Finite Volume Methods for Hyperbolic Problems / Edition 1

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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 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.

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Editorial Reviews

From the Publisher
"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
From The Critics
Hyperbolic partial differential equations can be used to describe a range of wave-propagation and transport phenomena in a number of areas of science and engineering. Focusing primarily on nonlinear problems, LeVeque (applied mathematics, U. of Washington) presents a discussion of finite volume methods for solving these equations. The methods are presented and implemented using a software package called CLAWPACK (source code available online). Annotation c. Book News, Inc., Portland, OR
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Product Details

  • ISBN-13: 9780521009249
  • Publisher: Cambridge University Press
  • Publication date: 8/26/2002
  • Series: Cambridge Texts in Applied Mathematics Series , #31
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 578
  • Sales rank: 1,334,255
  • Product dimensions: 5.98 (w) x 8.98 (h) x 1.18 (d)

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.

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