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Mathematical Development and Verification of a Finite Volume Model for Morphodynamic Flow Applications

Published online by Cambridge University Press:  03 June 2015

Fayssal Benkhaldoun ,
Mohammed Seaïd  and
Slah Sahmim
Fayssal Benkhaldoun*
Affiliation:
LAGA, Université Paris 13, 99 Av J.B. Clement, 93430 Villetaneuse, France
Mohammed Seaïd*
Affiliation:
School of Engineering and Computing Sciences, University of Durham, South Road, Durham DH1 3LE, UK
Slah Sahmim*
Affiliation:
Laboratoire D’ingénierie Mathématique, Ecole Polytechnique de Tunisie, B.P. 743-2078 La Marsa, Tunisia
*
Corresponding author. URL: http://www.math.univ-paris13.fr/∼fayssal/ Email: fayssal@math.univ-paris13.fr
Email: m.seaid@durham.ac.uk
Email: s.sahmim@gmail.com
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Abstract

The accuracy and efficiency of a class of finite volume methods are investigated for numerical solution of morphodynamic problems in one space dimension. The governing equations consist of two components, namely a hydraulic part described by the shallow water equations and a sediment part described by the Exner equation. Based on different formulations of the morphodynamic equations, we propose a family of three finite volume methods. The numerical fluxes are reconstructed using a modified Roe’s scheme that incorporates, in its reconstruction, the sign of the Jacobian matrix in the morphodynamic system. A well-balanced discretization is used for the treatment of the source terms. The method is well-balanced, non-oscillatory and suitable for both slow and rapid interactions between hydraulic flow and sediment transport. The obtained results for several morphodynamic problems are considered to be representative, and might be helpful for a fair rating of finite volume solution schemes, particularly in long time computations.

Keywords

65M0876B1576M12Morphodynamic modelshallow water equationssediment transportfinite volume methodwell-balanced discretization
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 4 , August 2011 , pp. 470 - 492
Copyright
Copyright © Global-Science Press 2011

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