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

• Authors: Hala Hejazi , Timothy Moroney , Fawang Liu
• Languages of publication: EN

Abstracts

EN

We present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. The spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes. We demonstrate how the finite volume formulation provides a natural, convenient and accurate means of discretising this equation in conservative form, compared to using a conventional finite difference approach. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

Keywords

EN

two-sided time-space fractional advection-dispersion; fractional Fick’s law; finite volume; finite difference; shifted Grünwald

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 10
• Pages: 1275-1283

Dates

published

1 - 10 - 2013

online

19 - 12 - 2013

Contributors

author

Hala Hejazi

• School of Mathematical Sciences, Queensland University of Technology, GPO BOX 2434, Brisbane, QLD., 4001, Australia

author

Timothy Moroney

• School of Mathematical Sciences, Queensland University of Technology, GPO BOX 2434, Brisbane, QLD., 4001, Australia

author

Fawang Liu

• School of Mathematical Sciences, Queensland University of Technology, GPO BOX 2434, Brisbane, QLD., 4001, Australia

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Identifiers

DOI

10.2478/s11534-013-0317-y