{"title":"A note on the relaxation process in a class of non-equilibrium two-phase flow models","authors":"Jean-Marc Hérard","doi":"10.4310/cms.2024.v22.n6.a2","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"31 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cms.2024.v22.n6.a2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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.
在此，我们重点研究一类两相流模型的弛豫过程，首先考虑气-液流动，然后考虑液-汽混合物。通过整个分析，我们可以对流动提出一些条件，以保证某些变量的时间衰减。前者可能取决于初始条件，但也取决于各相内的状态方程。正如附录 B 所强调的，本分析旨在提供对内在过程的更好理解，同时也有助于数值计算。这是论文[J.M. Hérard 和 G. Jomée，ESAIM Proc. Surv.，72:19-40，2023]的续篇，其中研究了一些多相流模型中的唯一压力松弛过程。
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Covers modern applied mathematics in the fields of modeling, applied and stochastic analyses and numerical computations—on problems that arise in physical, biological, engineering, and financial applications. The journal publishes high-quality, original research articles, reviews, and expository papers.
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