Benchmark solutions for the natural convective heat transfer problem in a square cavity

Abstract

In this study, benchmark solutions are derived for the problem of two-dimensional laminar flow of air in a square cavity which is heated on the left, cooled on the right and insulated on the top and bottom boundaries. The temperature differences between the hot and the cold wall are large. No Boussinesq nor low-Mach number approximations of the Navier-Stokes equations are used. The ideal-gas law is used and viscosity is given by Sutherland's law. A constant local Prandtl number is assumed. An accurate and fast multigrid solver is used, which was developed in previous work. The solver is constructed so that its convergence behaviour is independent of grid size, grid aspect ratio, Mach number and Rayleigh number. Grid converged results with an accuracy of 4 up to 5 digits are obtained for a variety of Rayleigh numbers.