# A Galerkin-RBF approach for the streamfunction-vorticity-temperature formulation of natural convection in 2D enclosured domains

Ho-Minh, D. and Mai-Duy, Nam and Tran-Cong, Thanh (2009) A Galerkin-RBF approach for the streamfunction-vorticity-temperature formulation of natural convection in 2D enclosured domains. CMES: Computer Modeling in Engineering and Sciences, 44 (3). pp. 219-248. ISSN 1526-1492

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Ho-Minh_Mai-Duy_Tran-Cong_2009_AV.pdf

This paper reports a new discretisation technique for the streamfunction-vorticity-temperature ($\psi - \omega - T$) 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 ($\psi-\omega-T$ 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 10/8.