AN EVALUATION OF DIFFERENT DISCRETIZATION SCHEMES FOR NATURAL CONVECTION OF LOW-PRANDTL-NUMBER FLUIDS IN CAVITIES

Abstract

A comparative study of four discretization schemes for the equations describing convection-diffusion transport phenomena in low-Prandtl-number fluids is presented. Discussion is focused on steady and transient laminar thermal convection in a square cavity. The differencing schemes considered are the conventional central differencing, Spalding's hybrid, Patankar's power law, and Leonard's QUICK differencing schemes. On a relatively coarse grid (31 × 31), the power law and hybrid differencing schemes were unable to predict secondary circulation in the four corners of the cavity for Gr = 1 × 10⁷ and Pr = 0.005, while the quadratic differencing scheme was able to do so. But with a finer mesh (51 × 51), the power law differencing scheme was also able to predict weak circulation in the corners of the cavity.