Open Access

ARTICLE

A Galerkin-RBF Approach for the Streamfunction-Vorticity-Temperature Formulation of Natural Convection in 2D Enclosured Domains

by D. Ho-Minh¹, N. Mai-Duy¹, T. Tran-Cong¹

1 Computational Engineering and Science Research Centre (CESRC), Faculty of Engineering and Surveying (FoES), The University of Southern Queensland, Toowoomba, QLD 4350, Australia.

Computer Modeling in Engineering & Sciences 2009, 44(3), 219-248. https://doi.org/10.3970/cmes.2009.044.219

Abstract

This paper reports a new discretisation technique for the streamfunc -tion-vorticity-temperature (ψ−ω−T) formulation governing natural convection defined in 2D enclosured domains. The proposed technique combines strengths of three schemes, i.e. smooth discretisations (Galerkin formulation), powerful high-order approximations (one-dimensional integrated radial-basis-function networks) and pressure-free low-order system (ψ−ω−T formulation). In addition, a new effective way of deriving computational boundary conditions for the vorticity is proposed. Two benchmark test problems, namely free convection in a square slot and a concentric annulus, are considered, where a convergent solution for the former is achieved up to the Rayleigh number of 10⁸.

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