Spectral influence matrix for vorticity without corner pathology

This paper describes a spectral method for the uncoupled solution of the vo rticity and stream function equations in which two-dimensional integral con ditions for the vorticity are imposed according to the Glowinski-Pironneau method. A nonsingular influence matrix is obtained which allows to determin e the trace of vorticity under no-slip conditions along the entire boundary of a rectangular domain. The method is based on a Galerkin formulation usi ng Legendre polynomials in both directions and fully exploits the direct pr oduct structure of the two equations of the Stokes time-discretized problem . Numerical tests for the driven cavity problem are presented to demonstrat e that no theoretical or numerical difficulty arises in the proposed 2D spe ctral approximation, which does not require any a priori regularization of the boundary condition at the corners. The algorithm is found to guarantee convergence to the correct solution for steady and unsteady problems, altho ugh spectral accuracy cannot be achieved due to the expected Gibbs' phenome non. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved .