Numerical Methods for Conservation Laws (Lectures in Mathematics) [Paperback]

Randall J. Leveque (Author)

Book Description

ISBN-10: 0817627235 | ISBN-13: 978-0817627232 | Publication Date: February 1992 | Edition: 2 Sub

These notes were developed for a graduate-level course on the theory and numerical solution of nonlinear hyperbolic systems of conservation laws. Part I deals with the basic mathematical theory of the equations: the notion of weak solutions, entropy conditions, and a detailed description of the wave structure of solutions to the Riemann problem. The emphasis is on tools and techniques that are indispensable in developing good numerical methods for discontinuous solutions. Part II is devoted to the development of high resolution shock-capturing methods, including the theory of total variation diminishing (TVD) methods and the use of limiter functions. The book is intended for a wide audience, and will be of use both to numerical analysts and to computational researchers in a variety of applications.

--This text refers to an alternate Paperback edition.

Editorial Reviews

Review

"The computing community needs a good text on modern methods for conservation laws, and these notes provide an excellent start on that text. Equally important, LeVeque's perspective and writing style make for wonderful reading and learning. (How often do we find important content and good writing in one book?)"   —SIAM Review "The book by Randall LeVeque is among the first that makes the material in this area accessible to first and second year graduate students in the mathematical sciences. It should be an excellent introduction to this topic for any researcher in the mathematical sciences…This book is based on [the] lecture notes of the author and should serve well as a text for a graduate course…There are many interesting exercises that serve to illuminate and expand on the text, and there are also many well-drawn figures."   —Bulletin of the AMS --This text refers to an alternate Paperback edition.

Product Details

• Paperback
• Publisher: Birkhauser; 2 Sub edition (February 1992)
• Language: English
• ISBN-10: 0817627235
• ISBN-13: 978-0817627232
• Product Dimensions: 9.4 x 6.6 x 0.5 inches
• Shipping Weight: 1 pounds
• Average Customer Review: 4.4 out of 5 stars  See all reviews (11 customer reviews)
• Amazon Best Sellers Rank: #2,509,066 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

1 of 1 people found the following review helpful:

5.0 out of 5 stars Excellent introductory book, May 12, 2011

By 

A. Dowling - See all my reviews
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This review is from: Numerical Methods for Conservation Laws (Paperback)

This is an excellent, inexpensive introductory book. I am a first year graduate student specializing in optimization, somewhat of a "sister field" to CFD. The particular system I am working with for a research project involves nonlinear conservation laws and shockwaves, a topic I knew only a little about before reading this book. Now that I have read this book, I am able to understand more advance text. This has ultimately lead to me successfully implement a flux limiter to solve a numerics problem for my current research.

The book is very readable provide one has a basic math background. Most of the proofs are "hand-wavy" with details omitted and other resources referenced. In my opinion this is excellent for an introductory book, but may annoy readers already familiar with the field.

1 of 1 people found the following review helpful:

4.0 out of 5 stars Decent mathematical oriented book, January 29, 2010

By 

A. I. Haque - See all my reviews
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This review is from: Numerical Methods for Conservation Laws (Paperback)

This book focuses on the basic theory for hyperbolic conservation laws and how they are solved using finite difference and finite volume methods. I have used this book as a text for a graduate seminar on this topic in an applied math dept. It's a good place to start if one has no prior experience in this field. When in I first starting working in this field, my boss ordered me to read this book and memorize it! However, it is weak when it comes to Riemann solvers and higher order methods. You will need to buy Toro's book for that. Also, there will be no explanation or use of real material equations of state. Only the ideal gas law is used.

1 of 1 people found the following review helpful:

5.0 out of 5 stars Highly recommended, March 31, 1998

By 

[e-mail] (Princeton, NJ) - See all my reviews

This review is from: Numerical Methods for Conservation Laws (Lectures in Mathematics) (Paperback)

Contains sufficient theoritical mathematics, with plenty of physical examples to illustrate the concepts.