A volume-of-fluid reconstruction based interface sharpening algorithm for a reduced equation model of two-material compressible flow

In this paper we present a numerical method for the simulation of two-material flows governed by the compressible unsteady Euler equations. A system of six equations is used, with a pressure relaxation step which ensures convergence to the equivalent five-equation model. The numerical method employs a volume-of-fluid interface tracking method in order to maintain a sharp interface indefinitely, along with a robust update procedure for interfacial cells which ensures density and internal energy positivity. Numerical results are presented for a range of test cases, including for liquid–gas shock–bubble interaction and cylindrically convergent Richtmyer–Meshkov instability between metal and air. Results are in agreement with theoretical data, and compare well to other approaches designed to sharpen the material interface in the five-equation model.