A note on the relaxation process in a class of non-equilibrium two-phase flow models

We focus here on the relaxation process in a class of two-phase flow models, considering first gas-liquid flows, and then liquid-vapour mixtures. The whole analysis enables to exhibit a few conditions on the flow in order to guarantee the time decay of some variables. The former may depend on initial conditions but also on equations of state within each phase. The present analysis aims at providing some better understanding of inner processes, and it is also useful for numerical purposes, as emphasized in appendix B. It is a sequel of paper [J.M. Hérard and G. Jomée, ESAIM Proc. Surv., 72:19–40, 2023] where the sole pressure relaxation process in some multiphase flow models is investigated.

Keywords

entropy, relaxation, two-phase flows, liquid-gas models, liquid-vapour mixture

2010 Mathematics Subject Classification

35L60, 35Q35, 76L05, 76T10

Full Text (PDF format)

Received 13 May 2023

Received revised 16 November 2023

Accepted 22 December 2023

Published 18 July 2024