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Numerical Methods for Shallow-Water Flow

  • Book
  • © 1994

Overview

Authors:
  1. C. B. Vreugdenhil

    1. Institute for Marine and Atmospheric Research Utrecht (IMAU), Utrecht University, Utrecht, The Netherlands

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Part of the book series: Water Science and Technology Library (WSTL, volume 13)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-x
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  2. Shallow-water flows

    • C. B. Vreugdenhil
    Pages 1-14

  3. Equations

    • C. B. Vreugdenhil
    Pages 15-46

  4. Some properties

    • C. B. Vreugdenhil
    Pages 47-55

  5. Behaviour of solutions

    • C. B. Vreugdenhil
    Pages 56-72

  6. Boundary conditions

    • C. B. Vreugdenhil
    Pages 73-88

  7. Discretization in space

    • C. B. Vreugdenhil
    Pages 89-116

  8. Effects of space discretization on wave propagation

    • C. B. Vreugdenhil
    Pages 117-138

  9. Time integration methods

    • C. B. Vreugdenhil
    Pages 139-167

  10. Effects of time discretization on wave propagation

    • C. B. Vreugdenhil
    Pages 168-195

  11. Numerical treatment of boundary conditions

    • C. B. Vreugdenhil
    Pages 196-216

  12. Three-dimensional shallow-water flow

    • C. B. Vreugdenhil
    Pages 217-246

  13. Back Matter

    Pages 247-262
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Keywords

About this book

A wide variety of problems are associated with the flow of shallow water, such as atmospheric flows, tides, storm surges, river and coastal flows, lake flows, tsunamis. Numerical simulation is an effective tool in solving them and a great variety of numerical methods are available. The first part of the book summarizes the basic physics of shallow-water flow needed to use numerical methods under various conditions. The second part gives an overview of possible numerical methods, together with their stability and accuracy properties as well as with an assessment of their performance under various conditions. This enables the reader to select a method for particular applications. Correct treatment of boundary conditions (often neglected) is emphasized. The major part of the book is about two-dimensional shallow-water equations but a discussion of the 3-D form is included.
The book is intended for researchers and users of shallow-water models in oceanographic and meteorological institutes, hydraulic engineering and consulting. It also provides a major source of information for applied and numerical mathematicians.

Authors and Affiliations

  • Institute for Marine and Atmospheric Research Utrecht (IMAU), Utrecht University, Utrecht, The Netherlands

    C. B. Vreugdenhil

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