Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources

✍ Scribed by François Bouchut

• Publisher: Birkauser
• Year: 2004
• Tongue: English
• Leaves: 143
• Series: Frontiers in mathematics
• Edition: 1
• Category: Library

✦ Synopsis

This book is devoted to finite volume methods for hyperbolic systems of conservation laws. The accent is put on the development of tools for analyzing the nonlinear stability of Godunov schemes. Starting from theoretical considerations, the schemes are derived until a very practical level, meeting some required features such as for example the treatment of vacuum in gas dynamics. In the case of sources, the general notions of consistency, order of accuracy and well-balancing are developed, and applied to the construction of effective schemes.

✦ Table of Contents

front-matter......Page 1
1Quasilinear systems and conservation laws......Page 9
2Conservative schemes......Page 21
3Source terms......Page 73
4Nonconservative schemes......Page 77
5Multidimensional finite volumes with sources......Page 115
6Numerical tests with source......Page 125
back-matter......Page 135