{"title":"Conditions aux limites fortement non lin{é}aires pour les {é}quations d'Euler de la dynamique des gaz","authors":"François DuboisLMO, LMSSC","doi":"arxiv-2409.11774","DOIUrl":null,"url":null,"abstract":"We study various formulations of the boundary conditions for the Euler\nequations of gas dynamics from a mathematical and numerical point of view. In\nthe case of one space dimension, we recall the classical results, based on an\nanalysis of the linearized problem. Then we present a more recent formulation\nof the problem, which allows for nonlinear effects at the boundary of the study\ndomain. This formulation fits naturally into a finite volume discretization,\nand we present a significant one-dimensional test case.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11774","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We study various formulations of the boundary conditions for the Euler
equations of gas dynamics from a mathematical and numerical point of view. In
the case of one space dimension, we recall the classical results, based on an
analysis of the linearized problem. Then we present a more recent formulation
of the problem, which allows for nonlinear effects at the boundary of the study
domain. This formulation fits naturally into a finite volume discretization,
and we present a significant one-dimensional test case.
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