Numerical Analysis of Free Convection flow in Square Enclosure Partially Heated from below using the Multigrid Method

Abstract

The present work investigates the efficiency of the Multigrid method when applied to solve two-dimensional laminar steady free convection flow in a square enclosure partially heated from below. The numerical method includes finite volume discretization with upwind scheme on structure orthogonal regular meshes. The performance of the correction storage (CS) Multigrid algorithm is compared for different numbers of sweeps in each grid level. Up to two grids, for both Multigrid V- and W- cycles, are presented. The results are mainly analyzed in terms of the average heat transfer at the walls of the enclosure and Multigrid performance on the rate of convergence. It is also shown that convective heat transfer has a characteristic behavior for each boundary conditions adopted in given ranges of the governing parameters.