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A high-order Godunov method for multiple condensed phases. (English) Zbl 0861.65117
Authors’ summary: We present a numerical algorithm for computing strong shock waves in problems involving multiple condensed phases. This method is based on a conservative high-order Godunov method in Eulerian form, similar to those that have been used extensively for gas dynamics computations, with an underlying thermodynamic model based on the Mie-Grüneisen equation of state together with a linear Hugoniot. This thermodynamic model is appropriate for a wide variety of nonporous condensed phases.
We model multiple phases by constructing an effective single phase in which the density, specific energy, and elastic properties are given by self-consistent averages of the individual phase properties, including their relative abundances. We use a second-order volume-of-fluid interface reconstruction algorithm to decompose the effective single-phases fluxes back into the appropriate individual component phase quantities. We have coupled a two-dimensional operator-split version of this method to an adaptive mesh refinement algorithm and used it to model problems that arise in experimental shock wave geophysics. Computations from this work are presented.

MSC:
65Z05 Applications to the sciences
35R35 Free boundary problems for PDEs
80A22 Stefan problems, phase changes, etc.
35Q72 Other PDE from mechanics (MSC2000)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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