The Riemann Problem for Reversible Reactive Flows with Metastability

Abstract

A hyperbolic model for dynamic phase transitions is studied. The model involves three phases: liquid, vapor, and a mixture of them. Metastable regions are present both in the liquid and in the vapor phase. Results on the behavior of traveling wave profiles of the model, involving viscosity, species diffusion and relaxation, are obtained. These behaviors are consistent with physical intuitions. Admissibility criteria (kinetic relations) that mimic the behavior of traveling wave profiles are then proposed. Admissible basic waves of the model are liquefaction, evaporation, and isobaric waves, in addition to Lax shock and rarefaction waves. Based on these waves, solutions of the Riemann problem for the model are constructed for general Riemann initial data. Most of the physical phenomena are embodied in the solver. For some Riemann initial data solutions are expected to be nonunique. Which solutions actually appear depends on whether nucleation already occurred or not. The model admits both solutions, as it should. The model also has two other types of waves, collapsing and explosion waves. More complicated solutions involving these two waves are also proposed and discussed.