A fluid-mixture type algorithm for compressible multicomponent flow with Mie-Gruneisen equation of state

A simple interface-capturing approach proposed previously by the author for efficient numerical resolution of multicomponent problems with a van der W aals fluid [J. Comput. Phys., 156 (1999), pp, 43-88] is extended to a more general case with real materials characterized by a Mie-Gruneisen equation of state. As before, the flow regime of interests is assumed to be homogene ous with no jumps in the pressure and velocity (the normal component of it) across the interfaces that separate two regions of different fluid compone nts. The algorithm uses a mixture type of the model system that is formed b y combining the Euler equations of gas dynamics for the basic conserved var iables and an additional set of effective equations for the problem-depende nt material quantities. In this approach, the latter equations are introduc ed 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 modelin g of the energy equation near the interfaces where two or more fluid compon ents are present in a grid cell, and also the fulfillment of the mass equat ion in the other single component regions. A standard high-resolution wave propagation method designed originally for single component flows is genera lized to solve the proposed system for multicomponent flows, giving an effi cient implementation of the algorithm. Several numerical results are presen ted in both one and two space dimensions that show the feasibility of the m ethod with the Roe Riemann solver as applied to a reasonable class of pract ical problems without introducing any spurious oscillations in the pressure near the interfaces. This includes results obtained using a multicomponent version of the ANIRCLANV software package of Berger and LeVeque for the si mulation of the impact of an underwater aluminum plate to a copper plate in two space dimensions. (C) 2001 Academic Press.