Aïssiouene, Nora; Bristeau, Marie-Odile; Godlewski, Edwige; Mangeney, Anne; Parés, Carlos; Sainte-Marie, Jacques Application of a combined finite element – finite volume method to a 2D non-hydrostatic shallow water problem. (English) Zbl 1366.76046 Cancès, Clément (ed.) et al., Finite volumes for complex applications VIII – hyperbolic, elliptic and parabolic problems. FVCA 8, Lille, France, June 12–16, 2017. Cham: Springer (ISBN 978-3-319-57393-9/hbk; 978-3-319-57394-6/ebook; 978-3-319-58818-6/set). Springer Proceedings in Mathematics & Statistics 200, 219-226 (2017). Summary: We propose a numerical method for a two-dimensional non-hydrostatic shallow water system with topography [the second author et al., Discrete Contin. Dyn. Syst., Ser. B 20, No. 4, 961–988 (2015; Zbl 1307.35162)]. We use a prediction-correction scheme initially introduced by Chorin-Temam [R. Rannacher, Lect. Notes Math. 1530, 167–183 (1992; Zbl 0769.76053)], and which has been applied previously to the one dimensional problem in [the first author, Numerical analysis and discrete approximation of a dispersive shallow water model. Paris: Université Pierre et Marie Curie (Thesis) (2016)]. The prediction part leads to solving a shallow water system for which we use finite volume methods [E. Audusse and the second author, J. Comput. Phys. 206, No. 1, 311–333 (2005; Zbl 1087.76072)], while the correction part leads to solving a mixed problem in velocity/pressure using a finite element method. We present an application of the method with a comparison between a hydrostatic and a non-hydrostatic model.For the entire collection see [Zbl 1371.65001]. Cited in 6 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 76M12 Finite volume methods applied to problems in fluid mechanics Keywords:finite element; finite volume; dispersive wave; shallow water model; non-hydrostatic pressure Citations:Zbl 1307.35162; Zbl 0769.76053; Zbl 1087.76072 × Cite Format Result Cite Review PDF Full Text: DOI HAL References: [1] Aïssiouene, N.: Numerical analysis and discrete approximation of a dispersive shallow water model. Theses, Pierre et Marie Curie, Paris VI (2016). https://hal.archives-ouvertes.fr/tel-01418676 [2] Aïssiouene, N., Bristeau, M.O., Godlewski, E., Sainte-Marie, J.: A combined finite volume-finite element scheme for a dispersive shallow water system. Netw. Heterog. 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