Difference Scheme for Two-phase Flow

A numerical method for two-phase flow with hydrodynamics behavior was considered. The nonconservative hyperbolic governing equations proposed by Saurel and Gallout were adopted. Dissipative effects were neglected but they could be included in the model without major difficulties. Based on the opinion proposed by Abgrall that "a two phase system, uniform in velocity and pressure at t=0 will be uniform on the same variable during its temporal evolution", a simple accurate and fully Eulerian numerical method was presented for the simulation of multiphase compressible flows in hydrodynamic regime. The numerical method relies on Godunov-type scheme, with HLLC and Lax-Friedrichs type approximate Riemann solvers for the resolution of conservation equations, and nonconservative equation. Speed relaxation and pressure relaxation processes were introduced to account for the interaction between the phases. Test problem was presented in one space dimension which illustrated that our scheme is accurate, stable and oscillation free.