{"title":"Entropy-stable in- and outflow boundary conditions for the compressible Euler equations","authors":"","doi":"10.1016/j.jcp.2024.113543","DOIUrl":null,"url":null,"abstract":"<div><div>We propose general inflow and outflow boundary conditions for the Euler equations and prove that they are both linearly well-posed and lead to entropy-bounded solutions. Furthermore, we provide numerical boundary fluxes that enforce these boundary conditions and prove entropy stability for (entropy-stable) finite-volume schemes. The method is generalisable to most entropy-stable summation-by-parts schemes. Finally, we demonstrate their performance in various flow regimes using a second-order accurate entropy-stable finite-volume scheme.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":null,"pages":null},"PeriodicalIF":3.8000,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021999124007915","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
We propose general inflow and outflow boundary conditions for the Euler equations and prove that they are both linearly well-posed and lead to entropy-bounded solutions. Furthermore, we provide numerical boundary fluxes that enforce these boundary conditions and prove entropy stability for (entropy-stable) finite-volume schemes. The method is generalisable to most entropy-stable summation-by-parts schemes. Finally, we demonstrate their performance in various flow regimes using a second-order accurate entropy-stable finite-volume scheme.
期刊介绍：
Journal of Computational Physics thoroughly treats the computational aspects of physical problems, presenting techniques for the numerical solution of mathematical equations arising in all areas of physics. The journal seeks to emphasize methods that cross disciplinary boundaries.
The Journal of Computational Physics also publishes short notes of 4 pages or less (including figures, tables, and references but excluding title pages). Letters to the Editor commenting on articles already published in this Journal will also be considered. Neither notes nor letters should have an abstract.
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