A Discontinuous Galerkin Method for Compressible Gas/Liquid Interfacial Flows with Consistent and Conservative Phase-Fields

Simulating compressible gas/liquid interfacial flows efficiently and with high accuracy is a challenging multi-physics problem due to large gradients, variable material properties, and disparate time and length scales. To address these challenges, we develop a discontinuous Galerkin method to solve the compressible Navier-Stokes equations using the five-equations multiphase model. The temporal scheme is explicit (Runge-Kutta) and the spatial scheme relies on a discontinuity sensor to identify regions where high-order limiting is applied, i.e., at interfaces and shock waves. Viscous effects and heat transfer are included, and adaptive mesh refinement via AMReX provides efficient resolution of sharp flow features. Further, we demonstrate a novel consistent and conservative phase-field method that controls the numerical diffusion of the material indicator function in a physically accurate manner. We illustrate the viability of our method through a variety of one- and multi-dimensional compressible gas/liquid interfacial problems, including high-speed impact of a liquid droplet onto a rigid wall.