A spectral iterative domain decomposition technique for the incompressible Navier-Stokes equations

An efficient iterative domain decomposition technique associated with high order spectral methods is described for the resolution of the incompressible Navier-Stokes equations. This corresponds to an extension of the patching-collocation approach proposed by Zanolli (1987) for linear problems, and based on a relaxation parameter. Particular attention is focused on its efficiency for Neumann boundary conditions, as in the pressure Poisson equation. In such a case, it is shown that the convergence of the solution can be obtained after a limited number of internal iterations. Moreover, the present procedure is efficient in parallel computing. Applications to the prediction of the Hopf bifurcation occurring in a tall differentially heated cavity are presented for a low-Prandtl number fluid. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.