Dispersive Shallow Water Waves: Theory, Modeling, and Numerical Methods

by Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova, Oleg Gusev

Overview

This monograph presents cutting-edge research on dispersive wave modelling, and the numerical methods used to simulate the propagation and generation of long surface water waves. Including both an overview of existing dispersive models, as well as recent breakthroughs, the authors maintain an ideal balance between theory and applications. From modelling tsunami waves to smaller scale coastal processes, this book will be an indispensable resource for those looking to be brought up-to-date in this active area of scientific research.

Beginning with an introduction to various dispersive long wave models on the flat space, the authors establish a foundation on which readers can confidently approach more advanced mathematical models and numerical techniques. The first two chapters of the book cover modelling and numerical simulation over globally flat spaces, including adaptive moving grid methods along with the operator splitting approach, which was historically proposed at the Institute of Computational Technologies at Novosibirsk. Later chapters build on this to explore high-end mathematical modelling of the fluid flow over deformed and rotating spheres using the operator splitting approach. The appendices that follow further elaborate by providing valuable insight into long wave models based on the potential flow assumption, and modified intermediate weakly nonlinear weakly dispersive equations.

Dispersive Shallow Water Waves will be a valuable resource for researchers studying theoretical or applied oceanography, nonlinear waves as well as those more broadly interested in free surface flow dynamics.

Product Details

ISBN-13:	9783030462666
Publisher:	Springer International Publishing
Publication date:	09/16/2020
Series:	Lecture Notes in Geosystems Mathematics and Computing
Edition description:	1st ed. 2020
Pages:	284
Product dimensions:	6.10(w) x 9.25(h) x 0.00(d)

Table of Contents

Model Derivation on a Globally Flat Space.- Numerical Simulation on a Globally Flat Space.- Model Derivation on a Globally Spherical Geometry.- Numerical Simulation on a Globally Spherical Geometry.