A new finite volume method for flux-gradient and source-term balancing in shallow water equations |
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| Authors: | Fayssal Benkhaldoun Imad Elmahi Mohammed Seaïd |
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| Affiliation: | 1. LAGA, Université Paris 13, 99 Av. J.B. Clement, 93430 Villetaneuse, France;2. ENSAO Complex Universitaire, B.P. 669, 60000 Oujda, Morocco;3. School of Engineering and Computing Sciences, University of Durham, South Road, Durham DH1 3LE, UK;1. Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United States;2. Department of Mathematics, University of Tennessee, Knoxville, TN 37996, United States;1. CNR-ISMAR, Institute of Marine Sciences -National Research Council, Castello 2737/f, 30122, Venice, Italy;2. INRH Institut National de Recherche Halieutique, Tanger, Morocco;3. INRH Institut National de Recherche Halieutique, Casablanca, Morocco;4. Marine Research Institute, Klaip?da University, H. Manto 84, 92294, Klaip?da, Lithuania;5. University of Bologna, Department of Physics and Astronomy, Italy;6. Foundation Centro EuroMediterraneo sui Cambiamenti Climatici, Bologna, Italy;1. Université Paris-Est, Laboratory for Hydraulics Saint-Venant, ENPC, EDF R&D, CETMEF, 78400 Chatou, France;2. Indian Institute of Technology Mandi, Mandi 175 001, India;3. Research Institute for Knowledge Systems, P.O. Box 463, 6200 AL Maastricht, The Netherlands;1. Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, Swansea SA1 8EN, Wales, UK;2. Laboratori de Càlcul Numèric (LaCàN), ETS de Ingenieros de Caminos, Canales y Puertos, Universitat Politècnica de Catalunya, Barcelona, Spain |
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| Abstract: | We present a new finite volume method for flux-gradient and source-term balancing in the numerical solution of shallow water equations on nonflat topography. The method consists of a predictor stage for discretization of gradient terms and a corrector stage for treatment of source terms. The numerical fluxes at the interfaces of each triangle are reconstructed using an upwind scheme along with slope limiters to obtain high accuracy in the method. Using a three-sided decomposition, the source terms are balanced in the corrector stage. The proposed method is implemented on unstructured meshes and verifies the exact conservation property (C-property). We also discuss a mesh adaptive procedure by monitoring the water depth in the computational domain. Several standard test examples are used to verify high accuracy, exact C-property and good resolution properties for smooth and discontinuous solutions. |
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