Title of article :
Finite difference approximations for a fractional advection diffusion problem
Author/Authors :
Sousa، نويسنده , , Ercيlia، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2009
Pages :
17
From page :
4038
To page :
4054
Abstract :
The use of the conventional advection diffusion equation in many physical situations has been questioned by many investigators in recent years and alternative diffusion models have been proposed. Fractional space derivatives are used to model anomalous diffusion or dispersion, where a particle plume spreads at a rate inconsistent with the classical Brownian motion model. When a fractional derivative replaces the second derivative in a diffusion or dispersion model, it leads to enhanced diffusion, also called superdiffusion. We consider a one-dimensional advection–diffusion model, where the usual second-order derivative gives place to a fractional derivative of order α , with 1 < α ⩽ 2 . We derive explicit finite difference schemes which can be seen as generalizations of already existing schemes in the literature for the advection–diffusion equation. We present the order of accuracy of the schemes and in order to show its convergence we prove they are stable under certain conditions. In the end we present a test problem.
Keywords :
Fractional advection diffusion , stability , Finite differences
Journal title :
Journal of Computational Physics
Serial Year :
2009
Journal title :
Journal of Computational Physics
Record number :
1481497
Link To Document :
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