| Description |
1 online resource (214 pages) : illustrations |
| Series |
Lectures in mathematics ETH Zürich |
|
Lectures in mathematics ETH Zürich.
|
| Contents |
I Mathematical Theory -- 1 Introduction -- 2 The Derivation of Conservation Laws -- 3 Scalar Conservation Laws -- 4 Some Scalar Examples -- 5 Some Nonlinear Systems -- 6 Linear Hyperbolic Systems 58 -- 7 Shocks and the Hugoniot Locus -- 8 Rarefaction Waves and Integral Curves -- 9 The Riemann problem for the Euler equations -- II Numerical Methods -- 10 Numerical Methods for Linear Equations -- 11 Computing Discontinuous Solutions -- 12 Conservative Methods for Nonlinear Problems -- 13 Godunov's Method -- 14 Approximate Riemann Solvers -- 15 Nonlinear Stability -- 16 High Resolution Methods -- 17 Semi-discrete Methods -- 18 Multidimensional Problems |
| Summary |
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 |
| Bibliography |
Includes bibliographical references (pages 208-214) |
| Subject |
Differential equations, Hyperbolic -- Numerical solutions.
|
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Conservation laws (Mathematics)
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Shock waves.
|
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Ondas de choque
|
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Conservation laws (Mathematics)
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Differential equations, Hyperbolic -- Numerical solutions
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Shock waves
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| Form |
Electronic book
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| LC no. |
92003400 |
| ISBN |
9783034886291 |
|
3034886292 |
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