二维分数阶对流-弥散方程的数值解

二维分数阶对流-弥散方程的数值解

周璐莹1，吴吉春1,2，夏源1

1. 南京大学水科学系，南京 210093；2. 南京大学污染控制与资源化研究国家重点实验室，南京 210093

收稿日期:2009-12-20 修回日期:2009-12-20 出版日期:2009-12-20 发布日期:2009-12-20

Numerical Solutions of Two-Dimension Fractional Advection-Dispersion Equations

ZHOU Lu-ying1, WU Ji-chun1,2, XIA Yuan1

1. Department of Hydro-sciences , Nanjing University, Nanjing 210093, China;2. State Key Laboratory of Pollution Control and Resources Reuse, Nanjing University, Nanjing 210093, China

Received:2009-12-20 Revised:2009-12-20 Online:2009-12-20 Published:2009-12-20

摘要/Abstract

摘要： 对二维时间分数阶对流-弥散方程和二维空间分数阶对流-弥散方程分别建立了差分格式，实现了对其的数值求解。针对理想算例进行计算求解，分析了时间和空间分数阶阶数取不同值时的扩散变化规律，验证了各自所描述的时间相关性与空间相关性。同时与传统的二维整数阶对流-弥散方程的求解结果作了对比。当时间和空间分数阶阶数α与γ分别取整数时，二维时间分数阶对流-弥散方程和二维空间分数阶对流-弥散方程都与传统二维整数阶对流-弥散方程的计算结果相同，说明提出的对二维分数阶对流-弥散方程的数值求解方法是可行的。其结果对地下水溶质运移的进一步研究提供了有效的手段。

Abstract: In this paper, two numerical schemes were developed for both two-dimensional temporally and two-dimensional spatially fractional advection-dispersion equations and their numerical solutions were achieved. We analyzed the variation of diffusion with the fractional order by applying the numerical scheme in a test case and verified the temporal and spatial correlation. Then we compared the calculation results of our new schemes with the solution of traditional two-dimensional advection-dispersion equation. When the fractional orders are integer, the calculation results of both two-dimensional temporally and two-dimensional spatially fractional advection-dispersion equations are the same as that of the traditional integer order advection-dispersion equation. These indicate that the numerical schemes for the two-dimensional fractional advection-dispersion equations developed in this paper are feasible.

周璐莹，吴吉春,夏源. 二维分数阶对流-弥散方程的数值解[J]. J4.

ZHOU Lu-ying1, WU Ji-chun1,2, XIA Yuan1. Numerical Solutions of Two-Dimension Fractional Advection-Dispersion Equations[J]. J4.