta * (hh + uu * aa);
double R13 = beta;
double R23 = beta * (uu - aa);
double R33 = beta * (hh - uu * aa);
//Left eigenvector matrix
double L11 = 1.0 - phi2 / (aa * aa);
double L12 = gm * uu / (aa * aa);
double L13 = -gm / (aa * aa);
double L21= phi2 - uu * aa;
double L22 = aa - gm * uu;
double L23 = gm;
double L31 = phi2 + uu * aa;
double L32 = -aa - gm * uu;
double L33 = gm;
for (int m = 0; m < 3; m++)
{
v[m] = 0.5 * (uR[m][i] - uL[m][i]);
}
dd[0] = D11 * (L11 * v[0] + L12 * v[1] + L13 * v[2]);
dd[1] = D22 * (L21 * v[0] + L22 * v[1] + L23 * v[2]);
dd[2] = D33 * (L31 * v[0] + L32 * v[1] + L33 * v[2]);
dF[0] = R11 * dd[0] + R12 * dd[1] + R13 * dd[2];
dF[1] = R21 * dd[0] + R22 * dd[1] + R23 * dd[2];
dF[2] = R31 * dd[0] + R32 * dd[1] + R33 * dd[2];
for (int m = 0; m < 3; m++)
{
f[m][i] = 0.5 * (fR[m][i] + fL[m][i]) - dF[m];
}
}
}
vector<vector<double>> wenoL_roe(int nx, vector<vector<double>> q)
{
vector<vector<double>> f(3, vector<double>(nx + 1,0));
for (int m = 0; m < 3; m++)
{
int i = -1;
double v1 = q[m][i + 3];
double v2 = q[m][i + 2];
double v3 = q[m][i + 1];
double v4 = q[m][i + 1];
double v5 = q[m][i + 2];
f[m][i + 1] = wcL(v1, v2, v3, v4, v5);
i = 0;
v1 = q[m][i + 1];
v2 = q[m][i];
v3 = q[m][i];
v4 = q[m][i + 1];
v5 = q[m][i + 2];
f[m][i + 1] = wcL(v1, v2, v3, v4, v5);
i = 1;
v1 = q[m][i - 1];
v2 = q[m][i - 1];
v3 = q[m][i];
v4 = q[m][i + 1];
v5 = q[m][i + 2];
f[m][i + 1] = wcL(v1, v2, v3, v4, v5);
for (i = 2; i < nx - 2; i++)
{
v1 = q[m][i - 2];
v2 = q[m][i - 1];
v3 = q[m][i];
v4 = q[m][i + 1];
v5 = q[m][i + 2];
f[m][i + 1] = wcL(v1, v2, v3, v4, v5);
}
i = nx - 2;
v1 = q[m][i - 2];
v2 = q[m][i - 1];
v3 = q[m][i];
v4 = q[m][i + 1];
v5 = q[m][i + 1];
f[m][i + 1] = wcL(v1, v2, v3, v4, v5);
i = nx - 1;
v1 = q[m][i - 2];
v2 = q[m][i - 1];
v3 = q[m][i];
v4 = q[m][i];
v5 = q[m][i - 1];
f[m][i + 1] = wcL(v1, v2, v3, v4, v5);
}
return f;
}
vector<vector<double>> wenoR_roe(int nx, vector<vector<double>> q)
{
vector<vector<double>> f(3, vector<double>(nx + 1, 0));
for (int m = 0; m < 3; m++)
{
int i = 0;
double v1 = q[m][i + 1];
double v2 = q[m][i];
double v3 = q[m][i];
double v4 = q[m][i + 1];
double v5 = q[m][i + 2];
f[m][i] = wcR(v1, v2, v3, v4, v5);
i = 1;
v1 = q[m][i - 1];
v2 = q[m][i - 1];
v3 = q[m][i];
v4 = q[m][i + 1];
v5 = q[m][i + 2];
f[m][i] = wcR(v1, v2, v3, v4, v5);
for (i = 2; i < nx - 2; i++)
{
v1 = q[m][i - 2];
v2 = q[m][i - 1];
v3 = q[m][i];
v4 = q[m][i + 1];
v5 = q[m][i + 2];
f[m][i] = wcR(v1, v2, v3, v4, v5);
}
i = nx - 2;
v1 = q[m][i - 2];
v2 = q[m][i - 1];
v3 = q[m][i];
v4 = q[m][i + 1];
v5 = q[m][i + 1];
f[m][i] = wcR(v1, v2, v3, v4, v5);
i = nx - 1;
v1 = q[m][i - 2];
v2 = q[m][i - 1];
v3 = q[m][i];
v4 = q[m][i];
v5 = q[m][i - 1];
f[m][i] = wcR(v1, v2, v3, v4, v5);
i = nx;
v1 = q[m][i - 2];
v2 = q[m][i - 1];
v3 = q[m][i - 1];
v4 = q[m][i - 2];
v5 = q[m][i - 3];
f[m][i] = wcR(v1, v2, v3, v4, v5);
}
return f;
}