A DIVERGENCE-FREE SPECTRAL EXPANSIONS METHOD FOR 3-DIMENSIONAL FLOWS IN SPHERICAL-GAP GEOMETRIES

A spectral method for the solution of the incompressible Navier-Stokes equations in spherical-gap geometries is presented. The method uses divergence-free vector expansions which inherently satisfy the boundary conditions [1]. Basis and test functions are constructed from Chebyshev polynomials and vector spherical harmonics (VSH) yielding a Petrov-Galerkin weighted-residual method that produces spectral convergence. No rotational nor equatorial symmetry of the flow field is implicitly imposed. The approach makes extensive use of the convenient properties of the VSH which are presented in a computationally suitable form whenever possible. The alias-free implementation of the method rests upon a standard, explicit-implicit time-integration technique. A VSH-Chebyshev vector transform with two ''fast directions'' is also developed and briefly presented. Several test cases are used to validate the resulting initial-boundary-value code. Axisymmetric, basic spherical Couette flow computations are compared with available numerical results while a three-dimensional spiral Taylor-Gortler vortex flow simulation is tested against experimental measurements. Very good agreement is found in all cases. (C) 1994 Academic Press, Inc.