Abstract
In this paper we review the history and current state-of-the-art in 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.
Original language | British English |
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Pages (from-to) | 1-29 |
Number of pages | 29 |
Journal | Communications in Computational Physics |
Volume | 23 |
Issue number | 1 |
DOIs | |
State | Published - 2018 |
Keywords
- Long wave approximation
- Nonlinear dispersive waves
- Shallow water equations
- Solitary waves