Numerical methods for weakly ionized gas

This paper is devoted to the numerical approximation of the discontinuous s olutions of the Euler equations for weakly ionized mixtures of reacting gas es. The main difficulty stems from the non conservative formulation of thes e equations due to a widely used physical assumption. We show how to derive a well-posed conservative reformulation of the equations from the analysis of the associated full convective-diffusive system. We then propose an exa ct Roe-type linearization for the equivalent system of conservation laws on the basis of an original Lemma for averagings. Our results can be seen as an extension of the classical Roe average, for nonlinearities that cannot b e recast under quadratic form.