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Shock tube problem

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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  
'''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=u_L=0 , p=p_L , \rho=\rho_L, x<0, </math>
+
:<math> u=u_L=0 , p=p_L , \rho=\rho_L, x<0,</math>
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:<math> u=u_R=0 , p=p_R , \rho=\rho_R, x>0. </math>
+
:<math> u=u_R=0 , p=p_R , \rho=\rho_R, x>0.</math>
A well-known special case is the Sod problem (Sod, 1978) with initial conditions
A well-known special case is the Sod problem (Sod, 1978) with initial conditions
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:<math> p_L=1, \rho_L=1, p_R=0.1, \rho_R=0.125</math>.
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:<math> p_L=1, \rho_L=1, p_R=0.1, \rho_R=0.125.</math>

Revision as of 13:30, 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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