Following up the seminal Spectral Methods in Fluid Dynamics,
Spectral Methods: Evolution to Complex Geometries and Applications
to Fluid Dynamics contains an extensive survey of the essential
algorithmic and theoretical aspects of spectral methods for complex
geometries. These types of spectral methods were only just emerging
at the time the earlier book was published. The discussion of
spectral algorithms for linear and nonlinear fluid dynamics
stability analyses is greatly expanded. The chapter on spectral
algorithms for incompressible flow focuses on algorithms that have
proven most useful in practice, has much greater coverage of
algorithms for two or more non-periodic directions, and shows how
to treat outflow boundaries. Material on spectral methods for
compressible flow emphasizes boundary conditions for hyperbolic
systems, algorithms for simulation of homogeneous turbulence, and
improved methods for shock fitting. This book is a companion to
Spectral Methods: Fundamentals in Single Domains.
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