Shock Profiles for the Shallow-Water Exner Models

Shock Profiles for the Shallow-Water Exner Models

Year:    2015

Author:    C. Berthon, B. Boutin, R. Turpault

Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 3 : pp. 267–294

Abstract

This article is devoted to analyzing 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2013.m331

Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 3 : pp. 267–294

Published online:    2015-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    28

Keywords:   

Author Details

C. Berthon

B. Boutin

R. Turpault