A HIGH-ORDER GODUNOV METHOD FOR MULTIPLE CONDENSED PHASES

We present a numerical algorithm for computing strong shock waves in p roblems involving multiple condensed phases. This method is based on a conservative high-order Godunov method in Eulerian form, similar to t hose that have been used extensively for gas dynamics computations, wi th an underlying thermodynamic model based on the Mie-Gruneisen equati on of state together with a linear Hugoniot. This thermodynamic model is appropriate for a wide variety of nonporous condensed phases. We mo del multiple phases by constructing an effective single phase in which the density, specific energy, and elastic properties are given by sel f-consistent averages of the individual phase properties, including th eir relative abundances, We use a second-order volume-of-fluid interfa ce reconstruction algorithm to decompose the effective single-phase fl uxes back into the appropriate individual component phase quantities. We have coupled a two-dimensional operator-split version of this metho d to an adaptive mesh refinement algorithm and used it to model proble ms that arise in experimental shock wave geophysics. Computations from this work are presented. (C) 1996 Academic Press, Inc.