2018
Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space
CCommun. Comput. Phys.
G. Khakimzyanov, D. Dutykh, Z. Fedotova and D. Mitsotakis
Commun. Comput. Phys. 23(1): 1-29 (2018)
Open Access
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
nonlinear dispersive wavesrotating geometrynumerical simulationsolitary wavesspherical geometryrotation effectstsunami modelingsphericity effectshyperbolic equationChilean tsunami 2010splitting approachshallow water equationsdispersive shallow water wavespredictor-corrector schemelong wave approximationelliptic equationBulgarian tsunami 2007
Bibliographic record
BibTeX Citation
@article{Khakimzyanov2018dispersiveshallow,
author = {Khakimzyanov, G. and Dutykh, D. and Fedotova, Z. and Mitsotakis, D.},
title = {Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space},
journal = {Commun. Comput. Phys.},
year = {2018},
volume = {23},
number = {1},
pages = {1--29},
doi = {10.4208/cicp.OA-2016-0179a},
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 = {nonlinear dispersive waves, rotating geometry, numerical simulation, solitary waves, spherical geometry, rotation effects, tsunami modeling, sphericity effects, hyperbolic equation, Chilean tsunami 2010, splitting approach, shallow water equations, dispersive shallow water waves, predictor-corrector scheme, long wave approximation, elliptic equation, Bulgarian tsunami 2007}
}