A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Hejazi, H., Moroney, T., & Liu, F. (2012) A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients. In Turner, Ian (Ed.) 16th Biennial Computational Techniques and Applications Conference, 23-26 September 2012 , Queensland University of Technology, Brisbane, Qld.


Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps.

Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

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ID Code: 60008
Item Type: Conference Item (Presentation)
Refereed: Yes
Additional URLs:
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 Cambridge University Press
Deposited On: 15 May 2013 22:19
Last Modified: 24 Jun 2017 14:36

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