Approximate solutions of two-dimensional caputo fractional diffusion equations

D. P. Zielinski, Vaughan R Voller

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A standard model for non-local diffusive transport, applicable when the heterogeneity length scales are power-law distributed, is to represent the flux in terms of a fractional derivative. Here, a recently proposed scheme for fractional diffusive transport, the control volume weighted flux scheme (CVWFS), which is based on Caputo fractional derivatives, is extended to operate in two or more dimensions. The essential feature in the CVWFS is the representation of the flux at a point as a weighted sum of gradients operating up- and down-stream of that point. Following presentation of the scheme, the convergence and accuracy of the CVWFS, using alternative weightings, is demonstrated and its accuracy illustrated by comparing numerical predictions with two-dimensional analytical solutions.

Original languageEnglish (US)
Title of host publicationProceedings of the 8th International Conference on Engineering Computational Technology, ECT 2012
PublisherCivil-Comp Press
Volume100
ISBN (Print)9781905088553
StatePublished - Jan 1 2012
Event8th International Conference on Engineering Computational Technology, ECT 2012 - Dubrovnik, Croatia
Duration: Sep 4 2012Sep 7 2012

Other

Other8th International Conference on Engineering Computational Technology, ECT 2012
Country/TerritoryCroatia
CityDubrovnik
Period9/4/129/7/12

Keywords

  • Caputo derivative
  • Fractional diffusion
  • Two-dimensions

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