Effect of medium properties on convergence rates of multigrid solutions of laminar flows in permeable structures

The present work investigates the efficiency of the multigrid method when applied to solve laminar flow in a two-dimensional tank filled with a porous material. The numerical method includes finite volume discretization with the upwind scheme on structure orthogonal regular meshes. Linearization of the source term, which consists of viscous and form drags, increases the stiffness of the algebraic equation set. Performance of the correction storage (CS) multigrid algorithm is compared for different numbers of sweeps in each grid level. Up to four grids, for both multigrid V- and W- cycles, are considered. Effects of medium permeability and porosity on converged rates are presented. Results indicate that V-cycles perform slightly better in reducing the required computational effort and that the higher the permeability and the lower the porosity, faster solutions are obtained.