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Finite Volume Methods for Hyperbolic Problems

Finite Volume Methods for Hyperbolic Problems

$92.99 (P)

Part of Cambridge Texts in Applied Mathematics

  • Date Published: August 2002
  • availability: Available
  • format: Paperback
  • isbn: 9780521009249

$ 92.99 (P)

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About the Authors
  • 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 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 applied to eliminate numerical oscillations. The methods were orginally designed to capture shock waves accurately, but are also useful tools for studying linear wave-progagation 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.

    • 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
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    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: 246 x 174 x 29 mm
    • weight: 0.94kg
    • contains: 135 b/w illus. 108 exercises
    • availability: Available
  • Table of Contents

    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

  • Author

    Randall J. LeVeque, University of Washington

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