Title: Spectral methods in fluid dynamics
Description: 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.
Subjects: Partial Differential equations, Numerical analysis, Fluid dynamics, Numerical solutions, Mechanics, Mathematical physics, Physics, Applied mathematics, Fluid mechanics, Mathematics, Differential Equations - Partial Differential Equations, Mechanics - Dynamics - Fluid Dynamics, Aerodynamics, Aerodynamik, Hydromechanik, Numerische Analysis, Partial Differential Equation, Partielle Differentialgleichung, Science / Mathematical Physics, Spectral Methods, Spektralmethoden, Transition, Turbulence, Turbulenz, Differential equations, Partia, Mathematical Methods in Physics, Numerical and Computational Physics, Fluid- and Aerodynamics