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

Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova, Dimitrios Mitsotakis

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

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 languageBritish English
Pages (from-to)1-29
Number of pages29
JournalCommunications in Computational Physics
Volume23
Issue number1
DOIs
StatePublished - 2018

Keywords

  • Long wave approximation
  • Nonlinear dispersive waves
  • Shallow water equations
  • Solitary waves

Fingerprint

Dive into the research topics of 'Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space'. Together they form a unique fingerprint.

Cite this