Random sampling remap for compressible two-phase flows

In this paper we address the problem of solving accurately gas-liquid compressible flows without pressure oscillations at the gas-liquid interface. We introduce a new Lagrange-projection scheme based on a random sampling technique introduced by Chalons and Goatin (2007) [7]. We compare it to a ghost fluid approach introduced in Wang et al. (2006), Müller et al. (2009) [25], [20] which is based on the ghost fluid method for the poor (Abgrall and Karni, 2001) [2]. Despite the non-conservative feature of the schemes, we observe the numerical convergence towards the relevant weak solution for shock-contact interaction test cases.