# 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 | ||

- | :<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> |

- | :<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 | ||

- | :<math> p_L=1, \rho_L=1, p_R=0.1, \rho_R=0.125</math> | + | :<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

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