Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space

Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space

Year:    2018

Communications in Computational Physics, Vol. 23 (2018), Iss. 1 : pp. 30–92

Abstract

In this paper we describe a numerical method to solve numerically the weakly dispersive fully nonlinear SERRE–GREEN–NAGHDI (SGN) celebrated model. Namely, our scheme is based on reliable finite volume methods, proven to be very efficient for the hyperbolic part of equations. The particularity of our study is that we develop an adaptive numerical model using moving grids. Moreover, we use a special form of the SGN equations where non-hydrostatic part of pressure is found by solving a linear elliptic equation. Moreover, this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed (numerical) problem.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2016-0179b

Communications in Computational Physics, Vol. 23 (2018), Iss. 1 : pp. 30–92

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    63

Keywords:    Nonlinear dispersive waves non-hydrostatic pressure moving adaptive grids finite volumes conservative finite differences.

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