An Approximate Solver for Multi-medium Riemann Problem with Mie-Gr\"uneisen Equations of State

TL;DR

This paper introduces an approximate iterative solver for multi-medium Riemann problems using Mie-Gr"uneisen equations of state, validated through numerical tests on complex flow scenarios.

Contribution

It presents a novel approximate solver with proven convergence for multi-medium Riemann problems involving Mie-Gr"uneisen EOS, applicable to practical compressible flow simulations.

Findings

Solver accurately computes interface pressure and velocity.

Validated through Riemann problems, air blast, and underwater explosion simulations.

Demonstrates robustness and applicability in multi-medium flow modeling.

Abstract

We propose an approximate solver for multi-medium Riemann problems with materials described by a family of general Mie-Gr\"uneisen equations of state, which are widely used in practical applications. The solver provides the interface pressure and normal velocity by an iterative method. The well-posedness and convergence of the solver is verified with mild assumptions on the equations of state. To validate the solver, it is employed in computing the numerical flux on phase interfaces of a numerical scheme on Eulerian grids that was developed recently for compressible multi-medium flows. Numerical examples are presented for Riemann problems, air blast and underwater explosion applications.