Analysis and Simulation of a New Multi-Component Two-Phase Flow Model with Phase Transitions and Chemical Reactions

Abstract

A class-II model for multi-component mixtures recently introduced in D. Bothe, W. Dreyer, Continuum thermodynamics of chemically reacting fluid mixtures, Acta Mech., 226 (2015), 1757–1805 is investigated for simple mixtures. Bothe and Dreyer were aiming at deriving physically admissible closure conditions. Here the focus is on mathematical properties of this model. In particular, hyperbolicity of the inviscid flux Jacobian is verified for non-resonance states. Although the eigenvalues cannot be determined explicitly but have to be computed numerically an eigenvector basis is constructed depending on the eigenvectors. This basis is helpful to apply standard numerical solvers for the discretization of the model. This is verified by numerical computations for two- and three-component mixtures with and without phase transition and chemical reactions.