Customer Reviews

Numerical Methods for Conservation Laws (Lectures in Mathematics)

5 star:		(7)
4 star:		(2)
3 star:		(1)
2 star:		(1)
1 star:		(0)

 

 

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.

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.

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

This book is divided into 2 parts. The first part is a theoretical introduction to conservation laws. The second part deals with numerical methods for solving these equations. It's a little outdated and doesn't contain much about the more current methods used to solve CL's, but there are a number of important concepts (such as entropy solutions, etc), which will always be relevant. This book is a nice starting point if you are just starting to learn about conservation laws and how to solve them numerically.

This is a very good book, and covers all the main issues. It is clear and rigorous. Some topics are covered in brief and additional references may be needed to fully understand the topic.

Good overview, but not enough information if you are actually trying to solve real problems.

This book is organized into two main parts, the first of which deals with derivations of the conservation laws from physical principles, and theoretical treatment of such equations. The second part covers in detail the most popular (finite difference) schemes available for solving these PDE's and proofs on convergence. This book is really one I consider _the_ reference for conservation laws, and one I consult as a reference on a frequent basis. Easily accessible even if you are used to dealing mainly with elliptic systems.

Must read for those who are dealing with hyperbolic or nearly-hyperbolic systems.
Based on mesh based methods so the numerical model obtained can be used for control and optimization purpose easily.( that is my feeling)

Readable, concise discussion, plenty of examples

this is a discrete book, but i expect more especially in the part of the stability and convergence of numerical methods. However i found a very good explanation of the mathematical concepts that are beyond the cold formulas. Thi is a text for undergraduate students, non a text for reserchers.