Abstract
We 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 Lagoutiere (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.
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