A stabilized finite element method for compressible phase change phenomena

Abstract

This thesis presents 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 Lagrangian-Eulerian (ALE) framework. This motion is interspersed with a few steps of mesh modification. We demonstrate that the proposed method has desirable discrete conservation properties and justify these properties with some numerical simulation results. We describe how this method is implemented in a finite element code within an implicit predictor-corrector time-stepping scheme. Moreover, we outline the convergence of the model interface problems with respect to the mesh size and establish their connections to the proposed finite element based method. 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.

Multiphase problems arise in many fields in science and engineering. Generally, multiphase problems can be categorized into the processes with phase change and those without. The simulation of phase change processes that occur at high rates, like the collapse of a vapor bubble or the combustion of dense energetic material, poses significant challenges such as strong discontinuities in select field variables at the interface, high-speed flows in at least one phase, a significant role of compressibility, disparate phase rate and acoustic time scales and advection dominated processes.