h-adaptive finite element solution of high Rayleigh number thermally driven cavity problem

An h-adaptive finite element code for solving coupling Navier-Stokes and en ergy equations is used to solve the thermally driven cavity problem. The bu oyancy forces are represented using the Boussinesq approximation. The probl em is characterised by very thin boundary layers at high values of Rayleigh number (> 10(6)). However, steady state solutions are achievable with adeq uate discretisation. This is where the auto-adaptive finite element method provides a powerful means of achieving optimal solutions without having to pre-define a mesh, which may be either inadequate or too expensive. Steady state and transient results are given for six different Rayleigh numbers in the range 10(3) to 10(8) for a Prandtl number of 0.71. The use of h-adapti vity, based on a posteriori error estimation, is found to ensure a very acc urate problem solution ar a reasonable computational cost.