A DIVERGENCE-FREE CHEBYSHEV COLLOCATION PROCEDURE FOR INCOMPRESSIBLE FLOWS WITH 2 NONPERIODIC DIRECTIONS

The enforcement of divergence-free condition in the interior and on the boundaries of an incompressible flow with two non-periodic directions is discussed for a Chebyshev collocation formulation. An influence matrix technique along with a correction methodology is used to satisfy the continuity equation everywhere in the domain. Details of implementing this procedure in a collocation method are presented. An efficient solution procedure based on matrix diagonalization has been used to solve the resulting full matrices. Two test problems: (a) flow in a driven square cavity, and (b) fully-developed laminar flow in a square duct subject to a three-dimensional perturbation are studied. Run-time statistics (CPU, memory, MFLOPS) of the solution procedure are presented for representative grid sizes. © 1993 by Academic Press, Inc.