A compact 9 point stencil based on integrated RBFs for the convection-diffusion equation

Mai-Duy, N. and Thai-Quang, N. and Hoang-Trieu, T.-T. and Tran-Cong, T. (2014) A compact 9 point stencil based on integrated RBFs for the convection-diffusion equation. Applied Mathematical Modelling, 38 (4). pp. 1495-1510. ISSN 0307-904X

Abstract

In this paper, a high-order compact stencil for solving the convection-diffusion equation in two dimensions is proposed. The convection and diffusion terms are both approximated by means of radial basis functions (RBFs) that are constructed over 3 × 3 rectangular stencils. Salient features here are that (i) integration is employed to construct local RBF approximations; and (ii) through the constants of integration, values of the convection-diffusion equation at several selected nodes on the stencil are also enforced. Numerical results indicate that (i) the inclusion of the governing equation into the stencil leads to a significant improvement in accuracy; (ii) when the convection dominates, accurate solutions are obtained at a regime of the RBF width which makes the RBFs peaked; and (iii) high levels of accuracy are achieved using relatively coarse grids.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: © 2013 Elsevier Inc. Published version deposited in accordance with the copyright policy of the publisher.
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Mechanical and Electrical Engineering
Date Deposited: 09 Sep 2013 01:42
Last Modified: 05 Sep 2017 06:03
Uncontrolled Keywords: compact local stencils; convection-diffusion equation; high-order approximations; integrated radial basis functions
Fields of Research : 01 Mathematical Sciences > 0101 Pure Mathematics > 010110 Partial Differential 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: 10.1016/j.apm.2013.08.017
URI: http://eprints.usq.edu.au/id/eprint/24032

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