Compact local integrated RBF stencil based on finite volume formulation for second-order differential problems

Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2012) Compact local integrated RBF stencil based on finite volume formulation for second-order differential problems. In: 4th International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold Coast, Australia.

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Abstract

In this paper, compact local integrated radial basis function (RBF) stencils (Mai-Duy and Tran-Cong, 2011) are incorporated into the finite-volume formulation for the discretisation of second order differential problems. The unknown field variable and its derivatives are approximated using compact integrated RBFs defined on local regions that cover the problem domain. The governing equation is integrated over non-overlapping control volumes associated with nodes, and the divergence theorem is then applied to convert volume integrals into line integrals. Line integrals are evaluated by the middle point rule. The proposed scheme is numerically verified through the solution of several test problems including natural convection flows. Numerical results indicate that the proposed method outperforms the standard finite volume method.


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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed: Yes
Item Status: Live Archive
Additional Information: No evidence of copyright restrictions preventing deposit.
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 12 Apr 2013 23:49
Last Modified: 18 Sep 2014 03:38
Uncontrolled Keywords: integrated RBF; compact local IRBF approximations; finite volume method; thermal natural convection flows
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI: http://eprints.usq.edu.au/id/eprint/23075

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