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Shock Profiles for the Shallow-Water Exner Models

Published online by Cambridge University Press:  28 May 2015

C. Berthon ,
B. Boutin  and
R. Turpault
C. Berthon
Affiliation:
Université de Nantes, Laboratoire de Mathématiques Jean Leray, 2 rue de la Houssinière 44322 Nantes, France
B. Boutin
Affiliation:
Université de Rennes 1, Institut de Recherche Mathématiques de Rennes, Rennes, France
R. Turpault*
Affiliation:
Université de Nantes, Laboratoire de Mathématiques Jean Leray, 2 rue de la Houssinière 44322 Nantes, France Bordeaux-INP, Institut de Mathématiques de Bordeaux, 351 Cours de la Libération 33400 Talence, France
*
*Corresponding author. Email: rodolphe.turpault@univ-nantes.fr (R. Turpault)
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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 [18]. 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 a path is chosen to select the system's solution.

Keywords

35L6776N9965M08Exner modelsnonconservative hyperbolic systemsshock wave solutionsgeneralized Rankine-Hugoniot relationshugoniot curvesdam-break simulations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 3 , June 2015 , pp. 267 - 294
Copyright
Copyright © Global-Science Press 2015 

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