Introduction
This is an excellent introduction into
finite volume methods for solving conservation laws. The book is
divided into three main parts: Part I deals with linear equations
in predominately one spatial dimension, Part II introduces
nonlinear equations again in one spatial dimension, while Part III
introduces multidimensional problems. Beginning with an
introduction to the mathematics of these partial differential
equations, including all the basic hyperbolic theory for linear
equations (characteristics, Riemann problems, definition, and
examples), LeVeque then presents the basics of finite volume
methods for the integration of conservation laws. Extensions to
these basics in terms of high resolution methods such as the use
of limiters in multidimensional up-winding is then presented. The
nonlinear portion of the book begins with the mathematics of
nonlinear scalar conservation laws, the application of finite
volume methods for their numerical solution, extensions to systems
of equations, the nonlinear Riemann problem, non-classical
hyperbolic systems, and finally concludes with a chapter on
equations with source terms. The third part of the book deals
with multidimensional hyperbolic problems and numerical methods
both in scalar and vector form.
The book is exceptionally well written and the problems are worth
subsequent study. If you work in the area of hyperbolic systems
you must read this book.
One of the great bonuses that this book contains is that it
includes a description and introduction on the use of the
CLAWPACK
software. The CLAWPACK of codes is a large collection of FORTRAN 77 codes
for solving a large number of hyperbolic systems (both conservative
and nonconservative forms). Included is a "getting started" section
which can help new users become familiar with the codes and get them up and
solving problems very quickly.