A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

摘要：

The field of fractional dierential equations provides a means for modelling transport processes within complex media which are governed by anomalous transport. Indeed, the application to anomalous transport has been a significant driving force behind the rapid growth and expansion of the literature in the field of fractional calculus. In this paper, we present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. Such an equation allows modelling different flow regime impacts from either side. The finite volume formulation provides a natural way to handle fractional advection-dispersion equations written in conservative form. The novel spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes, while the L1-algorithm is used to discretise the Caputo time fractional derivative. Results of numerical experiments are presented to demonstrate the eectiveness of the approach.

关键词： two-sided time-space fractional advection-dispersion fractional Fick’s law finite volume finite difference shifted Grunwald L1-algorithm

作者: H. Hejazi T. Moroney F. Liu

作者单位: School of Mathematical Sciences, Queensland University ofTechnology, GPO Box 2434, Brisbane, Qld. 40 School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4

会议类型: 国际会议

会议名称: The Fifth Symposium on Fractional Differentiation and Its Applications(第五届国际自动控制联合会分数阶导数及其应用会议)

会议地点: 南京

会议语种:英文

页码: 1-6

在线出版日期: 2012-05-14（万方平台首次上网日期，不代表论文的发表时间）