A generalised finite difference scheme based on compact integrated radial basis function for flow in heterogeneous soils
Article
Article Title | A generalised finite difference scheme based on compact integrated radial basis function for flow in heterogeneous soils |
---|---|
ERA Journal ID | 188 |
Article Category | Article |
Authors | Ngo-Cong, D. (Author), Tien, C.M.T. (Author), Nguyen-Ky, T. (Author), An-Vo, D.-A. (Author), Mai-Duy, N. (Author), Strunin, D. V. (Author) and Tran-Cong, T. (Author) |
Journal Title | International Journal for Numerical Methods in Fluids |
Journal Citation | 85 (7), pp. 404-429 |
Number of Pages | 26 |
Year | 2017 |
Place of Publication | United Kingdom |
ISSN | 0271-2091 |
1097-0363 | |
Digital Object Identifier (DOI) | https://doi.org/10.1002/fld.4386 |
Web Address (URL) | http://onlinelibrary.wiley.com/doi/10.1002/fld.4386/abstract;jsessionid=DA0493844548E50CF42376E90D7DD2CC.f02t01?systemMessage=Please+be+advised+that+we+experienced+an+unexpected+issue+that+occurred+on+Saturday+and+Sunday+January+20th+and+21st+that+caused+ |
Abstract | In the present paper, we develop a generalised finite difference approach based on compact integrated radial basis function (CIRBF) stencils for solving highly nonlinear Richards equation governing fluid movement in heterogeneous soils. The proposed CIRBF scheme enjoys a high level of accuracy and a fast convergence rate with grid refinement owing to the combination of the integrated RBF approximation and compact approximation where the spatial derivatives are discretised in terms of the information of neighbouring nodes in a stencil. The CIRBF method is first verified through the solution of ordinary differential equations, 2-D Poisson equations and a Taylor-Green vortex. Numerical comparisons show that the CIRBF method outperforms some other methods in the literature. The CIRBF method in conjunction with a rational function transformation method and an adaptive time-stepping scheme is then applied to simulate 1-D and 2-D soil infiltrations effectively. The proposed solutions are more accurate and converge faster than those of the finite different method employed with a second-order central difference scheme. Additionally, the present scheme also takes less time to achieve target accuracy in comparison with the 1D-IRBF and HOC schemes. |
Keywords | subsurface flow; heterogeneous soil; Richards equation; radial basis functions; compact approximation; numerical method |
ANZSRC Field of Research 2020 | 490303. Numerical solution of differential and integral equations |
490302. Numerical analysis | |
401706. Numerical modelling and mechanical characterisation | |
Public Notes | File reproduced in accordance with the copyright policy of the publisher/author. |
Byline Affiliations | Computational Engineering and Science Research Centre |
School of Mechanical and Electrical Engineering | |
School of Agricultural, Computational and Environmental Sciences | |
Institution of Origin | University of Southern Queensland |
Funding source | Grant ID SRF-SRI |
https://research.usq.edu.au/item/q4748/a-generalised-finite-difference-scheme-based-on-compact-integrated-radial-basis-function-for-flow-in-heterogeneous-soils
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