A locally discontinuous ALE finite element formulation for compressible phase change problems

Abstract

The simulation of phase change processes that occur at high rates, like the collapse of a vapor bubble or the combustion of dense energetic materials, poses significant challenges that include strong discontinuities in select field variables at the interface, high-speed flows in at least one phase, significant role of compressibility, disparate phase rate and acoustic time scales and advection dominated processes. In this paper we present a finite element based method that addresses these challenges. The discretization is continuous everywhere except at the interface and it inherits its stability properties from both continuous and discontinuous finite element formulations like the SUPG and interior penalty methods. We track the evolution of the interface mesh and accommodate its motion in the volume by moving the mesh in accordance with an elastic analogy within an arbitrary eulerian lagrangian (ALE) framework. This motion is interspersed with a few select steps of mesh modification. We demonstrate that the proposed method has desirable discrete conservation properties and outline a proof for its stability. We also describe how this method is implemented in a finite element code within an implicit predictor-corrector time stepping scheme. Finally we apply this method to a series of phase change problems involving an energetic material, where we verify its implementation and demonstrate its utility.