A survey on isothermal and isentropic Baer-Nunziato-type models

TL;DR

This survey comprehensively reviews mathematical properties, entropy conditions, and numerical algorithms for multi-component Baer-Nunziato-type models in isothermal and isentropic fluids, highlighting their theoretical foundations and practical applications.

Contribution

It provides a detailed analysis of the mathematical structure, entropy conditions, and relaxation algorithms for Baer-Nunziato models, including new insights into their hyperbolicity and symmetrization.

Findings

Models are hyperbolic and symmetrizable.

Entropy-entropy flux pairs are derived.

Numerical results compare different fluid models.

Abstract

Multi-component Baer-Nunziato-type models for isothermal and isentropic fluids are investigated. These 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 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 are presented that ensure the entropy inequality to hold. Instantaneous relaxation to equilibrium is investigated and appropriate algorithms are presented. Numerical results for the isothermal Baer-Nunziato model are compared to an isothermal Euler model and to an isothermal phase-field model.