An Arbitrary Lagrangian-Eulerian Reconstructed Discontinuous Galerkin Method for Compressible Multiphase Flows

摘要

A high-order discontinuous Galerkin arbitrary Lagrangian-Eulerian (ALE) formulation for compressible multi-material flow interface tracking has been developed. A general equation of state has been used to allow for multiple materials. The ALE formulation has been successfully implemented on a one-dimensional domain using 1st order finite volume (DGP_0), 2nd order DG (DGP_1) and 3rd order reconstructed DG (rDGP_1P_2) spatial discretization schemes and 3rd order accurate TVD Runge-Kutta time discretization. A robust positivity-preserving limiter is used to preserve the positivity of density and pressure in the neighborhood of strong discontinuities. One-dimensional numerical test problems have been presented to establish that the scheme is geometric conservation law (GCL) preserving; achieves the desired order of convergence; and is able to track interfaces very accurately. Moreover, the positivity-preserving limiter is shown to guarantee positivity of the solution for the extremely challenging Riemann problems considered in this work.