Mathematical Development and Verification of a Finite Volume Model for Morphodynamic Flow Applications
Year: 2011
Author: Fayssal Benkhaldoun, Mohammed Seaid, Slah Sahmim
Advances in Applied Mathematics and Mechanics, Vol. 3 (2011), Iss. 4 : pp. 470–492
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.10-m1056
Advances in Applied Mathematics and Mechanics, Vol. 3 (2011), Iss. 4 : pp. 470–492
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Morphodynamic model shallow water equations sediment transport finite volume method well-balanced discretization.