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

Randall J. LeVeque (Author)

Book Description

ISBN-10: 0521009243 | ISBN-13: 978-0521009249 | Publication Date: August 26, 2002 | Edition: 1

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 applied to eliminate numerical oscillations. The methods were orginally designed to capture shock waves accurately, but are also useful tools for studying linear wave-progagation problems, particulary in heterogenous material. The methods studied are in the CLAWPACK software package. 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.

Editorial Reviews

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

Book Description

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. 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.

Product Details

• Paperback: 578 pages
• Publisher: Cambridge University Press; 1 edition (August 26, 2002)
• Language: English
• ISBN-10: 0521009243
• ISBN-13: 978-0521009249
• Product Dimensions: 9.7 x 6.8 x 1.1 inches
• Shipping Weight: 2.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.7 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #491,696 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

9 of 10 people found the following review helpful:

5.0 out of 5 stars Good book to start with. Highly recommended., October 23, 2003

By 

Anton Kulchitsky (Fairbanks, Alaska United States) - See all my reviews
(REAL NAME)   

Amazon Verified Purchase

This review is from: Finite Volume Methods for Hyperbolic Problems (Cambridge Texts in Applied Mathematics) (Paperback)

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.

3 of 3 people found the following review helpful:

5.0 out of 5 stars nice introduction, July 10, 2003

By A Customer

This review is from: Finite Volume Methods for Hyperbolic Problems (Cambridge Texts in Applied Mathematics) (Paperback)

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:

5.0 out of 5 stars best textbook you can find for modern finite volume methods for hyperbolic system, and very low price, January 15, 2009

By 

Mike IX - See all my reviews

This review is from: Finite Volume Methods for Hyperbolic Problems (Cambridge Texts in Applied Mathematics) (Paperback)

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.