A Hybrid Scheme of Level Set and Diffuse Interface Methods for Simulating Multi-Phase Compressible Flows

We propose a hybrid scheme combing the level set method and the multicomponent diffuse interface method to simulate complex multi-phase flows. The overall numerical scheme is based on a sharp interface framework where the level set method is adopted to capture the material interface, the Euler equation is used to describe a single-phase flow on one side of the interface and the six-equation diffuse interface model is applied to model the multi-phase mixture or gas-liquid cavitation on the other side. An exact Riemann solver, between the Euler equation nd the six-equation model with highly nonlinear Mie-Gruneisen equations of state, is developed to predict the interfacial states and compute the phase interface flux. Several numerical examples, including shock tube problems, cavitation problems, air blast and underwater explosion applications are presented to validate the numerical scheme and the Riemann solver.