Spectral Methods in Fluid Dynamics

This textbook presents the modern unified theory of spectralmethods and their implementation in the numerical analysisof partial differential equations occuring in fluiddynamical problems of transition, turbulence, andaerodynamics. It provides the engineer with the tools andguidance necessary to apply the methods successfully, and itfurnishes the mathematician with a comprehensive, rigoroustheory of the subject. All of the essential components ofspectral algorithms currently employed for large-scalecomputations in fluid mechanics are described in detail.Some specific applications are linear stability, boundarylayer calculations, direct simulations of transition andturbulence, and compressible Euler equations. The authorsalso present complete algorithms for Poisson's equation,linear hyperbolic systems, the advection diffusion equation,isotropic turbulence, and boundary layer transition. Somerecent developments stressed in the book are iterativetechniques (including the spectral multigrid method),spectral shock-fitting algorithms, and spectral multidomainmethods.The book addresses graduate students and researchers influid dynamics and applied mathematics as well as engineersworking on problems of practical importance.