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Title: Finite Volume Methods for Hyperbolic Problems by Randall J. LeVeque, D. G. Crighton ISBN: 0-521-00924-3 Publisher: Cambridge University Press Pub. Date: 26 August, 2002 Format: Paperback Volumes: 1 List Price(USD): $47.00 |
Average Customer Rating: 5 (2 reviews)
Rating: 5
Summary: Good book to start with. Highly recommended.
Comment: 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.
Rating: 5
Summary: nice introduction
Comment: 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.
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Title: Numerical Methods for Conservation Laws by R. Leveque, Randall J. Leveque ISBN: 3764327235 Publisher: Birkhauser Boston Pub. Date: 18 July, 1996 List Price(USD): $32.95 |
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Title: Level Set Methods and Dynamic Implicit Surfaces by Stanley J. Osher, Ronald P. Fedkiw ISBN: 0387954821 Publisher: Springer Verlag Pub. Date: 01 November, 2002 List Price(USD): $79.95 |
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Title: Chebyshev and Fourier Spectral Methods : Second Revised Edition by John P. Boyd ISBN: 0486411834 Publisher: Dover Pubns Pub. Date: 03 December, 2001 List Price(USD): $32.95 |
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Title: Level Set Methods and Fast Marching Methods : Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science by J. A. Sethian, P. G. Ciarlet, A. Iserles, R. V. Kohn, M. H. Wright ISBN: 0521645573 Publisher: Cambridge University Press Pub. Date: 13 June, 1999 List Price(USD): $37.00 |
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Title: An Introduction to Computational Fluid Dynamics : The Finite Volume Method by H. K. Versteeg, W. Malalasekera ISBN: 0582218845 Publisher: Addison-Wesley Pub Co Pub. Date: 13 February, 1996 List Price(USD): $49.95 |
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