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Finite Volume Methods for Hyperbolic Problems

Finite Volume Methods for Hyperbolic Problems


Part of Cambridge Texts in Applied Mathematics

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

£ 58.99

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About the Authors
  • This 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
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    Reviews & endorsements

    'It is moreover advantageous that the algorithms presented are public and easily available via the web-page cited. Similar to the book of R. J. LeVeque titled Numerical Methods for Conservation Laws, this manuscript will certainly become a part of the standard literature in the field of numerical methods for hyperbolic partial differential equations.' Journal of Applied Mathematics and Physics

    'The text is very well written and can serve for self-study as well as an accompanying text book for teaching purposes … a very sound and comprehensive introduction into hyperbolic problems and their numerical treatment.' Zentralblatt MATH

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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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