Spectral Element Computations of Rotating Flows in Complex Geometries

Tony Harkin (School of Mathematical Sciences, Rochester Institute of Technology )

The objective of this talk is to describe a spectrally accurate numerical scheme suitable for the computation of rotating flows in complex geometries. The numerical scheme employed is based on the spectral element method introduced by A. Patera (1984) for the solution of incompressible flow problems of low to moderate Reynolds number. The method blends domain decomposition along with high order polynomial expansions over quadrilateral elements. The discretization is achieved through a weighted-residual technique using Gaussian quadrature. The axisymmetric Stokes problem is presented as a natural prelude to the study of the fully nonlinear Navier-Stokes equations. In this fashion, it is determined that the viscous and pressure terms are to be treated implicitly, while the Coriolis term and nonlinear advection are treated explicitly. The classical Uzawa algorithm is used to invert the resulting discrete system.