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A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

Hejazi, H., Moroney, T.J., & Liu, F. (2012) A finite volume method for solving the two-sided time-space fractional advection-dispersion equation. In Chen, Wen, Sun, HongGuang, & Baleanu, Dumitru (Eds.) The Proceedings of the 5th Symposium on Fractional Differentiation and Its Applications, Hohai University, Hohai University, Nanjing.

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Abstract

The field of fractional differential equations provides a means for modelling transport processes within complex media which are governed by anomalous transport. Indeed, the application to anomalous transport has been a significant driving force behind the rapid growth and expansion of the literature in the field of fractional calculus. In this paper, we present a finite volume method to solve the time-space two-sided fractional advection dispersion equation on a one-dimensional domain. Such an equation allows modelling different flow regime impacts from either side. The finite volume formulation provides a natural way to handle fractional advection-dispersion equations written in conservative form. The novel spatial discretisation employs fractionally-shifted Gr¨unwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes, while the L1-algorithm is used to discretise the Caputo time fractional derivative. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

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ID Code: 51457
Item Type: Conference Paper
Keywords: two-sided time-space fractional advection-dispersion, fractional Fick’s law, finite volume, finite difference, shifted Gr¨unwald, L1-algorithm
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 09:13
Last Modified: 13 Jun 2013 00:54

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