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Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space

Abstract : In this paper, we review the history and current state-of-the-art in the modelling of long nonlinear dispersive waves. For the sake of conciseness of this review, we omit the unidirectional models and focus especially on some classical and improved Boussinesq-type and Serre-Green-Naghdi equations. Finally, we propose also a unified modelling framework which incorporates several well-known and some less known dispersive wave models. The present manuscript is the first part of a series of two papers. The second part will be devoted to the numerical discretization of a practically important model on moving adaptive grids.
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https://hal.archives-ouvertes.fr/hal-01547833
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Submitted on : Tuesday, May 1, 2018 - 12:02:28 PM
Last modification on : Wednesday, February 19, 2020 - 1:43:08 PM
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Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova, Dimitrios Mitsotakis. Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space. Communications in Computational Physics, Global Science Press, 2018, 23 (1), pp.1-29. ⟨10.4208/cicp.OA-2016-0179a⟩. ⟨hal-01547833v3⟩

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