Wave propagation in multicomponent flow models

Abstract

We consider systems of hyperbolic balance laws governing flows of an arbitrary number of components equipped with general equations of state. The components are assumed to be immiscible. We compare two such models: one in which thermal equilibrium is attained through a relaxation procedure, and a fully relaxed model in which equal temperatures are instantaneously imposed. We describe how the relaxation procedure may be made consistent with the second law of thermodynamics. Exact wave velocities for both models are obtained and compared. In particular, our formulation directly proves a general subcharacteristic condition: For an arbitrary number of components and thermodynamically stable equations of state, the mixture sonic velocity of the relaxed system can never exceed the sonic velocity of the relaxation system.