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Volume 7, Issue 3
Shock Profiles for the Shallow-Water Exner Models

C. Berthon, B. Boutin & R. Turpault

Adv. Appl. Math. Mech., 7 (2015), pp. 267-294.

Published online: 2018-05

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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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@Article{AAMM-7-267, author = {Berthon , C.Boutin , B. and Turpault , R.}, title = {Shock Profiles for the Shallow-Water Exner Models}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {7}, number = {3}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m331}, url = {http://global-sci.org/intro/article_detail/aamm/12048.html} }
TY - JOUR T1 - Shock Profiles for the Shallow-Water Exner Models AU - Berthon , C. AU - Boutin , B. AU - Turpault , R. JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 267 EP - 294 PY - 2018 DA - 2018/05 SN - 7 DO - http://doi.org/10.4208/aamm.2013.m331 UR - https://global-sci.org/intro/article_detail/aamm/12048.html KW - AB -

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.

C. Berthon, B. Boutin & R. Turpault. (1970). Shock Profiles for the Shallow-Water Exner Models. Advances in Applied Mathematics and Mechanics. 7 (3). 267-294. doi:10.4208/aamm.2013.m331
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