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  3. Finite Volume Methods for Hyperbolic Problems
  • Cited by 2818
Publisher:
Cambridge University Press
Online publication date:
September 2012
Print publication year:
2002
Online ISBN:
9780511791253
DOI:
https://doi.org/10.1017/CBO9780511791253
Subjects:
Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Mathematical Physics, Geometry and Topology, Numerical Analysis and Computational Science
Series:
Cambridge Texts in Applied Mathematics (31)
Information

Book description

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.

Reviews

'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.'

Source: 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.’

Source: Zentralblatt MATH

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