# Shock tube problem

The test case involves the 1-D Euler equation describing the flow.The initial condition is given by

$u\equiv u_L ,p=p_L,\rho=\rho_L,x
$u\equiv u_R ,p=p_R,\rho=\rho_R,x>x_o$

where $p_L>p_R$ diaphragm being located at $x=x_o$

Two cases are considered and the flow is simulated using Roe first-order scheme and Steger-Warming vector splitting scheme.

Case 1 $p_R \equiv 1.2*10^4 Pa,p_L=10^5 Pa,u_L=u_R=0,\rho_R=0.125,\rho_L=1.0 kg/m^3 ,x_o=5 m ,t_f=0.0061 s$
Case 2 $p_R \equiv 1.2*10^3 Pa,p_L=10^5 Pa,u_L=u_R=0,\rho_R=0.01,\rho_L=1.0 kg/m^3 ,x_o=5 m ,t_f=0.0039 s$

The computational domain is $[0,2x_o]$.The boundary conditions are set equal to the intial conditions of the undisturbed gas.The computations are carried out with 600 grid points.