Numerical Simulation on a Globally Flat Space

Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova, Oleg Gusev

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

In this chapter 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 nonlinear elliptic equation. Moreover, this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed (numerical) problem.

Original languageBritish English
Title of host publicationLecture Notes in Geosystems Mathematics and Computing
PublisherSpringer Nature
Pages45-134
Number of pages90
DOIs
StatePublished - 2020

Publication series

NameLecture Notes in Geosystems Mathematics and Computing
ISSN (Electronic)2512-3211

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