Runge–Kutta discontinuous Galerkin method for interface flows with a maximum preserving limiter

We propose a high order diffuse interface method for dealing with compressible multiphase flows with interfaces. This scheme is based on the discontinuous Galerkin formulation of Franquet and Perrier [1]. As it is linear, this scheme is oscillating, so that the volume fraction can become negative or greater than 1. For stabilizing it, the maximum preserving limiter introduced in Zhang et al. (2012) [2] is used. The scheme is applied to the computation of a Rayleigh–Taylor instability.