Finite difference approximations for a fractional advection diffusion problem

  • Authors:

  • Ercília Sousa

  • Affiliations:

  • CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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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 @a, with 1