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

D. Ngo-Cong1,2, N. Mai-Duy1, W. Karunasena2, T. Tran-Cong1,3

Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia.
Centre of Excellence in Engineered Fibre Composites, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia.
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.

## Keywords

APA Style
Ngo-Cong, D., Mai-Duy, N., Karunasena, W., Tran-Cong, T. (2012). Local moving least square - one-dimensional IRBFN technique: part I - natural convection flows in concentric and eccentric annuli. Computer Modeling in Engineering & Sciences, 83(3), 275-310. https://doi.org/10.3970/cmes.2012.083.275
Vancouver Style
Ngo-Cong D, Mai-Duy N, Karunasena W, Tran-Cong T. Local moving least square - one-dimensional IRBFN technique: part I - natural convection flows in concentric and eccentric annuli. Comput Model Eng Sci. 2012;83(3):275-310 https://doi.org/10.3970/cmes.2012.083.275
IEEE Style
D. Ngo-Cong, N. Mai-Duy, W. Karunasena, and T. Tran-Cong "Local Moving Least Square - One-Dimensional IRBFN Technique: Part I - Natural Convection Flows in Concentric and Eccentric Annuli," Comput. Model. Eng. Sci., vol. 83, no. 3, pp. 275-310. 2012. https://doi.org/10.3970/cmes.2012.083.275

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