An asymptotic expansion for the solution of the generalized Riemann problem. Part 2 : application to the equations of gas dynamics

Abstract

We apply to the gas dynamics equations the general method of approximation for the generalized Riemann problem proposed by Le Floch-Raviart [6]. We both consider the equations of gas dynamics in Lagrangian coordinates in slab symmetry with a source term and the equations in Eulerian coordinates in plane, cylindrical or spherical symmetry. Explicit formulae are derived for the first order approximation of the solution of the generalized Riemann problem. Such an approximate solution may be easily used to construct a second order version of the numerical Godunov method.