《natural convection of air in a square cavity》.pdf

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, VOL. 3, 249-264 (1983) NATURAL CONVECTION OF AIR IN A SQUARE CAVITY A BENCH MARK NUMERICAL SOLUTION G. DE VAHL DAVIS University of New South Wales,Kensington 2033, Australia SUMMARY Details are given of the computational method used t o obtain an accurate solution of the equations describing two-dimensional natural convection in a square cavity with differentially heated side walls. Second-order, central difference approximations were used. Mesh refinement and extrapolation led to solutions for 1 0 3 R a s 10‘ which are believed to be accurate to better than 1per cent at the highest Rayleigh number and down to one-tenth of that at the lowest value. KEY WORDS Natural Convection Numerical Methods Bench Mark Solution Square Cavity INTRODUCTION Buoyancy-driven flow in a square cavity with vertical sides which are differentially heated is a suitable vehicle for testing and validating computer codes used for a wide variety of practical problems such as nuclear reactor insulation, ventilation of rooms, solar energy collection and crystal growth in liquids. Following a suggestion to this effect by Jones,’ contributions were to the solution of this problem. At the Venice conference on Numerical Methods in Thermal Problems, the contributions were reported in detail’ and omp pa red^,^ with a bench mark solution. The present paper describes the development and characteristics of the bench mark solution in greater detail than previously published. It is hoped that it will l