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Finite Volume Methods for Hyperbolic Problems (Cambridge Texts in Applied Mathematics) | 
 enlarge | Author: Randall J. Leveque
Publisher: Cambridge University Press
Category: Book
List Price: $55.00
Buy New: $30.98
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Rating:  4 reviews
Sales Rank: 124963
Media: Paperback
Edition: 1
Pages: 578
Number Of Items: 1
Shipping Weight (lbs): 2.2
Dimensions (in): 9.6 x 6.9 x 1.6
ISBN: 0521009243
Dewey Decimal Number: 515.353
EAN: 9780521009249
Publication Date: August 26, 2002
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Product 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. 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.
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.
Download 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. 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.
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| Customer Reviews:
Good book to start with. Highly recommended. October 23, 2003
Anton Kulchitsky (Fairbanks, Alaska United States)
7 out of 8 found this review helpful
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.
an excellent book on hyperbolic equations October 18, 2005
JIANGHUI CHAO (Gainesville, FL, USA)
2 out of 3 found this review helpful
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.
nice introduction July 11, 2003
2 out of 2 found this review helpful
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.
It is a must!! December 24, 2007
Konstanti Kontzialis
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.
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