Multi-grid solution of Neumann pressure problem for viscous flows using primitive variables

The multi-grid (MG) technique has been advanced for use with the Neumann boundary-value problem in clustered curvilinear orthogonal coordinates. This comprises an important step in the analysis of viscous flows using the velocity-pressure formulation of the Navier-Stokes equations. With successive over-relaxation (SOR) as the smoothing operator and with suitably formulated restriction and coarse-grid-correction operators, a 4-grid procedure enhances the efficiency of fine-grid solutions of the Neumann problem by a factor of 3 to 5, depending on the problem parameters. Thy influence of the smoothing operator is also examined by employing the alternating-direction implicit and the strongly implicit techniques instead of SOR.