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Please use this identifier to cite or link to this item: http://hdl.handle.net/10373/152

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Title: A mass balance based numerical method for the fractional advection-dispersion equation: Theory and application
Authors: Zhang, Xiaoxian
Crawford, John W.
Deeks, Lynda K.
Stutter, Marc I.
Bengough, A. Glyn
Young, Iain M.
Affiliation: University of Abertay Dundee. Scottish Informatics, Mathematics, Biology and Statistics Centre
Keywords: Fractional advection-dispersion equation
Anomalous dispersion
Tracer transport
Numerical solutions
Continuous time random walk
Issue Date: Jul-2005
Publisher: American Geophysical Union
Type: Journal Article
Refereed: peer-reviewed
Rights: Published version (c)American Geophysical Union, available from http://www.agu.org/pubs/crossref/2005/2004WR003818.shtml
Citation: Zhang, X. et al. 2005. A mass balance based numerical method for the fractional advection-dispersion equation: Theory and application. Water Resources Research. 41(7). [Online] Available from: DOI: 10.1029/2004WR003818
Abstract: 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.
URI: http://hdl.handle.net/10373/152
ISSN: 0043-1397
Appears in Collections:SIMBIOS Collection

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