Simulation of an Homogeneous Relaxation Model for a three-phase mixture with miscible phases

Jean Bussac (1) , Hélène Mathis (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

This paper addresses the numerical approximation of a compressible three-phase flow. The mixture is composed of a liquid, its vapor and an inert gas, with realistic equations of state. Since the liquid is immiscible and the gaseous phases are miscible, it yields constrictive volume and mass constraints. The fluid dynamics is depicted by a one-velocity hyperbolic system with relaxation terms toward the thermodynamical equilibrium of the mixture. The core of the paper is the comparison and the analysis of two possible choices of relaxation terms, accounting for a detailed analysis of mixture entropy and the associated thermodynamical equilibrium. As numerics are concerned, a fractional step approach is proposed, based on a finite volume approximation of the convective part. The complexity of the source term requires an implicit Broyden resolution. Numerical results allow to compare both the performance of the chosen numerical schemes and the impact of the source term choices.

Domaines: Equations aux dérivées partielles [math.AP]

Jean Bussac, Hélène Mathis. Simulation of an Homogeneous Relaxation Model for a three-phase mixture with miscible phases. 2022. ⟨hal-03566970v1⟩