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.

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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.

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ID Code: 51445
Item Type: Conference Paper
Refereed: Yes
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 > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 [please consult the author]
Deposited On: 05 Jul 2012 22:22
Last Modified: 24 Jun 2017 14:35

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