BERTHON, Christophe; BOUTIN, Benjamin; TURPAULT, Rodolphe

doi:10.4208/aamm.2013.m331

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BERTHON, Christophe
Laboratoire de Mathématiques Jean Leray [LMJL]

BOUTIN, Benjamin
Institut de Recherche Mathématique de Rennes [IRMAR]

TURPAULT, Rodolphe
Institut de Mathématiques de Bordeaux [IMB]

Langue

Article de revue

Ce document a été publié dans

Advances in Applied Mechanics. 2015-06, vol. 7, n° 3, p. 267-294

New York ; London ; Paris [etc] : Academic Press

Résumé en anglais

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.< Réduire

Mots clés en anglais

Non-conservative products

Shallaow water equations

Exner equation

Shock Profile

Finite volumes

URI

https://oskar-bordeaux.fr/handle/20.500.12278/194317

DOI

http://dx.doi.org/10.4208/aamm.2013.m331

Project ANR

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

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251