二维分数阶对流-弥散方程的数值解  

Numerical Solutions of Two-Dimension Fractional Advection-Dispersion Equations

作　　者：周璐莹[1] 吴吉春[1,2] 夏源[1] 

机构地区：[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

出　　处：《高校地质学报》2009年第4期569-575,共7页Geological Journal of China Universities

基　　金：国家自然科学基金(40672160)资助

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。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.

关 键 词：二维分数阶对流-弥散方程 反常扩散 时空相关性 数值解 溶质运移 

分 类 号：P641[天文地球—地质矿产勘探]