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Numerical simulation for the 3D seepage flow with fractional derivatives in porous media

Liu, Q., Liu, F., Turner, I.W., & Anh, V. (2008) Numerical simulation for the 3D seepage flow with fractional derivatives in porous media. IMA Journal of Applied Mathematics, 74(2), pp. 201-229.

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Abstract

In this paper, the numerical simulation of the 3D seepage flow with fractional derivatives in porous media is considered under two special cases: non-continued seepage flow in uniform media (NCSFUM) and continued seepage flow in non-uniform media (CSF-NUM). A fractional alternating direction implicit scheme (FADIS) for the NCSF-UM and a modified Douglas scheme (MDS) for the CSF-NUM are proposed. The stability, consistency and convergence of both FADIS and MDS in a bounded domain are discussed. A method for improving the speed of convergence by Richardson extrapolation for the MDS is also presented. Finally, numerical results are presented to support our theoretical analysis.

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15 citations in Web of Science®

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228 since deposited on 19 Jan 2010
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ID Code: 29757
Item Type: Journal Article
Keywords: seepage flow, fractional derivative, fractional alternating direction implicit scheme, modified Douglas scheme, stability and convergence, Richardson extrapolation.
DOI: 10.1093/imamat/hxn044
ISSN: 0272-4960
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2008 Oxford University Press
Deposited On: 19 Jan 2010 12:28
Last Modified: 01 Mar 2012 00:04

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