A Fluid-Mixture Type Algorithm for Compressible Multicomponent Flow with Mie–Grüneisen Equation of State

Abstract

A simple interface-capturing approach proposed previously by the author for efficient numerical resolution of multicomponent problems with a van der Waals fluid [J. Comput. Phys., 156 (1999), pp. 43–88] is extended to a more general case with real materials characterized by a Mie–Grüneisen equation of state. As before, the flow regime of interests is assumed to be homogeneous with no jumps in the pressure and velocity (the normal component of it) across the interfaces that separate two regions of different fluid components. The algorithm uses a mixture type of the model system that is formed by combining the Euler equations of gas dynamics for the basic conserved variables and an additional set of effective equations for the problem-dependent material quantities. In this approach, the latter equations are introduced in the algorithm primarily for an easy computation of the pressure from the equation of state, and are derived so as to ensure a consistent modeling of the energy equation near the interfaces where two or more fluid components are present in a grid cell, and also the fulfillment of the mass equation in the other single component regions. A standard high-resolution wave propagation method designed originally for single component flows is generalized to solve the proposed system for multicomponent flows, giving an efficient implementation of the algorithm. Several numerical results are presented in both one and two space dimensions that show the feasibility of the method with the Roe Riemann solver as applied to a reasonable class of practical problems without introducing any spurious oscillations in the pressure near the interfaces. This includes results obtained using a multicomponent version of the AMRCLAW software package of Berger and LeVeque for the simulation of the impact of an underwater aluminum plate to a copper plate in two space dimensions.