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

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

• Publisher: Springer International Publishing;Birkhäuser
• Year: 2020
• Tongue: English
• Leaves: 296
• Series: Lecture Notes in Geosystems Mathematics and Computing
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xx
Model Derivation on a Globally Flat Space (Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova, Oleg Gusev)....Pages 1-43
Numerical Simulation on a Globally Flat Space (Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova, Oleg Gusev)....Pages 45-134
Model Derivation on a Globally Spherical Geometry (Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova, Oleg Gusev)....Pages 135-190
Numerical Simulation on a Globally Spherical Geometry (Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova, Oleg Gusev)....Pages 191-237
Back Matter ....Pages 239-284

✦ Subjects

Mathematics; Mathematical Modeling and Industrial Mathematics; Numerical Analysis; Oceanography