Finite difference approximations for a fractional advection diffusion problem

被引:151
作者
Sousa, Ercilia [1 ]
机构
[1] Univ Coimbra, Dept Math, CMUC, P-3001454 Coimbra, Portugal
关键词
Fractional advection diffusion; Finite differences; Stability; DISPERSION EQUATION; STABILITY ANALYSIS; DYNAMICS APPROACH; ACCURACY; MOTION; ORDER;
D O I
10.1016/j.jcp.2009.02.011
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
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 < alpha <= 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. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码:4038 / 4054
页数:17
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