{"title":"Shock profiles for the Shallow-water Exner models","authors":"C. Berthon, B. Boutin, R. Turpault","doi":"10.4208/AAMM.2013.M331","DOIUrl":null,"url":null,"abstract":"This article is devoted to analyze some ambiguities coming from a class of sediment transport models. The models under consideration are governed by the coupling between the shallow-water and the Exner equations. Since the PDE system turns out to be an hyperbolic system in non conservative form, ambiguities may occur as soon as the solution contains shock waves. To enforce a unique definition of the discontinuous solutions, we adopt the path-theory introduced by Dal Maso, LeFLoch and Murat. According to the path choices, we exhibit several shock definitions and we prove that a shock with a constant propagation speed and a given left state may connect an arbitrary right state. As a consequence, additional assumptions (coming from physical considerations or other arguments) must be chosen to enforce a unique definition. Moreover, we show that numerical ambiguities may still exist even when such a choice is made.","PeriodicalId":56331,"journal":{"name":"Advances in Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2015-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4208/AAMM.2013.M331","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Mechanics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.4208/AAMM.2013.M331","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 8
Abstract
This article is devoted to analyze some ambiguities coming from a class of sediment transport models. The models under consideration are governed by the coupling between the shallow-water and the Exner equations. Since the PDE system turns out to be an hyperbolic system in non conservative form, ambiguities may occur as soon as the solution contains shock waves. To enforce a unique definition of the discontinuous solutions, we adopt the path-theory introduced by Dal Maso, LeFLoch and Murat. According to the path choices, we exhibit several shock definitions and we prove that a shock with a constant propagation speed and a given left state may connect an arbitrary right state. As a consequence, additional assumptions (coming from physical considerations or other arguments) must be chosen to enforce a unique definition. Moreover, we show that numerical ambiguities may still exist even when such a choice is made.
期刊介绍:
Advances in Applied Mechanics draws together recent significant advances in all areas of applied mechanics. Published since 1948, it aims to provide the highest quality, authoritative review articles on topics in the mechanical sciences. It is of primary interest to scientists and engineers working in the various branches of mechanics and is also valuable to those who apply the results of investigations in mechanics to areas such as aerospace, chemical, civil, environmental, mechanical and nuclear engineering.