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

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

Finite Volume Methods for Hyperbolic Problems (Cambridge Texts in Applied
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Finite Volume Methods for Hyperbolic Problems (Cambridge Texts in Applied Mathematics) Paperback - 2002

by Randall J. LeVeque

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  • Title Finite Volume Methods for Hyperbolic Problems (Cambridge Texts in Applied Mathematics)
  • Author Randall J. LeVeque
  • Binding Paperback
  • Edition International Ed
  • Condition New
  • Pages 580
  • Volumes 1
  • Language ENG
  • Publisher Cambridge University Press
  • Publication date 2002-08-26
  • Features Bibliography
  • Bookseller's Inventory # 694242-n
  • 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
  • Quantity available 5

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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.

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