Open Access

ARTICLE

Local Moving Least Square - One-Dimensional IRBFN Technique: Part I - Natural Convection Flows in Concentric and Eccentric Annuli

D. Ngo-Cong^1,2, N. Mai-Duy¹, W. Karunasena², T. Tran-Cong^1,3

1 Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia.
2 Centre of Excellence in Engineered Fibre Composites, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia.
3 Corresponding author, Email: trancong@usq.edu.au.

Computer Modeling in Engineering & Sciences 2012, 83(3), 275-310. https://doi.org/10.3970/cmes.2012.083.275

Abstract

In this paper, natural convection flows in concentric and eccentric annuli are studied using a new numerical method, namely local moving least square - one dimensional integrated radial basis function networks (LMLS-1D-IRBFN). The partition of unity method is used to incorporate the moving least square (MLS) and one dimensional-integrated radial basis function (1D-IRBFN) techniques in an approach that leads to sparse system matrices and offers a high level of accuracy as in the case of 1D-IRBFN method. The present method possesses a Kronecker-Delta function property which helps impose the essential boundary condition in an exact manner. The method is first verified by the solution of the two-dimensional Poisson equation in a square domain with a circular hole, then applied to natural convection flow problems. Numerical results obtained are in good agreement with the exact solution and other published results in the literature.

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