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

An h‐adaptive finite element code for solving coupled Navier‐Stokes and energy equations is used to solve the thermally driven cavity problem for Rayleigh numbers at which no steady state exists (greater than 1.9 × 10⁸). This problem is characterised by sharp thermal and flow boundary layers and highly advection dominated transport, which normally requires special algorithms, such as streamline upwinding, to achieve stable and smooth solutions. It will be shown that h‐adaptivity provides a suitable solution to both of these problems (sharp gradients and advection dominated transport). Adaptivity is also very effective in resolving the flow physics, characterised by unsteady internal waves, are calculated for three Rayleigh numbers; 2 × 10⁸, 3 × 10⁸ and 4 × 10⁸ using a Prandtl number of 0.71 and results are compared with other published results.