A new fractional finite volume method for solving the fractional diffusion equation

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	A new fractional finite volume method for solving the fractional diffusion equation
	Liu, F. ; Zhuang, P. ; Turner, I. ; Burrag ; Anh, V. ; Zhuang PH(庄平辉)
刊名	http://dx.doi.org/10.1016/j.apm.2013.10.007
	2013
关键词	Boundary conditions Nonlinear equations Numerical methods Partial differential equations Solute transport Three dimensional Two dimensional
英文摘要	The inherent heterogeneities of many geophysical systems often gives rise to fast and slow pathways to water and chemical movement. One approach to model solute transport through such media is by fractional diffusion equations with a space-time dependent variable coefficient. In this paper, a two-sided space fractional diffusion model with a space-time dependent variable coefficient and a nonlinear source term subject to zero Dirichlet boundary conditions is considered. Some finite volume methods to solve a fractional differential equation with a constant dispersion coefficient have been proposed. The spatial discretisation employs fractionally-shifted Grunwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes. However, these finite volume methods have not been extended to two-dimensional and three-dimensional problems in a natural manner. In this paper, a new weighted fractional finite volume method with a nonlocal operator (using nodal basis functions) for solving this two-sided space fractional diffusion equation is proposed. Some numerical results for the Crank-Nicholson fractional finite volume method are given to show the stability, consistency and convergence of our computational approach. This novel simulation technique provides excellent tools for practical problems even when a complex transition zone is involved. This technique can be extend to two-dimensional and three-dimensional problems with complex regions. Crown Copyright ? 2013.
语种	英语
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/91179]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Liu, F.,Zhuang, P.,Turner, I.,et al. A new fractional finite volume method for solving the fractional diffusion equation[J]. http://dx.doi.org/10.1016/j.apm.2013.10.007,2013.
APA	Liu, F.,Zhuang, P.,Turner, I.,Burrag,Anh, V.,&庄平辉.(2013).A new fractional finite volume method for solving the fractional diffusion equation.http://dx.doi.org/10.1016/j.apm.2013.10.007.
MLA	Liu, F.,et al."A new fractional finite volume method for solving the fractional diffusion equation".http://dx.doi.org/10.1016/j.apm.2013.10.007 (2013).