Analysis of Non-Darcy Models for Mixed Convection in a Porous Cavity Using a Multigrid Approach

Abstract

This article investigates the performance of two models; namely the Brinkman-Forchheimer Darcy model (BFDM) and the Brinkman-extended Darcy model (BDM), in a problem involving mixed convection in a square cavity filled with a porous medium using the multigrid method. The left and right walls, moving in opposite directions, are maintained at different constant temperatures, while the top and bottom walls are thermally insulated. The transport equations were solved numerically by the finite-volume method on a colocated grid arrangement using a quadratic upwind interpolation for convective kinematics (QUICK) scheme. The influence of the key parameters, namely the Darcy number (Da) and Grashof number (Gr) on the flow and heat transfer pattern is examined. Further, the issue of reliability of the results is addressed. The results demonstrate that BDM over-predicts the momentum and heat transfer rates compared with BFDM, which is in conformity with the fact that the additional term present in the BFDM hinders convective effects. The full approximation storage (FAS) multigrid method achieves considerable acceleration of convergence for the present relatively unexplored problem.