Spectral 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 developed by Zanolli (see [9]) for linear problems having Dirichlet or mixed boundary conditions. The algorithm is based on a relaxation parameter, used to satisfy the continuity requirements of variables and their normal derivative at interfaces. 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 for an optimum value of the relaxation parameter, 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 different bifurcations of flow regimes occurring in a tall differentially heated cavity and in a box having thermal boundary discontinuities ar...

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