Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws: and Well-Balanced Schemes for Sources

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.