A finite-volume method based on compact local integrated radial basis function approximations for second-order differential problems
Article
Article Title | A finite-volume method based on compact local integrated radial basis function approximations for second-order differential problems |
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ERA Journal ID | 3460 |
Article Category | Article |
Authors | Hoang-Trieu, T.-T. (Author), Mai-Duy, N. (Author), Tran, C.-D. (Author) and Tran-Cong, T. (Author) |
Journal Title | CMES Computer Modeling in Engineering and Sciences |
Journal Citation | 91 (6), pp. 485-516 |
Number of Pages | 32 |
Year | 2013 |
Place of Publication | United States |
ISSN | 1526-1492 |
1526-1506 | |
Digital Object Identifier (DOI) | https://doi.org/10.3970/cmes.2013.091.485 |
Web Address (URL) | https://www.techscience.com/CMES/v91n6/26929 |
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. |
Keywords | compact local stencils; finite volume method; high-order approximations; integrated radial basis functions; natural convection |
ANZSRC Field of Research 2020 | 490303. Numerical solution of differential and integral equations |
490101. Approximation theory and asymptotic methods | |
460605. Distributed systems and algorithms | |
Public Notes | Files associated with this item cannot be displayed due to copyright restrictions. |
Byline Affiliations | Computational Engineering and Science Research Centre |
Institution of Origin | University of Southern Queensland |
https://research.usq.edu.au/item/q204z/a-finite-volume-method-based-on-compact-local-integrated-radial-basis-function-approximations-for-second-order-differential-problems
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