Two-dimensional Natural Convection Analysis by the Fourth-order Finite Difference Method : In Case of Non-uniform Meshes

The natural convection problem in a square cavity has been analized as a benchmark problem for a two dimensional thermal fluid flow analysis. In this paper, we solve this problem up to Rayleigh numbers of 109 using the fourth-order finite difference method. Fourth-order weighted average method (FWA) is a combination of (a centered-difference) × W and (an upstream-difference) × (1-W), and W is a weighting parameter. FWA (C) was proposed using the error analysis approach for FWA. Then, FWA (C) was used for the two dimensional natural convection problems using nonuniform meshes. The effectiveness of FWA (C) was confirmed by comparing our numerical results with other research works.