Compact local integrated RBF stencil based on finite volume formulation for second-order differential problems
Paper
Paper/Presentation Title | Compact local integrated RBF stencil based on finite volume formulation for second-order differential problems |
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Presentation Type | Paper |
Authors | Hoang-Trieu, T.-T. (Author), Mai-Duy, N. (Author), Tran, C.-D. (Author) and Tran-Cong, T. (Author) |
Editors | Gu, Y. T. and Saha, Suvash C. |
Journal or Proceedings Title | Proceedings of the 4th International Conference on Computational Methods (ICCM 2012) |
Number of Pages | 10 |
Year | 2012 |
Place of Publication | Brisbane, Australia |
ISBN | 9781921897542 |
Web Address (URL) of Paper | http://www.iccm-2012.org/ |
Conference/Event | 4th International Conference on Computational Methods (ICCM 2012) |
Event Details | 4th International Conference on Computational Methods (ICCM 2012) Event Date 25 to end of 28 Nov 2012 Event Location Gold Coast, Australia |
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. |
Keywords | integrated RBF; compact local IRBF approximations; finite volume method; thermal natural convection flows |
ANZSRC Field of Research 2020 | 490303. Numerical solution of differential and integral equations |
401706. Numerical modelling and mechanical characterisation | |
Public Notes | No evidence of copyright restrictions preventing deposit. |
Byline Affiliations | Computational Engineering and Science Research Centre |
Institution of Origin | University of Southern Queensland |
https://research.usq.edu.au/item/q1x12/compact-local-integrated-rbf-stencil-based-on-finite-volume-formulation-for-second-order-differential-problems
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