How to Solve Compressible Multifluid Equations: a Simple, Robust, and Accurate Method

Abstract

Solving multifluid equations of compressible multiphase flows has proven to be extremely demanding because of some peculiar mathematical properties, such as nonhyperbolicity, nonconservative form, and stiffness due to disparity in fluid properties and flow scales occurring typically. In this paper, we first consider the mathematical issues concerning nonhyperbolicity and nonconservative form. Their effects on the stability and convergence of numerical solutions are the theme of our presentation; we shall present solutions for a range of problems selected to illuminate these numerical issues. To this end, we present a new numerical method that is simple to implement for a general class of fluids and yet is capable of robustly and accurately calculating phenomena involving material and shock discontinuities and interactions between them. Additionally, the paper is completed with a new information for ensuring hyperbolicity under an interfacial pressure representation.