A generalised finite difference scheme based on compact integrated radial basis function for flow in heterogeneous soils

Ngo-Cong, D. and Tien, C.M.T. and Nguyen-Ky, T. and An-Vo, D.-A. and Mai-Duy, N. and Strunin, D. V. and Tran-Cong, T. (2017) A generalised finite difference scheme based on compact integrated radial basis function for flow in heterogeneous soils. International Journal for Numerical Methods in Fluids, 85 (7). pp. 404-429. ISSN 0271-2091

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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.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: This is the peer reviewed version of the following article: Ngo-Cong D, Tien CMT, Nguyen-Ky T, et al. A generalised finite difference scheme based on compact integrated radial basis function for flow in heterogeneous soils. Int J Numer Meth Fluids. 2017;85:404–429., which has been published in final form at https://doi.org/10.1002/fld.4386. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Mechanical and Electrical Engineering
Date Deposited: 29 Jan 2018 01:19
Last Modified: 06 Nov 2018 02:45
Uncontrolled Keywords: subsurface flow; heterogeneous soil; Richards equation; radial basis functions; compact approximation; numerical method
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
E Expanding Knowledge > 97 Expanding Knowledge > 970107 Expanding Knowledge in the Agricultural and Veterinary Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Funding Details:
Identification Number or DOI: 10.1002/fld.4386
URI: http://eprints.usq.edu.au/id/eprint/33258

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