Finite Volume Methods for Hyperbolic Problems
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Published by Cambridge University Press in 2002.
This is a revised and expanded version of |
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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 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. software package and source code for all the examples presented can be found on the web, along with animations of many time-dependent solutions. This provides an excellent learning environment for understanding wave-propagation phenomena and finite volume methods. Table of Contents and Introduction
Additional Materials to Accompany the Book
Most of the figures in the book showing computational results were created using Clawpack Version 4.3. Many of the examples have since been converted to the newer Clawpack Version 5.x form, and can be viewed in the Gallery of fvmbook applications, while the source code is located in the apps repository, in the fvmbook directory, which you can view on GitHub. For more information, see also the documentation page Examples from the book FVMHP.
A series of 25 lectures recorded in 2023, originally as supplementary material for the graduate level course Applied Math 574 at the University of Washington, Videos are available on the Clawpack YouTube channel in the FVMHP playlist.
Slides to accompany these lectures (both pdf and the latex source) are available on GitHub in the clawpack/fvmhp_materials repository.
See slides_pdf/README.md for a brief list of the contents of each slide deck, and this page from AMath 574 for more detailed contents of each lecture and links to individual videos and slide decks.
See slides/README.md for instructions on how to use the latex files to create your own modified slide decks.