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