N-dimensional fractional Fokker-Planck equation and its solutions for anomalous radial two-phase flow in porous media
Su, Ninghu (2009) N-dimensional fractional Fokker-Planck equation and its solutions for anomalous radial two-phase flow in porous media. Applied Mathematics and Computation, 213 (2). pp. 506-515.
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Abstract
In this paper we present a time fractional Fokker–Planck equation (fFPE) for radial two-phase flow of liquid and gas in porous media. The fFPE of order α is solved for both two- and three-dimensional flow patterns using the Laplace transform method. The general solutions of the fFPE for both two- and three- dimensional flows are given as a convolution integral of the input and a kernel in the Laplace domain. Special solutions for a large value and a periodic boundary condition are also given in the time domain when the inverse Laplace transform can be found analytically. The fFPE for two-phase flow in porous media presented in this paper is the first report of its kind.
| Item ID: | 4762 |
|---|---|
| Item Type: | Article (Research - C1) |
| ISSN: | 1873-5649 |
| Keywords: | anomalous two-phase flow; fractional Fokker–Planck equation; porous media; 2D and 3D solutions; Laplace transform |
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| Funders: | NSFC; ARC; Fok Ying Tung Edu. Foundation; the Youth Foundation, Dept. Edu., Hunan Province |
| Date Deposited: | 06 Aug 2009 03:44 |
| FoR Codes: | 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010299 Applied Mathematics not elsewhere classified @ 100% |
| SEO Codes: | 96 ENVIRONMENT > 9609 Land and Water Management > 960999 Land and Water Management of Environments not elsewhere classified @ 100% |
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