An improved dynamical approximation to Boussinesq equation using Karhunen-Loeve basis

Tarman I. H.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, vol.144, no.1-2, pp.153-162, 1997 (SCI-Expanded) identifier identifier


Karhunen-Loeve (K-L) basis is used to provide an efficient relatively low dimensional dynamical approximation to Boussinesq equation governing thermal convection phenomena. K-L basis is empirically generated from an ensemble of numerically obtained realizations of turbulent thermal convection flow field. Fourier collocation spectral method is used to numerically integrate Boussinesq equation with stress-free boundary conditions at Pr = 0.72 and Ra approximate to 10 000. An algorithm, which incorporates the lost dissipative effects of the truncation into the dynamical approximation without increasing the number of degrees of freedom involved, is proposed and numerically tested.