Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space
Fluid Dynamics
2020-02-20 v4 Analysis of PDEs
Classical Physics
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
Cite
@article{arxiv.1706.08815,
title = {Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space},
author = {Gayaz Khakimzyanov and Denys Dutykh and Zinaida Fedotova and Dimitrios Mitsotakis},
journal= {arXiv preprint arXiv:1706.08815},
year = {2020}
}
Comments
33 pages, 1 figure, 79 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/