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

被引：24

作者：

Hejazi, Hala ^{[1
]}

Moroney, Timothy ^{[1
]}

Liu, Fawang ^{[1
]}

机构：

[1] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia

来源：

CENTRAL EUROPEAN JOURNAL OF PHYSICS | 2013年 / 11卷 / 10期

关键词：

two-sided time-space fractional advection-dispersion; fractional Fick's law; finite volume; finite difference; shifted Grunwald; ANOMALOUS DIFFUSION;

D O I：

10.2478/s11534-013-0317-y

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. 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. We demonstrate how the finite volume formulation provides a natural, convenient and accurate means of discretising this equation in conservative form, compared to using a conventional finite difference approach. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

引用

页码：1275 / 1283

页数：9

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