h-adaptive finite element solution of unsteady thermally driven cavity problem

An h-adaptive finite element code for solving coupled Navier-Stokes and ene rgy equations is used to solve the thermally driven cavity problem for Rayl eigh numbers at which no steady state exists (greater than 1.9 x 10(8)). Th is problem is characterised by sharp thermal and low boundary layers and hi ghly advection dominated transport, which normally requires special algorit hms, such as streamline upwinding to achieve stable and smooth solutions. I t will be shown that h-adaptivity provides a suitable solution to both of t hese problems (sharp gradients and advection dominated transport). Adaptivi ty is also very effective in resolving the flow physics, characterised by u nsteady internal waves, are calculated for three Rayleigh numbers; 2 x 10(8 ), 3 x 10(8) and 4 x 10(8) using a Prandtl number of 0.71 and results are c ompared with other published results.