A Cartesian grid technique based on one-dimensional integrated radial basis function networks for natural convection in concentric annuli

Mai-Duy, Nam and Le-Cao, Khoa and Tran-Cong, Thanh (2008) A Cartesian grid technique based on one-dimensional integrated radial basis function networks for natural convection in concentric annuli. International Journal for Numerical Methods in Fluids, 57 (12). pp. 1709-1730. ISSN 0271-2091

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Abstract

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 high-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.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Deposited in accordance with the copyright policy of the publisher.
Depositing User: Dr Nam Mai-Duy
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 28 Nov 2008 10:56
Last Modified: 02 Jul 2013 23:08
Uncontrolled Keywords: natural convection; Cartesian grid method; multiply-connected domain; integral collocation formulation; radial basis functions
Fields of Research (FOR2008): 09 Engineering > 0915 Interdisciplinary Engineering > 091508 Turbulent Flows
09 Engineering > 0915 Interdisciplinary Engineering > 091504 Fluidisation and Fluid Mechanics
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: doi: 10.1002/fld.1675
URI: http://eprints.usq.edu.au/id/eprint/4571

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