Shock profiles for the Shallow-water Exner models
Language
en
Article de revue
This item was published in
Advances in Applied Mechanics. 2015-06, vol. 7, n° 3, p. 267-294
New York ; London ; Paris [etc] : Academic Press
English 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 ...Read more >
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.Read less <
English Keywords
Non-conservative products
Shallaow water equations
Exner equation
Shock Profile
Finite volumes
ANR Project
Nouveaux schémas numériques pour des phénomènes géophysiques extrêmes - ANR-12-IS01-0004
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
Origin
Hal imported