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

Gayaz Khakimzyanov 1 Denys Dutykh 2, * Zinaida Fedotova 1 Dimitrios Mitsotakis 3 Oleg Gusev 1 Nina Shokina 1 Arxiv Org / Hal
* Auteur correspondant
1 Institute of Computational Technologies
2 LAMA - Laboratoire de Mathématiques
3 Victoria University of Wellington
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.
Keywords : solitary waves shallow water equations nonlinear dispersive waves long wave approximation
Type de document :
Pré-publication, Document de travail
33 pages, 1 figure, 79 references. Published in Commun. Comput. Phys. Other author's papers can b.. 2017
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Contributeur : Denys Dutykh <>
Soumis le : mardi 1 mai 2018 - 12:02:28
Dernière modification le : dimanche 6 mai 2018 - 01:06:25

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  • HAL Id : hal-01547833, version 3
  • ARXIV : 1706.08815

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Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova, Dimitrios Mitsotakis, Oleg Gusev, et al.. Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space: Dispersive shallow water wave modelling. Part I. 33 pages, 1 figure, 79 references. Published in Commun. Comput. Phys. Other author's papers can b.. 2017. 〈hal-01547833v3〉

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