A Hierarchy of Non-Equilibrium Two-Phase Flow Models

TL;DR

This paper develops a hierarchy of non-equilibrium two-phase flow models derived from the Baer-Nunziato framework, analyzing their stability via the subcharacteristic condition and providing explicit sound speed formulas.

Contribution

It extends previous relaxation models to two-fluid systems with separate velocities, ensuring the subcharacteristic condition holds across the hierarchy under fundamental assumptions.

Findings

Subcharacteristic condition is satisfied throughout the hierarchy.

Explicit formulas for sound speeds are derived.

Models are extended to include two-fluid velocities.

Abstract

We consider a hierarchy of relaxation models for two-phase flow. The models are derived from the non-equilibrium Baer-Nunziato model, which is endowed with relaxation source terms to drive it towards equilibrium. The source terms cause transfer of volume, heat, mass and momentum due to differences between the phases in pressure, temperature, chemical potential and velocity, respectively. The subcharacteristic condition is closely linked to the stability of such relaxation systems, and in the context of two-phase flow models, it implies that the sound speed of an equilibrium system can never exceed that of the relaxation system. Here, previous work by Fl{\aa}tten and Lund [Math. Models Methods Appl. Sci., 21 (12), 2011, 2379--2407] and Lund [SIAM J. Appl. Math. 72, 2012, 1713--1741] is extended to encompass two-fluid models, i.e. models with separately governed velocities for the two phases. Each remaining model in the hierarchy is derived, and analytical expressions for the sound speeds are presented. Given only physically fundamental assumptions, the subcharacteristic condition is shown to be satisfied in the entire hierarchy, either in a weak or in a strong sense.