Communications in Mathematical Sciences

Volume 21 (2023)

Number 8

A non-equilibrium multi-component model with miscible conditions

Pages: 2195 – 2211



Jean Bussac (Laboratoire de Mathématiques Jean Leray, Nantes Université, Nantes, France)


This paper concerns the study of a full non-equilibrium model for a compressible mixture of any number of phases. Miscible conditions are considered in one phase, which lead to non-symmetric constraints on the statistical fractions. These models are subject to the choice of interfacial and source terms. We show that under a standard assumption on the interfacial velocity, the interfacial pressures are uniquely defined. The model is hyperbolic and symmetrizable under nonresonance conditions. Classes of entropy-consistent source terms are then proposed.


multiphase flows, Baer–Nunziato, nonconservative, closure laws

2010 Mathematics Subject Classification

35L60, 35L65, 76T30

Received 17 June 2022

Accepted 6 February 2023

Published 15 November 2023