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

Abstract 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.