# Shock tube problem

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:<math> u\equiv u_R ,p=p_R,\rho=\rho_R,x>x_o </math> | :<math> u\equiv u_R ,p=p_R,\rho=\rho_R,x>x_o </math> | ||

where <math> p_L>p_R </math> diaphragm being located at <math> x=x_o </math> | where <math> p_L>p_R </math> diaphragm being located at <math> x=x_o </math> | ||

+ | |||

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

+ | |||

+ | :Case 1 <math> 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 </math> | ||

+ | :Case 2 <math> 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 </math> | ||

+ | |||

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

## Revision as of 04:30, 21 September 2005

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

where diaphragm being located at

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

- Case 1
- Case 2

The computational domain is .The boundary conditions are set equal to the intial conditions of the undisturbed gas.The computations are carried out with 600 grid points.