Baer-Nunziato type models for isothermal and isentropic flows

¹ Institute for Mathematics, Martin-Luther-Universität Halle-Wittenberg, Halle (Saale), D-06099, Germany
² Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, Aachen, D-52056, Germany
³ Division of Mathematics, Universität Köln, Weyertal 86 – 90, Köln, D-50931, Germany
⁴ Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55128 Mainz, Germany

Abstract

Multi-component Baer-Nunziato-type models for isothermal and isentropic flows are investigated where each component is characterized by an equation of state for the pressure assuming constant temperature and entropy, respectively. These models are given by balance equations for volume fractions, density and momentum for each component accounting for the relaxation to equilibrium by means of relaxation terms. Mathematical properties of the models are derived for the larger class of barotropic flows such as hyperbolicity and symmetrization. The fields are characterized and corresponding Riemann invariants are determined. Appropriate entropy-entropy flux pairs are derived taking into account the phasic energy equations including the heat flux. Physically meaningful constraints on the interfacial velocity and the interfacial pressures are presented that ensure the entropy inequality to hold.