This edited review book on Godunov methods contains 97 articles,
all of which were presented at the international conference on
Godunov Methods: Theory and Applications, held at Oxford, in
October 1999, to commemorate the 70th birthday of the Russian
mathematician Sergei K. Godunov. The central theme of this book is
numerical methods for hyperbolic conservation laws following
Godunov's key ideas contained in his celebrated paper of 1959.
Hyperbolic conservation laws play a central role in mathematical
modelling in several distinct disciplines of science and
technology. Application areas include compressible, single (and
multiple) fluid dynamics, shock waves, meteorology, elasticity,
magnetohydrodynamics, relativity, and many others. The successes in
the design and application of new and improved numerical methods of
the Godunov type for hyperbolic conservation laws in the last
twenty years have made a dramatic impact in these application
areas. The 97 papers cover a very wide range of topics, such as
design and analysis of numerical schemes, applications to
compressible and incompressible fluid dynamics, multi-phase flows,
combustion problems, astrophysics, environmental fluid dynamics,
and detonation waves. This book will be a reference book on the
subject of numerical methods for hyperbolic partial differential
equations for many years to come. All contributions are
self-contained but do contain a review element. There is a key
paper by Peter Sweby in which a general overview of Godunov methods
is given. This contribution is particularly suitable for beginners
on the subject. This book is unique: it contains virtually
everything concerned with Godunov-type methods for conservation
laws. As such it will be of particular interest to academics
(applied mathematicians, numerical analysts, engineers,
environmental scientists, physicists, and astrophysicists) involved
in research on numerical methods for partial differential
equations; scientists and engineers concerned with new numerical
methods and applications to scientific and engineering problems
e.g., mechanical engineers, aeronautical engineers, meteorologists;
and academics involved in teaching numerical methods for partial
differential equations at the postgraduate level.
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