A Galerkin-RBF Approach for the Streamfunction-Vorticity-Temperature Formulation of Natural Convection in 2D Enclosured Domains
D. Ho-Minh; N. Mai-Duy and T. Tran-Cong

doi:10.3970/cmes.2009.044.219
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 44, No. 3, pp. 219-248, 2009
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Keywords Integrated RBFNs, Galerkin approach, streamfunction-vorticity-tem -perature formulation, natural convection.
Abstract This paper reports a new discretisation technique for the streamfunc -tion-vorticity-temperature (y-w-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 (y-w-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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