Mathematical analysis of a two-phase continuum mixture theory

Abstract

In this paper, we study the mathematical structure of a continuum reactive mixture model of the combustion of granular energetic materials. We obtain and classify the wave fields associated with this description. This analysis shows that this system of hyperbolic equations becomes degenerate when the relative flow is locally sonic. We derive the corresponding Riemann invariants and construct simple wave solutions. We also discuss special discontinuous solutions of the system of equations. For fixed upstream conditions, different downstream states are possible when the relative velocities exceed the speed of the sound gas.