Shock profiles for the Shallow-water Exner models

1区 工程技术 Q1 Engineering Advances in Applied Mechanics Pub Date : 2015-06-01 DOI:10.4208/AAMM.2013.M331
C. Berthon, B. Boutin, R. Turpault
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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.
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浅水Exner模型的激波剖面
本文分析了一类泥沙输运模型的一些不明确之处。所考虑的模型是由浅水和Exner方程之间的耦合控制的。由于PDE系统是一个非保守形式的双曲系统,一旦解中包含激波,就可能产生歧义。为了加强不连续解的唯一定义,我们采用了Dal Maso, LeFLoch和Murat引入的路径理论。根据路径选择,我们给出了几种激波的定义,并证明了具有恒定传播速度和给定左状态的激波可以连接任意的右状态。因此,必须选择额外的假设(来自物理考虑或其他参数)来强制执行唯一的定义。此外,我们表明,即使做出这样的选择,数字歧义可能仍然存在。
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来源期刊
Advances in Applied Mechanics
Advances in Applied Mechanics 工程技术-工程:机械
CiteScore
23.30
自引率
0.00%
发文量
4
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.
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