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A non-homogeneous Riemann solver for shallow water equations in porous media

Benkhaldoun, F.; Elmahi, I.; Moumna, A.; Seaid, M.

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Authors

F. Benkhaldoun

I. Elmahi

A. Moumna



Abstract

The purpose of the current research is to develop an accurate and efficient solver for shallow water flows in porous media. The hydraulics is modeled by the two-dimensional shallow water flows with variable horizontal porosity. The variation of porosity in the water flows can be attributed to the variation of bed properties of the water system. As an example of porous shallow water flows is the passage of water discharge over vegetated areas in a river. Driving force of the phase separation and the mixing is the gradient of the porosity. For the numerical solution procedure, we propose a non-homogeneous Riemann solver in the finite volume framework. The proposed method consists of a predictor stage for the discretization of gradient terms and a corrector stage for the treatment of source terms. The gradient fluxes are discretized using a modified Roe’s scheme using the sign of the Jacobian matrix in the coupled system. A well-balanced discretization is used for the treatment of source terms. The efficiency of the solver is evaluated by several test problems for shallow water flows in porous media. The numerical results demonstrate high resolution of the proposed non-homogeneous Riemann solver and confirm its capability to provide accurate simulations for porous shallow water equations under flow regimes with strong shocks.

Citation

Benkhaldoun, F., Elmahi, I., Moumna, A., & Seaid, M. (2016). A non-homogeneous Riemann solver for shallow water equations in porous media. Applicable Analysis, 95(10), 2181-2202. https://doi.org/10.1080/00036811.2015.1067304

Journal Article Type Article
Acceptance Date Jun 25, 2015
Online Publication Date Jul 24, 2015
Publication Date Oct 1, 2016
Deposit Date Nov 30, 2015
Publicly Available Date Mar 28, 2024
Journal Applicable Analysis
Print ISSN 0003-6811
Electronic ISSN 1563-504X
Publisher Taylor and Francis Group
Peer Reviewed Peer Reviewed
Volume 95
Issue 10
Pages 2181-2202
DOI https://doi.org/10.1080/00036811.2015.1067304
Keywords Shallow water equations, Porous media, Finite volume method, Unstructured grids, Riemann solver, 76S99, 35L65, 65M08.

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