Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws
and Well-Balanced Schemes for Sources
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Beschreibung
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 casse of sources, the general notions of consistency, order of accuracy and well-balancing are developed, and applied to the construction of effective schemes.
The schemes are analyzed regarding their nonlinear stability Recently developed entropy schemes are presented A formalism is introduced for source terms
Autor*in
François Bouchut
Themen in »Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws«
Conservation laws Hyperbolic systems Kinetic solvers Partial differential equations CFL condition differential equation dynamics inequality numerical analysis partial differential equation
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From the reviews:
“This is a very interesting and useful book which provides a systematic presentation of the theory of finite volume methods and numerical simulations for hyperbolic systems of conservation laws. The author provides a unified approach and notation to the study of nonlinear stability of finite volume methods for hyperbolic systems of conservation laws as the accent is put on the development of tools and design of schemes. The exposition of the book is very clear. It will be a very useful tool for the researchers in this field as well as for engineers.”(ZENTRALBLATT MATH)
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