Numerical simulation of compressible, inviscid time-dependent flow
is a major branch of computational fluid dynamics. Its primary goal
is to obtain accurate representation of the time evolution of
complex flow patterns, involving interactions of shocks,
interfaces, and rarefaction waves. The Generalized Riemann Problem
(GRP) algorithm, developed by the authors for this purpose,
provides a unifying 'shell' which comprises some of the most
commonly used numerical schemes of this process. This monograph
gives a systematic presentation of the GRP methodology, starting
from the underlying mathematical principles, through basic scheme
analysis and scheme extensions (such as reacting flow or
two-dimensional flows involving moving or stationary boundaries).
An array of instructive examples illustrates the range of
applications, extending from (simple) scalar equations to
computational fluid dynamics. Background material from mathematical
analysis and fluid dynamics is provided, making the book accessible
to both researchers and graduate students of applied mathematics,
science and engineering.
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