Finite Volume Methods for Hyperbolic Problems
By (author) Randall J. LeVeque
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Finite Volume Methods for Hyperbolic Problems by Randall J. LeVeque
Book DescriptionThis 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.
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Book DetailsISBN: 9780521009249
(228mm x 152mm x 30mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 26-Aug-2002
Country of Publication: United Kingdom
Books By Author Randall J. LeVeque
Finite Difference Methods for Ordinary and Partial Differential Equations, Paperback (September 2007)» View all books by Randall J. LeVeque
Introductory textbook from which students can approach more advance topics relating to finite difference methods.
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