Shock and detonation modeling with the Mie-Grüneisen equation of state

Abstract

We consider the numerical simulation of inviscid reactive flows with application to high density explosive detonation. The numerical model is based on the Euler equations and the Mie-Grüneisen equation of state extended to treat chemical energy release and expanded states. The equations are computed with a Roe-Glaister solver on a Cartesian mesh. We present results for two substances, a binder and an explosive. Our solution method is verified against the exact solution of the shock tube problem for solid materials. We show under what conditions a "physical" expansion shock can appear in this example. We then address the problem of modeling expanded states, and show results for a two-dimensional shock distraction around a sharp corner. In the last part of the paper, we introduce a detonation model that extends the Mie-Grüneisen equation of state to enable high explosive simulations without the complexity of mixture equations of state. We conclude with two examples of corner-turning computations carried out with a pressure-dependent reaction rate law.