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Shock tube problem

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The test case involves the 1-D Euler equation describing the flow.The initial condition is given by  
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'''Shock tube problem''' is a special case of [[Riemann problem]] with velocities on both sides of discontinuity set to zero. It is often used as a test case for validation of numerical codes, because analytical solutions are available.The initial condition is given by  
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:<math> u\equiv u_L ,p=p_L,\rho=\rho_L,x<x_o </math>
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:<math> u=u_L=0 , p=p_L , \rho=\rho_L, x<0, </math>
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:<math> u\equiv u_R ,p=p_R,\rho=\rho_R,x>x_o </math>
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:<math> u=u_R=0 , p=p_R , \rho=\rho_R, x>0. </math>
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where <math> p_L>p_R </math> diaphragm being located at <math> x=x_o </math>
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Two cases are considered and the flow is simulated using Roe first-order scheme and Steger-Warming  vector splitting scheme.
 
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: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>
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A well-known special case is the Sod problem (Sod, 1978) with initial conditions
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: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>
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:<math> p_L=1, \rho_L=1, p_R=0.1, \rho_R=0.125</math>.
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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.
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Revision as of 13:23, 14 November 2006

Shock tube problem is a special case of Riemann problem with velocities on both sides of discontinuity set to zero. It is often used as a test case for validation of numerical codes, because analytical solutions are available.The initial condition is given by

u=u_L=0 , p=p_L , \rho=\rho_L, x<0,
u=u_R=0 , p=p_R , \rho=\rho_R, x>0.


A well-known special case is the Sod problem (Sod, 1978) with initial conditions

p_L=1, \rho_L=1, p_R=0.1, \rho_R=0.125.
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