heat transfer problem in a square cavity Benchmark solutions for the natural convective Ghent University, Belgium. 'Department of Flow, Heat and Combustion Mechanics, J. Vierendeels', B. Merci' &L E. Dick' Abstract Rayleigh numbers. converged results with an accuracy of 4 up to 5 digits are obtained for a variety of pendent of grid size, grid aspect ratio, Mach number and Rayleigh number. Grid previous work. The solver is constructed so that its convergence behaviour is inde- is assumed. An accurate and fast multigrid solver is used, which was developed in used and viscosity is given by Sutherland's law. A constant local Prandtl number ber approximations of the Navier-Stokes equations are used. The ideal-gas law is between the hot and the cold wall are large. No Boussinesq nor low-Mach num- right and insulated on the top and bottom boundaries. The temperature differences laminar flow of air in a square cavity which is heated on the left, cooled on the In this study, benchmark solutions are derived for the problem of two-dimensional 1 Introduction ied incompressible flow in a thermally driven square cavity with a pseudo-spectral of the flow equations, simplifiedfor low-Mach number flows. Le QuCrC [3] stud- ture differences between vertical isothermal walls. They used the transient form [l] investigated the steady-state flow in rectangular cavities with large tempera- function-vorticityformulationof the governing equations. Chenoweth and Paolucci on the right and insulated on the top and bottom boundaries. They used the stream flow of a Boussinesq fluid in a square cavity which is heated on the left, cooled which resulted into a benchmark solution for the problem of a two-dimensional domains with differentaspectratios. De Vahl Davis and Jones [2] presented a study ough study for over 50 years. Most studies in the past have dealt with rectangular Buoyancy-drivenflows,especially in two dimensions, have been the object of thor- © 2002 WIT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved. Web: www.witpress.com Email witpress@witpress.com Paper from: Advances in Fluid Mechanics IV, M Rahman, R Verhoeven and CA Brebbia (Editors). ISBN 1-85312-910-0