Close Search Advanced
Journals
Resources
About Us
Open Access

Shock Profiles for the Shallow-Water Exner Models

Shock Profiles for the Shallow-Water Exner Models
Preview
Add to basket

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.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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

  1. The use of proper orthogonal decomposition (POD) meshless RBF-FD technique to simulate the shallow water equations

    Dehghan, Mehdi | Abbaszadeh, Mostafa

    Journal of Computational Physics, Vol. 351 (2017), Iss. P.478

    https://doi.org/10.1016/j.jcp.2017.09.007 [Citations: 69]

  2. Artificial Viscosity to Get Both Robustness and Discrete Entropy Inequalities

    Berthon, Christophe | Castro Díaz, Manuel J. | Duran, Arnaud | Morales de Luna, Tomás | Saleh, Khaled

    Journal of Scientific Computing, Vol. 97 (2023), Iss. 3

    https://doi.org/10.1007/s10915-023-02385-1 [Citations: 0]

  3. Sediment minimization in canals: An optimal control approach

    Alvarez-Vázquez, L.J. | Martínez, A. | Rodríguez, C. | Vázquez-Méndez, M.E.

    Mathematics and Computers in Simulation, Vol. 149 (2018), Iss. P.109

    https://doi.org/10.1016/j.matcom.2018.02.007 [Citations: 5]

  4. Schemes with Well-Controlled Dissipation. Hyperbolic Systems in Nonconservative Form

    Beljadid, Abdelaziz | LeFloch, Philippe G. | Mishra, Siddhartha | Parés, Carlos

    Communications in Computational Physics, Vol. 21 (2017), Iss. 4 P.913

    https://doi.org/10.4208/cicp.OA-2016-0019 [Citations: 12]

  5. Well balancing of the SWE schemes for moving-water steady flows

    Caleffi, Valerio | Valiani, Alessandro

    Journal of Computational Physics, Vol. 342 (2017), Iss. P.85

    https://doi.org/10.1016/j.jcp.2017.04.031 [Citations: 13]

  6. A comparison between bottom-discontinuity numerical treatments in the DG framework

    Caleffi, Valerio | Valiani, Alessandro | Li, Gang

    Applied Mathematical Modelling, Vol. 40 (2016), Iss. 17-18 P.7516

    https://doi.org/10.1016/j.apm.2015.09.025 [Citations: 14]

  7. Mathematical Analysis and Numerical Simulation of Hyperbolic Sediment Transport Models (Hstm)

    Ngatcha Ndengna, Arno Roland

    SSRN Electronic Journal , Vol. (2022), Iss.

    https://doi.org/10.2139/ssrn.4184204 [Citations: 0]