A Cartesian grid technique based on one-dimensional integrated radial basis function networks for natural convection in concentric annuli
Corresponding Author
N. Mai-Duy
Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia
Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia===Search for more papers by this authorK. Le-Cao
Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia
Search for more papers by this authorT. Tran-Cong
Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia
Search for more papers by this authorCorresponding Author
N. Mai-Duy
Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia
Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia===Search for more papers by this authorK. Le-Cao
Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia
Search for more papers by this authorT. Tran-Cong
Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia
Search for more papers by this authorAbstract
This paper reports a radial basis function (RBF)-based Cartesian grid technique for the simulation of two-dimensional buoyancy-driven flow in concentric annuli. The continuity and momentum equations are represented in the equivalent stream function formulation that reduces the number of equations from three to one, but involves higher-order derivatives. The present technique uses a Cartesian grid to discretize the problem domain. Along a grid line, one-dimensional integrated RBF networks (1D-IRBFNs) are employed to represent the field variables. The capability of 1D-IRBFNs to handle unstructured points with accuracy is exploited to describe non-rectangular boundaries in a Cartesian grid, while the method's ability to avoid the reduction of convergence rate caused by differentiation is instrumental in improving the quality of the approximation of higher-order derivatives. The method is applied to simulate thermally driven flows in annuli between two circular cylinders and between an outer square cylinder and an inner circular cylinder. High Rayleigh number solutions are achieved and they are in good agreement with previously published numerical data. Copyright © 2007 John Wiley & Sons, Ltd.
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