Numerical Methods for Conservation Laws

ISBN-10: 3764327235

ISBN-13: 9783764327231

Edition: 2nd 1992 (Revised)

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Description: These notes were developed for a graduate-level course on the theory and numerical solution of nonlinear hyperbolic systems of conservation laws. Part I deals with the basic mathematical theory of the equations: the notion of weak solutions, entropy conditions, and a detailed description of the wave structure of solutions to the Riemann problem. The emphasis is on tools and techniques that are indispensable in developing good numerical methods for discontinuous solutions. Part II is devoted to the development of high resolution shock-capturing methods, including the theory of total variation diminishing (TVD) methods and the use of limiter functions. The book is intended for a wide audience, and will be of use both to numerical analysts and to computational researchers in a variety of applications.

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Book details

List price: $39.95
Edition: 2nd
Copyright year: 1992
Publisher: Springer
Publication date: 8/29/2008
Binding: Paperback
Pages: 220
Size: 6.75" wide x 9.50" long x 0.50" tall
Weight: 0.836
Language: English

Introduction
The Derivation of Conservation Laws
Scalar Conservation Laws
Some Scalar Examples
Some Nonlinear Systems
Linear Hyperbolic Systems
Shocks and the Hugoniot Locus
Rarefaction Waves and Integral Curves
The Riemann problem for the Euler equations
Numerical Methods for Linear Equations
Computing Discontinuous Solutions
Conservative Methods for Nonlinear Problems
Godunov's Method
Approximate Riemann Solvers
Nonlinear Stability
High Resolution Methods
Semi-discrete Methods
Multidimensional Problems
Bibliography
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