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Numerical Methods for Shallow-Water Flow: Water Science and Technology Library, Vol 13

C. B. Vreugdenhil

Numerical methods for shallow water flows, including atmospheric flows, tides, storm surges, river and coastal flows, lake flows, and tsunamis.

Format: Hardcover, English, 276 pages
ISBN: 0792331648
Publisher: Kluwer Academic Publishers
Pub. Date: 1994

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Publisher Comments

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.


Table of Contents

  Preface  
  Acknowledgements  
1 Shallow-water flows 1
2 Equations 15
3 Some properties 47
4 Behaviour of solutions 56
5 Boundary conditions 73
6 Discretization in space 89
7 Effects of space discretization on wave propagation 117
8 Time integration methods 139
9 Effect of time discretization on wave propagation 168
10 Numerical treatment of boundary conditions 196
11 Three-dimensional shallow-water flow 217
  List of notation 247
  References 249

Related Book Categories

Free-Surface and Sub-Surface Flows, River and Coastal Engineering Applications, Environmental Applications


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