A finite-volume method based on compact local integrated radial basis function approximations for second-order differential problems

Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2013) A finite-volume method based on compact local integrated radial basis function approximations for second-order differential problems. CMES: Computer Modeling in Engineering and Sciences, 91 (6). pp. 485-516. ISSN 1526-1492

Abstract

In this paper, compact local integrated radial basis function (IRBF) stencils reported in [Mai-Duy and Tran-Cong (2011) Journal of Computational Physics 230(12), 4772-4794] are introduced into the finite-volume/subregion - collocation formulation for the discretisation of second-order differential problems defined on rectangular and non-rectangular domains. The problem domain is simply represented by a Cartesian grid, over which overlapping compact local IRBF stencils are utilised to approximate the field variable and its derivatives. The governing differential equation is integrated over non-overlapping control volumes associated with grid nodes, and the divergence theorem is then applied to convert volume integrals into surface/line integrals. Line integrals are evaluated by means of the middle point rule (i.e. second-order integration scheme) and three-point Gaussian quadrature rule (i.e. high-order integration scheme). The accuracy of the proposed method is numerically investigated through the solution of several test problems including natural convection in an annulus. Numerical results indicate that (i) the proposed method produces accurate results using relatively coarse grids and (ii) the three-point integration scheme is generally more accurate than the middle point scheme.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Copyright © 2013 Tech Science Press. Published version deposited in accordance with the copyright policy of the publisher.
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - No Department
Date Deposited: 05 Aug 2013 02:53
Last Modified: 12 Nov 2015 05:45
Uncontrolled Keywords: compact local stencils; finite volume method; high-order approximations; integrated radial basis functions; natural convection
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods
08 Information and Computing Sciences > 0805 Distributed Computing > 080501 Distributed and Grid Systems
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.3970/cmes.2013.091.485
URI: http://eprints.usq.edu.au/id/eprint/23852

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