QUT ePrints

Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

Chen, S., Liu, F., & Burrage, K. (2012) Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media. In Chen, Wen, Sun, HongGuang, & Balaenu, Dumitru (Eds.) The Proceedings of the 5th Symposium on Fractional Differentiation and Its Applications, Hohai University, Hohai University, Nanjing, pp. 1-7.

View at publisher

Abstract

Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcys law with variable order Riemann-Liouville fractional derivatives, this leads to a new variable-order fractional percolation equation. In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.

Impact and interest:

Citation countsare sourced monthly from Scopus and Web of Science® citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.

ID Code: 51445
Item Type: Conference Paper
Keywords: Percolation flow problems, fractional-order behavior, fractional derivative of variable order, fractional percolation equation, implicit difference method, alternating direct method, stability, convergence.
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 [please consult the author]
Deposited On: 06 Jul 2012 08:22
Last Modified: 13 Jun 2013 00:54

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page