Finite Volume Methods for Hyperbolic Problems
Finite Volume Methods for Hyperbolic Problems
$104.00
USDThis book, first published in 2002, 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 self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and 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.
- Contains an introduction to the mathematical theory along with complete development of a class of numerical methods that are broadly applicable
- Freely-available 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
Product details
August 2002Paperback
9780521009249
580 pages
246 × 174 × 29 mm
0.94kg
135 b/w illus. 108 exercises
Available
Table of Contents
- Preface
- 1. Introduction
- 2. Conservation laws and differential equations
- 3. Characteristics and Riemann problems for linear hyperbolic equations
- 4. Finite-volume methods
- 5. Introduction to the CLAWPACK software
- 6. High resolution methods
- 7. Boundary conditions and ghost cells
- 8. Convergence, accuracy, and stability
- 9. Variable-coefficient linear equations
- 10. Other approaches to high resolution
- 11. Nonlinear scalar conservation laws
- 12. Finite-volume methods for nonlinear scalar conservation laws
- 13. Nonlinear systems of conservation laws
- 14. Gas dynamics and the Euler equations
- 15. Finite-volume 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. Finite-volume methods on quadrilateral grids
- Bibliography
- Index.
