A second order anti-diffusive Lagrange-remap scheme for two-component flows

CEMRACS'10 research achievements: numerical modeling of fusion. Papers from the 15th Annual Summer Research Session (Centre d'étude Mathématique de Recherche Avancée en Calcul Scientifique) held in Marseille, July 19-August 27, 2010International audienceWe build a non-dissipative second order algorithm for the approximate resolution of the one-dimensional Euler system of compressible gas dynamics with two components. The considered model was proposed in Allaire, Clerc and Kokh (2002). The algorithm is based on Kokh and Lagoutière (2010) which deals with a non-dissipative first order resolution in Lagrange-remap formalism. In the present paper we describe, in the same framework, an algorithm that is second order accurate in time and space, and that preserves sharp interfaces. Numerical results reported at the end of the paper are very encouraging, showing the interest of the second order accuracy for genuinely non-linear waves