A discontinuous Galerkin method for the five-equations multiphase model

The five-equations model has been used extensively to study compressible multiphase and multi-component flows using lower-order numerical schemes, while the solution to these equations with a high-order scheme has received far less attention. In this work, we present a discontinuous Galerkin finite element scheme with a novel limiting procedure that can efficiently resolve compressible multiphase and multi-component flows with high-order accuracy. The proposed scheme is conservative, preserves velocity, pressure, and temperature equilibria, bounds the phasic masses, the volume fraction, and the pressure for various convex equations of state, and can be used with a variety of limiters. We present several numerical tests in one and two dimensions to verify and validate our methodology, including a multi-material Richtmyer-Meshkov instability, the impingement of a shock in air with an SF6 block, and the interaction of a strong shock in water with an air bubble.