# 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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## Abstract

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.

Item Type: Article (Commonwealth Reporting Category C) Yes Live Archive Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering (Up to 30 Jun 2013) Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering (Up to 30 Jun 2013) 09 Jan 2010 04:06 27 Sep 2013 02:00 integrated RBFNs; Galerkin approach; streamfunction-vorticity-temperature formulation; natural convection 08 Information and Computing Sciences > 0802 Computation Theory and Mathematics > 080202 Applied Discrete Mathematics01 Mathematical Sciences > 0101 Pure Mathematics > 010104 Combinatorics and Discrete Mathematics (excl. Physical Combinatorics)09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490199 Applied mathematics not elsewhere classified49 MATHEMATICAL SCIENCES > 4904 Pure mathematics > 490404 Combinatorics and discrete mathematics (excl. physical combinatorics)40 ENGINEERING > 4017 Mechanical engineering > 401706 Numerical modelling and mechanical characterisation E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering https://doi.org/10.3970/cmes.2009.044.219 http://eprints.usq.edu.au/id/eprint/6479