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

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

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: Jul 24, 2016
• 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.
• Public URL: https://durham-repository.worktribe.com/output/1417640