Finite difference approximations for fractional advection-dispersion flow equations

Authors:
Mark M. Meerschaert;Charles Tadjeran
Affiliations:
Department of Mathematics and Statistics, University of Nevada, Reno, NV;Department of Mathematics and Statistics, University of Nevada, Reno, NV
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

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Abstract

Fractional advection-dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper we develop practical numerical methods to solve one dimensional fractional advection-dispersion equations with variable coefficients on a finite domain. The practical application of these results is illustrated by modeling a radial flow problem. Use of the fractional derivative allows the model equations to capture the early arrival of tracer observed at a field site.