A mass balance based numerical method for the fractional advection-dispersion equation: Theory and application

Xiaoxian Zhang, John W. Crawford, Lynda K. Deeks, Marc I. Stutter, A. Glyn Bengough, Iain M. Young

Research output: Contribution to journalArticlepeer-review

80 Scopus citations


The inherent heterogeneity of many geophysical systems often gives rise to fast and slow pathways to water and chemical movement, and one approach to model solute transport through such media is the continuous time random walk (CTRW). One special asymptotic case of the CTRW is the fractional advection-dispersion equation (FADE), which has proven to be a promising alternative to model anomalous dispersion and has been increasingly used in hydrology to model chemical transport in both surface and subsurface water. Most practical problems in hydrology have complicated initial and boundary conditions and need to be solved numerically, but the numerical solution of the FADE is not trivial. In this paper we present a finite volume approach to solve the FADE where the spatial derivative of the dispersion term is fractional. We also give methods to solve different boundary conditions often encountered in practical applications. The linear system resulting from the temporal-spatial discretization is solved using a semi-implicit scheme. The numerical method is derived on the basis of mass balance, and its accuracy is tested against analytical solutions. The method is then applied to simulate tracer movement in a stream and a near-saturated hillslope in a naturally structured upland podzol field in northeast Scotland. Copyright 2005 by the American Geophysical Union.
Original languageEnglish (US)
Pages (from-to)1-10
Number of pages10
JournalWater Resources Research
Issue number7
StatePublished - Jul 1 2005
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

  • Water Science and Technology


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