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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| 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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