1R40. Spectral Methods for Incompressible Viscous Flow. Applied Mathematical Sciences, Vol 148. - Edited by R Peyret (Lab JA Dieudonne, Univ de Nice-Sophia Antipolis, Parc Valrose, Nice, 06000, France). Springer-Verlag, New York. 2002. 432 pp. ISBN 0-387-95221-7. $59.95.

Reviewed by G de Vahl Davis (Sch of Mech and Manuf Eng, Univ of New S Wales, Sydney, 2052 NSW, Australia).

The foundations of spectral methods are not new. They lie in the use of series expansions, typically a Fourier series, to attack problems in mathematical physics, and especially fluid mechanics, and have so done since the 19th century. However, computational limitations in the BC (before computer) era—and even in the early AC years—limited their application. It was not until the 1970s, as Peyret points out, that a revival of the Fourier method was applied to the direct simulation of turbulence. Historically,...

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