A second order finite volume technique for simulating transport in anisotropic media

Pasdunkorale Arachchige, Jayantha & Turner, Ian W. (2003) A second order finite volume technique for simulating transport in anisotropic media. International Journal of Numerical Methods for Heat and Fluid Flow, 13(1), pp. 31-56.

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An existing two-dimensional finite volume technique is modified by introducing a correction term to increase the accuracy of the method to second order. It is well known that the accuracy of the finite volume method strongly depends on the order of the approximation of the flux term at the control volume (CV) faces. For highly orthotropic and anisotropic media, first order approximations produce inaccurate simulation results, which motivates the need for better estimates of the flux expression. In this article, a new approach to approximate the flux term at the CV face is presented. The discretisation involves a decomposition of the flux and an improved least squares approximation technique to calculate the derivatives of the dependent function on the CV faces for estimating both the cross diffusion term and a correction for the primary flux term. The advantage of this method is that any arbitrary unstructured mesh can be used to implement the technique without considering the shapes of the mesh elements. It was found that the numerical results well matched the available exact solution for a representative transport equation in highly orthotropic media and the benchmark solutions obtained on a fine mesh for anisotropic media. Previously proposed CV techniques are compared with the new method to highlight its accuracy for different unstructured meshes.

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25 citations in Scopus
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5 citations in Web of Science®

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ID Code: 8191
Item Type: Journal Article
Refereed: Yes
Keywords: Flux, Finite volume
DOI: 10.1108/09615530310456750
ISSN: 0961-5539
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)
Divisions: Current > Schools > School of Teacher Education & Leadership
Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2003 Emerald
Deposited On: 22 Jun 2007 00:00
Last Modified: 26 Mar 2013 07:00

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