Finite Volume Methods for Hyperbolic Problems
$78.00 (Z)
Part of Cambridge Texts in Applied Mathematics
 Author: Randall J. LeVeque
 Date Published: August 2002
 availability: Manufactured on demand: supplied direct from the printer
 format: Paperback
 isbn: 9780521009249
$78.00 (Z)
Paperback
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This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, (including both linear problems and nonlinear conservation laws). These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a selfcontained manner, along with much of the mathematical theory of hyperbolic problems. Highresolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are applied to eliminate numerical oscillations. The methods were orginally designed to capture shock waves accurately, but are also useful tools for studying linear waveprogagation problems, particulary in heterogenous material. The methods studied are in the CLAWPACK software package. Source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
Read more Contains an introduction to the mathematical theory along with complete development of a class of numerical methods that are broadly applicable
 Freelyavailable software (CLAWPACK) that implements these methods is used for all the examples in the book
 Greatly expanded version of the author's earlier book which has been used for over ten years, both by individuals and in classes at many major universities
Reviews & endorsements
"This book is the most complete book on the finite volume method I am aware of (very few books are entirely devoted to finite volumes, despite their massive use in CFD). The book includes both theoretical and numerical aspects and is mainly intended as a handbook: it is clear, easily readable, and of special interest to students.... The book is to be strongly recommended." Mathematical Reviews
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×Product details
 Date Published: August 2002
 format: Paperback
 isbn: 9780521009249
 length: 580 pages
 dimensions: 244 x 170 x 30 mm
 weight: 0.91kg
 contains: 135 b/w illus. 108 exercises
 availability: Manufactured on demand: supplied direct from the printer
Table of Contents
Preface
1. Introduction
2. Conservation laws and differential equations
3. Characteristics and Riemann problems for linear hyperbolic equations
4. Finitevolume methods
5. Introduction to the CLAWPACK software
6. High resolution methods
7. Boundary conditions and ghost cells
8. Convergence, accuracy, and stability
9. Variablecoefficient linear equations
10. Other approaches to high resolution
11. Nonlinear scalar conservation laws
12. Finitevolume methods for nonlinear scalar conservation laws
13. Nonlinear systems of conservation laws
14. Gas dynamics and the Euler equations
15. Finitevolume methods for nonlinear systems
16. Some nonclassical hyperbolic problems
17. Source terms and balance laws
18. Multidimensional hyperbolic problems
19. Multidimensional numerical methods
20. Multidimensional scalar equations
21. Multidimensional systems
22. Elastic waves
23. Finitevolume methods on quadrilateral grids
Bibliography
Index.