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Pseudospectral method -- Navier-Stokes equations.
February 2007.
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 irregular domains.
Unsteady algorithms Fully Implicit and Crank Nicholson were developed for body fitted curvilinear coordinate system to study the incompressible flow over two-dimensional ellipses. In addition, explicit cyclic boundary condition was implemented to facilitate analysis of vortex shedding. Unsteady flow over circular cylinders was simulated for different Reynolds numbers and compared with experimental data. Flow over ellipses was simulated to study the effect of aspect ratio on drag coefficient. It was observed that the drag coefficient increased as the aspect ratio increased reaching an asymptotic value as the ellipse approached a flat plate.