ARTICLE:

• h-ADAPTIVE FINITE ELEMENT SOLUTION OF NATURAL CONVECTION IN AN AIR FILLED CAVITY  download article

D. A. Mayne
School of Civil and Environmental Engineering, University of Edinburgh, The Kings Buildings Edinburgh EH9 3JN, UNITED KINGDOM

A. S. Usmani
School of Civil and Environmental Engineering, University of Edinburgh, The Kings Buildings Edinburgh EH9 3JN, UNITED KINGDOM

M. Crapper
School of Civil and Environmental Engineering, University of Edinburgh, The Kings Buildings Edinburgh EH9 3JN, UNITED KINGDOM

ABSTRACT

An h-adaptive finite element code for solving coupled Navier-Stokes and energy equations is used to solve natural convection in an air filled cavity with three different directions chosen for gravity. The buoyancy forces are represented using the Boussinesq approximation. This problem is characterised by very thin boundary layers at high values of Rayleigh number (> 10⁶). 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. The use of h-adaptivity, based on a-posteriori error estimation is found to ensure an accurate problem solution at a reasonable computational cost. Accurate values of Nusselt number are achieved at lower Rayleigh numbers however the three-dimensional nature of the flow for the bottom heated case precludes solution of the problem using two-dimensional modelling.

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