改进时间分数阶模型模拟非Fick溶质运移

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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。

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	夏源
	吴吉春
	张勇

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

Abstract：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.

Key words： tempered time fractional model advection-dispersion equation non-Fickian transport heavy tail groundwater numerical simulation

收稿日期: 2012-05-15

中图分类号:

P641

基金资助:国家自然科学基金资助项目(41030746;41172207)

作者简介: 夏源(1982-),男,贵州遵义人,博士,主要从事地下水数值模拟研究。E-mail:xiayuan82@gmail.com

引用本文:

夏源, 吴吉春, 张勇. 改进时间分数阶模型模拟非Fick溶质运移[J]. , 2013, 24(3): 349-357. XIA Yuan, WU Jichun, ZHANG Yong. Tempered time-fractional advection-dispersion equation for modeling non-Fickian transport. , 2013, 24(3): 349-357.

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http://journal16.magtechjournal.com/Jweb_skxjz/CN/ 或 http://journal16.magtechjournal.com/Jweb_skxjz/CN/Y2013/V24/I3/349

[1]	NEUMAN S P, TARTAKOVSKY D M. Perspective on theories of non-Fickian transport in heterogeneous media[J]. Advances in Water Resources, 2009, 32(5): 670-680.
[2]	施小清,吴吉春,吴剑锋,等. 多个相关随机参数的空间变异性对溶质运移的影响[J]. 水科学进展, 2012,23(4): 509-515.(SHI Xiaoqing,WU Jichun,WU Jianfeng,et al. Effects of the heterogeneity of multiple correlated random parameters on solute transport[J]. Advances in Water Science, 2012,23(4):509-515.(in Chinese))
[3]	陆乐,吴吉春,王晶晶. 多尺度非均质多孔介质中溶质运移的蒙特卡罗模拟[J]. 水科学进展, 2008, 19(3): 333-338.(LU Le,WU Jichun,WANG Jingjing. Monte Carlo modeling of solute transport in a porous medium with multi-scale heterogeneity[J]. Advances in Water Science, 2008,19(3):333-338.(in Chinese))
[4]	陈彦,吴吉春. 含水层渗透系数空间变异性对地下水数值模拟的影响[J]. 水科学进展, 2005, 16(4): 482-487.(CHEN Yan,WU JiChun. Effect of the spatial variability of hydraulic conductivity in aquifer on the numerical simulation of groundwater[J]. Advances in Water Science, 2005,16(4):482-487.(in Chinese))
[5]	施小清,吴吉春,袁永生,等. 含水介质各向异性对渗透系数空间变异性统计的影响[J]. 水科学进展, 2005, 16(5): 679-684.(SHI Xiaoqing,WU Jichun,YUAN Yongsheng,et al. Effect of the anisotropy in porous media on the spatial variability of the hydraulic conductivity[J]. Advances in Water Science, 2005,16(5):679-684.(in Chinese))
[6]	施小清,吴吉春,袁永生. 渗透系数空间变异性研究[J]. 水科学进展, 2005, 16(2): 210-215.(SHI Xiaoqing,WU Jichun,YUAN Yongsheng. Study on the spatial variability of hydraulic conductivity[J]. Advances in Water Science, 2005,16(2): 210-215.(in Chinese))
[7]	张德生,沈冰,沈晋,等. 非均匀土壤中溶质运移的两区模型及其解析解[J]. 水科学进展, 2003, 14(1): 72-78.(ZHANG Desheng,SHEN Bing,SHEN Jin,et al. Two-Region model for solute transport through heterogeneous soils and calculation of the analytical solution[J]. Advances in Water Science, 2003,14(1):72-78.(in Chinese))
[8]	马东豪,王全九. 土壤溶质迁移的两区模型与两流区模型对比分析[J]. 水利学报, 2004(6): 92-97.(MA Donghao,WANG Quanjiu. Analysis of two-region model and two-flow domain model for soil solute transport[J]. Journal of Hydraulic Engineering,2004(6):92-97.(in Chinese))
[9]	HAGGERTY R, GORELICK S M. Multiple-rate mass-transfer for modeling diffusion and surface-reactions in media with pore-scale heterogeneity[J]. Water Resources Research, 1995, 31(10): 2383-2400.
[10]	PATRICK W P, ZHENG C, GORELICK S M. A general approach to advective-dispersive transport with multirate mass transfer[J]. Advances in Water Resources, 2005, 28(1): 33-42.
[11]	SCHUMER R, BENSON D A, MEERSCHAERT M M, et al. Fractal mobile/immobile solute transport[J]. Water Resources Research, 2003, 39(10): 1296.
[12]	夏源,吴吉春. 分数阶对流--弥散方程的数值求解[J]. 南京大学学报:自然科学版, 2007, 43(4): 441-446.(XIA Yuan,WU Jichun. Numerical solutions of fractional advection-dispersion equations[J]. Journal of Nanjing University: Natural Sciences,2007,43(4):441-446.(in Chinese))
[13]	BERKOWITZ B, EMMANUEL S, SCHER H. Non-Fickian transport and multiple-rate mass transfer in porous media[J]. Water Resources Research, 2008, 44(3): W03402.
[14]	METZLER R, KLAFTER J. The random walk's guide to anomalous diffusion: A fractional dynamics approach[J]. Physics Reports, 2000, 339(1): 1-77.
[15]	FOMIN S, CHUGUNOV V, HASHIDA T. Application of fractional differential equations for modeling the anomalous diffusion of contaminant from fracture into porous rock matrix with bordering alteration zone[J]. Transport in Porous Media, 2010, 81(2): 187-205.
[16]	ZHANG Y. Moments for tempered fractional advection-diffusion equations[J]. Journal of Statistical Physics, 2010, 139(5): 915-939.
[17]	黄冠华,黄权中,詹红兵,等. 均质介质中污染物迁移的分数微分对流-弥散模拟[J]. 中国科学:D辑, 2005, 35(z1): 249-254.(HUANG Guanhua,HUANG Quanzhong,ZHAN Hongbing, et al. Fractional advection-dispersion simulation on contaminant transport in homogeneous media[J]. Science in China: Ser D,2005,35(z1):249-254.(in Chinese))
[18]	MEERSCHAERT M M, SCHEFFLER H P, TADJERAN C. Finite difference methods for two-dimensional fractional dispersion equation[J]. Journal of Computational Physics, 2006, 211(1): 249-261.
[19]	ZHANG Y, MEERSCHAERT M M. Gaussian setting time for solute transport in fluvial systems[J]. Water Resour Res, 2011, 47(8): W8601.
[20]	ZHANG Y, BENSON D A, BAEUMER B. Predicting the tails of breakthrough curves in regional-scale alluvial systems[J]. Ground Water, 2007, 45(4): 473-484.