✍ Scribed by Randall J. LeVeque (auth.)
No coin nor oath required. For personal study only.
These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. Without the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are. not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.
Front Matter....Pages i-x
Front Matter....Pages N1-N1
Introduction....Pages 1-13
The Derivation of Conservation Laws....Pages 14-18
Scalar Conservation Laws....Pages 19-40
Some Scalar Examples....Pages 41-50
Some Nonlinear Systems....Pages 51-57
Linear Hyperbolic Systems....Pages 58-69
Shocks and the Hugoniot Locus....Pages 70-80
Rarefaction Waves and Integral Curves....Pages 81-88
The Riemann problem for the Euler equations....Pages 89-93
Front Matter....Pages 95-95
Numerical Methods for Linear Equations....Pages 97-113
Computing Discontinuous Solutions....Pages 114-121
Conservative Methods for Nonlinear Problems....Pages 122-135
Godunov’s Method....Pages 136-145
Approximate Riemann Solvers....Pages 146-157
Nonlinear Stability....Pages 158-172
High Resolution Methods....Pages 173-192
Semi-discrete Methods....Pages 193-199
Multidimensional Problems....Pages 200-207
Back Matter....Pages 208-219
Computational Mathematics and Numerical Analysis; Analysis
📜 SIMILAR VOLUMES
This is a very good book, and covers all the main issues. It is clear and rigorous. Some topics are covered in brief and additional references may be needed to fully understand the topic.
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
<p>This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics. Ultimately, it highlights what is specific to and beneficial in the Lagrangian approach and its numerical methods. The two first