This book deals with the application of spectral methods to problems of
uncertainty propagation and quanti?cation in model-based computations.
It speci?cally focuses on computational and algorithmic features of
these methods which are most useful in dealing with models based on
partial differential equations, with special att- tion to models arising
in simulations of ?uid ?ows. Implementations are illustrated through
applications to elementary problems, as well as more elaborate examples
selected from the authors' interests in incompressible vortex-dominated
?ows and compressible ?ows at low Mach numbers. Spectral stochastic
methods are probabilistic in nature, and are consequently rooted in the
rich mathematical foundation associated with probability and measure
spaces. Despite the authors' fascination with this foundation, the
discussion only - ludes to those theoretical aspects needed to set the
stage for subsequent applications. The book is authored by
practitioners, and is primarily intended for researchers or graduate
students in computational mathematics, physics, or ?uid dynamics. The
book assumes familiarity with elementary methods for the numerical
solution of time-dependent, partial differential equations; prior
experience with spectral me- ods is naturally helpful though not
essential. Full appreciation of elaborate examples in computational ?uid
dynamics (CFD) would require familiarity with key, and in some cases
delicate, features of the associated numerical methods. Besides these
shortcomings, our aim is to treat algorithmic and computational aspects
of spectral stochastic methods with details suf?cient to address and
reconstruct all but those highly elaborate examples.
