Spectral methods have a long history of application to fluid flow
simulations. Their main advantages are high-order accuracy and
convergence properties. The basic spectral methods only work on
rectangular or circular domains. A very important and active
research area is to adapt spectral methods for domains with complex
boundary. In this monograph the application of pseudospectral (PS)
method to viscous flow over a two-dimensional cylinder with dimples
on the boundary is presented. By using a series of coordinate
transformations, the exterior domain is mapped to the interior of
the unit disk. Then the Fourier-Chebyshev PS approximation is
applied to the transformed system of partial differential
equations. Both steady and unsteady solutions are discussed. This
monograph should be useful to applied mathematicians and engineers
interested in high-order methods for fluid flow simulations in
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