A control volume scheme using compact integrated radial basis function stencils for solving the Richards equation

Ngo-Cong, Duc and Mai-Duy, Nam and Antille, Diogenes L. and van Genuchten, Martinus Th. (2019) A control volume scheme using compact integrated radial basis function stencils for solving the Richards equation. Journal of Hydrology, 580. pp. 1-10. ISSN 0022-1694

Abstract

A new control volume approach is developed based on compact integrated radial basis function (CIRBF) stencils for solution of the highly nonlinear Richards equation describing transient water flow in variably saturated soils. Unlike the conventional control volume method, which is regarded as second-order accurate, the proposed approach has high-order accuracy owing to the use of a compact integrated radial basis function approximation that enables improved flux predictions. The method is used to solve the Richards equation for transient flow in 1D homogeneous and heterogeneous soil profiles. Numerical results for different boundary conditions, initial conditions and soil types are shown to be in good agreement with Warrick's semi-analytical solution and simulations using the HYDRUS-1D software package. Results obtained with the proposed method were far less dependent upon the grid spacing than the HYDRUS-1D finite element solutions.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Pre-print embargoed until 17 October 2020.
Faculty/School / Institute/Centre: Current - Institute for Advanced Engineering and Space Sciences (1 Aug 2018 -)
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Mechanical and Electrical Engineering (1 July 2013 -)
Date Deposited: 21 Jan 2020 02:50
Last Modified: 29 Jan 2020 01:39
Uncontrolled Keywords: Richards equation; finite volume method; integrated radial basis function; compact stencil; unsaturated flow.
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis
01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010399 Numerical and Computational Mathematics not elsewhere classified
05 Environmental Sciences > 0503 Soil Sciences > 050305 Soil Physics
Funding Details:
Identification Number or DOI: 10.1016/j.jhydrol.2019.124240
URI: http://eprints.usq.edu.au/id/eprint/37201

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