A compact 9 point stencil based on integrated RBFs for the convection-diffusion equation
Article
Article Title | A compact 9 point stencil based on integrated RBFs for the convection-diffusion equation |
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ERA Journal ID | 48 |
Article Category | Article |
Authors | Mai-Duy, N. (Author), Thai-Quang, N. (Author), Hoang-Trieu, T.-T. (Author) and Tran-Cong, T. (Author) |
Journal Title | Applied Mathematical Modelling: simulation and computation for engineering and environmental systems |
Journal Citation | 38 (4), pp. 1495-1510 |
Number of Pages | 16 |
Year | 2014 |
Publisher | Elsevier |
Place of Publication | New York, NY. United States |
ISSN | 0307-904X |
1872-8480 | |
Digital Object Identifier (DOI) | https://doi.org/10.1016/j.apm.2013.08.017 |
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. |
Keywords | compact local stencils; convection-diffusion equation; high-order approximations; integrated radial basis functions |
ANZSRC Field of Research 2020 | 490410. Partial differential equations |
490101. Approximation theory and asymptotic methods | |
460605. Distributed systems and algorithms | |
Public Notes | © 2013 Elsevier Inc. Published version deposited in accordance with the copyright policy of the publisher. |
Byline Affiliations | Computational Engineering and Science Research Centre |
Institution of Origin | University of Southern Queensland |
https://research.usq.edu.au/item/q2104/a-compact-9-point-stencil-based-on-integrated-rbfs-for-the-convection-diffusion-equation
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