Download Finite Volume Methods for Hyperbolic Problems (Cambridge Texts in Applied Mathematics), by Randall J. LeVeque
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Finite Volume Methods for Hyperbolic Problems (Cambridge Texts in Applied Mathematics), by Randall J. LeVeque
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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.
- Sales Rank: #1756849 in eBooks
- Published on: 2002-08-26
- Released on: 2002-08-26
- Format: Kindle eBook
Review
"This book is the most complete book on the finite volume method I am aware of (very few books are entirely devoted to finite volumes, despite their massive use in CFD). The book includes both theoretical and numerical aspects and is mainly intended as a handbook: it is clear, easily readable, and of special interest to students.... The book is to be strongly recommended." Mathematical Reviews
About the Author
Previous books by this editor: Acta Numerica 1992 - 2003 (Vols 1 - 12); as author: First Course in the Numerical Analysis of Differential Equations (0521 553768), Approximation Theory and Optimization (0521 581907).
Most helpful customer reviews
14 of 15 people found the following review helpful.
Good book to start with. Highly recommended.
By Anton Kulchitsky
This book starts from simple things and moves to pretty complicated staff graciously. It is useful even as an introduction to the hyperbolic equations. Finally, this is the only book I use at most every day. This is the book I would strongly recommend to all students who study this field and to researchers. It has a very good and comprehensive reference.
The author develop even the software (unfortunately, this is FORTRAN, not C). The source is available and well discussed in the book (there is a whole chapter). I did not use it but found this is a very good practice. It should be useful for student also.
Many things are really nice. For example, the book gives a very good view of the nature of oscillations in high order schemes, not only formulas. And so on...
However, there are few things I was not satisfied.
1. There are no comprehensive discussion about non-uniform and non-rectangular grids. It is not good, for example, for people who works in spherical coordinates (for example in some brunches of geophysics).
2. There is no information about FCT methods that are still very popular because they give a very straightforward way to use 4th and higher order methods. However, there is a reference to the Oran and Boris book, for instance.
3. It is sometimes really pure mathematical description especially for non-linear equations. It was really inconvenient for me. Fortunately, good reference helped.
There are more things were bothered. However, this is personal. The author works with the advection equation a lot, but does not like to discuss more the conservation form of continuity equation which I would prefer. In spite of author's efforts, I think still that the wave propagation method is not so convenient as flux method even for non-conservative equations. But it depends.
Finally, this book is definitely fine and, I think, it is the best among all books in this field (maybe except the Hirsch book which is "Numerical computation of internal and external flows" 1988). I would highly recommend it to buy.
4 of 4 people found the following review helpful.
nice introduction
By A Customer
This book provides a nice introduction to the mathematics behind finite-volume methods. After reading through the first half of the book on scalar conservation laws and systems, papers in JCP no longer seem as intimidating. The book is laid out very well, and the notation is consistent throughout. It is the best of the bunch when compared to Toro's Riemann problem book and Laney's Computational Gasdynamics text.
1 of 1 people found the following review helpful.
sometimes complex notation and information overload
By truth-seeker
This book is the standard textbook used for my university course in advanced differential equations.
The book certainly contains all the information one would ever need to design numerical methods for linear and non-linear conservative systems,
but at times the author has used a very complex and confusing notation,
which i believe could have been more simply explained.
The first four chapters are a good introduction to general hyperbolic systems and how to start of modeling
the finite volume methods, but the last few sections of chapter 4 like 4.12 onwards, the author uses a very complex notation,
and mixes all kind of details, which would take days of digging through to understand what is going on in there.
I had to implement a Roe solver for a simple 2D problem.
Although all the information I need is present in the book but the notation and cross referencing between different chapters has made it very difficult to extract the things I need to implement.
However, at the same time i do not know if any other book on the topic covers all the information this one does??
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