改进时间分数阶模型模拟非Fick溶质运移  

Tempered time-fractional advection-dispersion equation for modeling non-Fickian transport

作　　者：夏源[1] 吴吉春[1] 张勇 

机构地区：[1]南京大学地球科学学院水科学系 [2]Desert Research Institute,NV Las Vegas 89119

出　　处：《水科学进展》2013年第3期349-357,共9页Advances in Water Science

基　　金：国家自然科学基金资助项目(41030746;41172207)~~

摘　　要：通过将经典时间分数阶对流-弥散方程的等待时间分布函数的尾部修改为指数型,推导出了改进时间分数阶对流-弥散方程,并提出有效的时空算子分裂数值求解方法。对两个理想算例和一个实际算例进行计算,结果表明,改进的时间分数阶对流-弥散方程继承了时间分数阶对流-弥散方程能模拟穿透曲线幂率型拖尾分布的优点,还可模拟穿透曲线尾部由幂率型转换到指数型的过程;特征时间λ、分数阶指数γ和两相容量比例系数β共同决定了运移行为。改进的新模型可以区分非均质介质中流动相和非流动相中的溶质浓度,更细微地模拟非Fick溶质运移行为。This study shows in detail how the classical time fractional advection-dispersion equation（TFADE） can be generalized using the concept of tempering.The generalized TFADE model is then approximated by a new spatiotemporal splitting method,which is computationally more efficient than the classical Eulerian solver due to the logic tempering of the time nonlocal dependence in solute transport.Numerical experiments show that the generalized TFADE model captures a broad range of non-Fickian diffusion,where the tempering parameter λ（which is the inverse of the characteristic time）,fractional index γ,and mobile/immobile capacity coefficient β can control the nuance of transport behavior.The model also efficiently distinguishes the mobile phase from the total phase for solute transport through heterogeneous media,which is critical for practical applications.

关 键 词：改进时间分数阶模型 对流-弥散方程 非Fick溶质运移 拖尾分布 地下水数值模拟 

分 类 号：P641[天文地球—地质矿产勘探]