Effect of permeability on convergence rates of multigrid solutions of laminar flows in porous media

Abstract

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 flux blended deferred correction scheme on structure orthogonal regular meshes. 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 on converged rates are presented. Results indicate that W-cycles perform better in reducing the required computational effort and that the lower the permeability, faster solutions are obtained.