A stable and accurate control-volume technique based on integrated radial basis function networks for fluid-flow problems

Mai-Duy, N. and Tran-Cong, T. (2011) A stable and accurate control-volume technique based on integrated radial basis function networks for fluid-flow problems. In: ACAM 6: 6th Australasian Congress on Applied Mechanics , 12-15 Dec 2010, Perth, Western Australia.

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Abstract

Radial basis function networks (RBFNs) have been widely used in solving partial differential equations as they
are able to provide fast convergence. Integrated RBFNs have the ability to avoid the problem of reduced convergence-rate caused by differentiation. This paper is concerned with the use of integrated RBFNs in the context of control-volume discretisations for the simulation of fluid-flow problems. Special attention is given to (i) the development of a stable high-order upwind scheme for the convection term and (ii) the development of a local high-order approximation scheme for the diffusion term. Benchmark
problems including the lid-driven triangular-cavity flow are
employed to validate the present technique. Accurate results at high values of the Reynolds number are obtained using relatively-coarse grids.

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Item Type:	Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed:	Yes
Item Status:	Live Archive
Additional Information:	Published Version not available due to copyright policy of publisher. Paper originally presented at the 6th Australasian Congress on Applied Mechanics (ACAM6), 12-15 December 2010, Perth, Western Australia pp510-519.
Faculty/School / Institute/Centre:	Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering (Up to 30 Jun 2013)
Faculty/School / Institute/Centre:	Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering (Up to 30 Jun 2013)
Date Deposited:	29 Jan 2012 04:42
Last Modified:	08 Mar 2018 23:46
Uncontrolled Keywords:	cartesian grid; control volume; deferred correction technique; integrated rbf; upwind scheme
Fields of Research (2008):	01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations 08 Information and Computing Sciences > 0802 Computation Theory and Mathematics > 080202 Applied Discrete Mathematics 09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Fields of Research (2020):	49 MATHEMATICAL SCIENCES > 4903 Numerical and computational mathematics > 490303 Numerical solution of differential and integral equations 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490199 Applied mathematics not elsewhere classified 40 ENGINEERING > 4017 Mechanical engineering > 401706 Numerical modelling and mechanical characterisation
Socio-Economic Objectives (2008):	E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI:	https://doi.org/10.1080/14484846.2011.11464606
URI:	http://eprints.usq.edu.au/id/eprint/20251

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