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Birkhäuser

Dispersive Shallow Water Waves

Theory, Modeling, and Numerical Methods

  • Book
  • © 2020

Overview

Authors:
  1. Gayaz Khakimzyanov

    1. Institute of Computational Technologies of the Siberian Branch of the Russian, Academy of Sciences, Novosibirsk, Russia

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  2. Denys Dutykh

    1. CNRS - LAMA UMR 5127, Department of Mathematics, University Savoie Mont Blanc, Campus Scientifique, Le Bourget-du-Lac, France

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  3. Zinaida Fedotova

    1. Institute of Computational Technologies of the Siberian Branch of the Russian, Academy of Sciences, Novosibirsk, Russia

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  4. Oleg Gusev

    1. Institute of Computational Technologies of the Siberian Branch of the Russian, Academy of Sciences, Novosibirsk, Russia

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  • Presents cutting-edge research on dispersive wave modelling, and the numerical methods used to simulate the propagation and generation of long surface water waves
  • Demonstrates state-of-the-art, adaptive techniques for modelling real-world natural phenomena, such as tsunami waves, and smaller scale coastal processes
  • Collects and expands upon the authors’ own research, while providing an overview on existing dispersive models

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xx
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  2. Model Derivation on a Globally Flat Space

    • Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova, Oleg Gusev
    Pages 1-43

  3. Numerical Simulation on a Globally Flat Space

    • Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova, Oleg Gusev
    Pages 45-134

  4. Model Derivation on a Globally Spherical Geometry

    • Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova, Oleg Gusev
    Pages 135-190

  5. Numerical Simulation on a Globally Spherical Geometry

    • Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova, Oleg Gusev
    Pages 191-237

  6. Back Matter

    Pages 239-284
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Keywords

About this book

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.


Authors and Affiliations

  • Institute of Computational Technologies of the Siberian Branch of the Russian, Academy of Sciences, Novosibirsk, Russia

    Gayaz Khakimzyanov, Zinaida Fedotova, Oleg Gusev

  • CNRS - LAMA UMR 5127, Department of Mathematics, University Savoie Mont Blanc, Campus Scientifique, Le Bourget-du-Lac, France

    Denys Dutykh

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