Dispersive Shallow Water Wave Modelling. Part I: Model Derivation on a Globally Flat Space (Communications in Computational Physics, 2018)
In this paper we review the history and current state-of-the-art in modellingof long nonlinear dispersive waves. For the sake of conciseness of this review weomit the unidirectional models and focus especially on some classical and improvedBOUSSINESQ-type and SERRE–GREEN–NAGHDI equations. Finally, we propose also aunified modelling framework which incorporates several well-known and some lessknown dispersive wave models. The present manuscript is the first part of a seriesof two papers. The second part will be devoted to the numerical discretization of apractically important model on moving adaptive grids.
Keywords: Long wave approximation; nonlinear dispersive waves; shallow water equations; solitary waves.