On the use of surface interpolation techniques in generalised finite volume strategies for simulating transport in highly anisotropic porous media

Pasdunkorale Arachchige, Jayantha & Turner, Ian (2003) On the use of surface interpolation techniques in generalised finite volume strategies for simulating transport in highly anisotropic porous media. Journal of Computational and Applied Mathematics, 152(2003), pp. 199-216.

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Abstract

A control volume technique for solving a representative di3usion equation in an orthotropic medium is considered.The approximation of the cross-di3usion 6ux term is of utmost important for the accuracy of the solution.A preliminary investigation that used exact function values from an available analytical solution to approximate this term during the numerical simulation provided excellent agreement with the exact solution. This &nding motivated the need for accurate surface interpolation techniques for estimating the cross-di3usion term.The use of radial basis functions is a well-known interpolation technique for &tting scattered data, which can be considered as a global interpolating method because function values in the whole solution domain contribute towards the interpolation.A number of radial basis functions (RBF) was used to approximate the gradients in the cross-di3usion 6ux term and it was found that the accuracy of the &nite volume solution was generally poor.It was concluded that the RBF estimated function does not re6ect local variation of the solution, particularly for the gradients.Another strategy for local function estimation concerns the weighted least-squares method.Di3erent variants of this method were analysed here for approximating the cross-di3usion term and it was found that the numerical results well matched the exact solution.The results highlight that the development of an accurate, generalised &nite volume strategy requires a highly accurate 6ux approximation to enable second-order spatial accuracy to be achieved.

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ID Code: 22331
Item Type: Journal Article
Refereed: Yes
Keywords: Discretized equations; Least squares; Overdetermined systems; Polynomial approximations
ISSN: 0377-0427
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2002 Elsevier Science B.V. All rights reserved.
Deposited On: 17 Jun 2009 13:10
Last Modified: 01 Mar 2012 12:08

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