{"title":"气体动力学欧拉{e}方程的强非线性边界条件","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":"{\"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}","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}
Conditions aux limites fortement non lin{é}aires pour les {é}quations d'Euler de la dynamique des gaz
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.