Write a Matlab code for solving 1D compressible Euler equation with an example that shock happens.
时间: 2024-03-09 07:50:30 浏览: 16
Sure, here is an example code for solving the 1D compressible Euler equation in Matlab with a shock happening:
```matlab
% Define the domain and initial conditions
x = linspace(0,1,1000);
rhoL = 1;
rhoR = 0.125;
uL = 0;
uR = 0;
pL = 1;
pR = 0.1;
gamma = 1.4;
x0 = 0.5;
tEnd = 0.25;
dx = x(2)-x(1);
dt = 0.01;
% Initialize the solution arrays
rho = ones(size(x))*rhoL;
u = ones(size(x))*uL;
p = ones(size(x))*pL;
% Set up the shock initial condition
for i = 1:length(x)
if x(i) >= x0
rho(i) = rhoR;
u(i) = uR;
p(i) = pR;
end
end
% Define the flux function
flux = @(rho,u,p) [rho.*u; rho.*u.^2+p; u.*(gamma*p./(gamma-1)+0.5*rho.*u.^2+u.^2)];
% Solve the Euler equations with an explicit upwind scheme
t = 0;
while t < tEnd
% Compute the time step
lambda = max(abs(u) + sqrt(gamma*p./rho));
dt = dx / lambda;
% Compute the fluxes at the cell interfaces
F = flux(rho,u,p);
Fp = F(:,2:end);
Fm = F(:,1:end-1);
% Compute the numerical flux using the upwind scheme
Fnum = 0.5*(Fp+Fm - lambda.*(rho(:,2:end)-rho(:,1:end-1)));
% Update the solution
rho(:,2:end-1) = rho(:,2:end-1) - dt/dx*(Fnum(1,2:end)-Fnum(1,1:end-1));
u(:,2:end-1) = u(:,2:end-1) - dt/dx*(Fnum(2,2:end)-Fnum(2,1:end-1));
p(:,2:end-1) = p(:,2:end-1) - dt/dx*(Fnum(3,2:end)-Fnum(3,1:end-1));
% Apply boundary conditions
rho(:,1) = rho(:,2);
u(:,1) = u(:,2);
p(:,1) = p(:,2);
rho(:,end) = rho(:,end-1);
u(:,end) = u(:,end-1);
p(:,end) = p(:,end-1);
% Update the time
t = t + dt;
end
% Plot the final solution
plot(x,rho,'-k',x,u,'-r',x,p,'-b')
xlabel('x')
ylabel('Density, Velocity, Pressure')
legend('Density','Velocity','Pressure')
title('1D Compressible Euler Equation with Shock')
```
Note that this code uses an explicit upwind scheme to solve the equations, which may not be stable for all choices of parameters. If you encounter stability issues, you may need to use a different numerical method. Additionally, this code assumes a constant gamma value of 1.4; if you need to use a different value of gamma, you will need to modify the code accordingly.