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

Title
A mass balance based equation method for the fractional advection-dispersion equation: Theory and application
Publication Date
2005
Author(s)
Zhang, Xiaoxian
Crawford, John W
Deeks, Lynda K
Sutter, Marc I
Bengough, A Glyn
Young, Iain
Type of document
Journal Article
Language
en
Entity Type
Publication
Publisher
Wiley-Blackwell Publishing, Inc
Place of publication
United States of America
DOI
10.1029/2004WR003818
UNE publication id
une:5665
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.
Link
Citation
Water Resources Research, v.41, p. 1-10
ISSN
1944-7973
0043-1397
Start page
1
End page
10

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