Please use this identifier to cite or link to this item:
https://hdl.handle.net/1959.11/5534
Title: | A mass balance based equation method for the fractional advection-dispersion equation: Theory and application | Contributor(s): | Zhang, Xiaoxian (author); Crawford, John W (author); Deeks, Lynda K (author); Sutter, Marc I (author); Bengough, A Glyn (author); Young, Iain (author) | Publication Date: | 2005 | DOI: | 10.1029/2004WR003818 | Handle Link: | https://hdl.handle.net/1959.11/5534 | 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. | Publication Type: | Journal Article | Source of Publication: | Water Resources Research, v.41, p. 1-10 | Publisher: | Wiley-Blackwell Publishing, Inc | Place of Publication: | United States of America | ISSN: | 1944-7973 0043-1397 |
Fields of Research (FoR) 2008: | 050399 Soil Sciences not elsewhere classified 050305 Soil Physics 050303 Soil Biology 060208 Terrestrial Ecology |
Socio-Economic Objective (SEO) 2008: | 961402 Farmland, Arable Cropland and Permanent Cropland Soils | Peer Reviewed: | Yes | HERDC Category Description: | C1 Refereed Article in a Scholarly Journal | Publisher/associated links: | http://hdl.handle.net/10373/152 |
---|---|
Appears in Collections: | Journal Article |
Files in This Item:
File | Description | Size | Format |
---|
SCOPUSTM
Citations
80
checked on May 4, 2024
Page view(s)
882
checked on Mar 9, 2023
Download(s)
2
checked on Mar 9, 2023
Items in Research UNE are protected by copyright, with all rights reserved, unless otherwise indicated.