A Discontinuous Galerkin Method for Compressible Gas/Liquid Interfacial Flows

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. The solution limiting is performed so as to prevent the generation of spurious oscillations at material interfaces by appropriately reconstructing the density, velocity, and pressure in a conservative fashion. Viscous effects and heat transfer are included and different kinds of meshes can be implemented while still maintaining arbitrarily high orders of accuracy. We demonstrate 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.