Spectral Methods in Fluid Dynamics

Spectral Methods in Fluid Dynamics

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This textbook presents the modern unified theory of spectral

methods and their implementation in the numerical analysis

of partial differential equations occuring in fluid

dynamical problems of transition, turbulence, and

aerodynamics. It provides the engineer with the tools and

guidance necessary to apply the methods successfully, and it

furnishes the mathematician with a comprehensive, rigorous

theory of the subject. All of the essential components of

spectral algorithms currently employed for large-scale

computations in fluid mechanics are described in detail.

Some specific applications are linear stability, boundary

layer calculations, direct simulations of transition and

turbulence, and compressible Euler equations. The authors

also present complete algorithms for Poisson's equation,

linear hyperbolic systems, the advection diffusion equation,

isotropic turbulence, and boundary layer transition. Some

recent developments stressed in the book are iterative

techniques (including the spectral multigrid method),

spectral shock-fitting algorithms, and spectral multidomain

methods.

The book addresses graduate students and researchers in

fluid dynamics and applied mathematics as well as engineers

working on problems of practical importance.