Customer Reviews

Finite Volume Methods for Hyperbolic Problems (Cambridge Texts in Applied Mathematics)

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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.

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.

This is a very good written textbook. Must have for those who learn modern numerical methods for solving hyperbolic systems. It explains all the fundamentals, concepts, physics, numerics, and ideas. Very comprehensive, yet clear, and easy to follow.

Especially, I thank Prof. LeVeque for making this book available at such a low price. This is something we should really appreciate, in comparison with other expensive, even not well written, textbooks.

I'm a Ph.D. student in CFD. I find this book very well written and quite thorough. I recommend it 100% to anyone who wants to get a good insight on FV methods for Hyperbolic problems. However, I need to say that I would expect to find practical guidelines and some information about the application of the FVM on unstructured meshes. But, in time the reader will realise that it is not difficult to work on unstructured meshes on his/her own, following the material covered throughout the book. I strongly recommend it.

The author gave almost all the basic knowledge related to hyperbolic equation, at least from the engineering point of view. I read it myself without any help. It's not hard to understand. Moreover, it gives all you need at beginning references.

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??