Numerical Methods for Shallow-Water Flow

✍ Scribed by C. B. Vreugdenhil (auth.)

• Publisher: Springer Netherlands
• Year: 1994
• Tongue: English
• Leaves: 272
• Series: Water Science and Technology Library 13
• Edition: 1
• Category: Library

✦ Synopsis

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

Front Matter....Pages i-x
Shallow-water flows....Pages 1-14
Equations....Pages 15-46
Some properties....Pages 47-55
Behaviour of solutions....Pages 56-72
Boundary conditions....Pages 73-88
Discretization in space....Pages 89-116
Effects of space discretization on wave propagation....Pages 117-138
Time integration methods....Pages 139-167
Effects of time discretization on wave propagation....Pages 168-195
Numerical treatment of boundary conditions....Pages 196-216
Three-dimensional shallow-water flow....Pages 217-246
Back Matter....Pages 247-262

✦ Subjects

Hydrogeology; Condensed Matter Physics; Oceanography; Geoengineering, Foundations, Hydraulics; Computational Mathematics and Numerical Analysis; Meteorology/Climatology