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Finite Volume Methods for Hyperbolic Problems
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Finite Volume Methods for Hyperbolic Problems Paperback - 2002

by Randall J. Leveque

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From the publisher

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.

First line

To see how conservation laws arise from physical principles, we will begin by considering the simplest possible fluid dynamics problem, in which a gas or liquid is flowing through a one-dimensional pipe with some known velocity u(x, t), which is assumed to vary only with x, the distance along the pipe, and time t.

Details

  • Title Finite Volume Methods for Hyperbolic Problems
  • Author Randall J. Leveque
  • Binding Paperback
  • Edition International Ed
  • Pages 580
  • Volumes 1
  • Language ENG
  • Publisher Cambridge University Press
  • Publication date 2002-08-26
  • Features Bibliography
  • ISBN 9780521009249 / 0521009243
  • Weight 2.08 lbs (0.94 kg)
  • Dimensions 9.7 x 6.84 x 1.14 in (24.64 x 17.37 x 2.90 cm)
  • Category Mathematics
  • Library of Congress subjects Differential equations, Hyperbolic -, Finite volume method
  • Library of Congress Catalogue Number 2001052642
  • Dewey Decimal Code 515.353
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Finite Volume Methods for Hyperbolic Problems (Cambridge Texts in Applied Mathematics, Series Number 31)

by LeVeque, Randall J

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Finite Volume Methods for Hyperbolic Problems

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Paperback / softback. New. 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. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
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Finite Volume Methods for Hyperbolic Problems

Finite Volume Methods for Hyperbolic Problems

by Randall J. Leveque

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Finite Volume Methods for Hyperbolic Problems (Cambridge Texts in Applied Mathematics, Series Number 31)

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Finite Volume Methods for Hyperbolic Problems (Cambridge Texts in Applied Mathematics)

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Finite Volume Methods for Hyperbolic Problems

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paperback. ISBN: 9780521009249
Publisher ‏ : ‎ Cambridge University Press, August 26, 2002
Paperback, 580 pages
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… Read more
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