Impact of absorbing and reflective boundaries on fractional derivative models: Quantification, evaluation and application

Zhang, Yong1,2; Yu, Xiangnan3; Li, Xicheng4; Kelly, James F.5,6; Sun, HongGuang1; Zheng, Chunmiao7

2019-06

10.1016/j.advwatres.2019.02.011

ADVANCES IN WATER RESOURCES   影响因子和分区

0309-1708

1872-9657

Fractional-derivative models are promising tools for characterizing non-Fickian transport in heterogeneous media. Most fractional models utilize an infinite domain, although realistic problems occur on bounded domains. To quantify the impact of a finite or semi-infinite boundary on non-Fickian transport in natural geological media, this study evaluates three representative fractional advection-dispersion equations (FADEs) with absorbing or reflective boundaries. Results show that the temporal FADE (t-FADE) with absorbing/reflective boundaries has analytical solutions, the one-sided spatial FADE (s-FADE) in bounded-domains can be simulated using an Eulerian solver, and the tempered spatiotemporal FADE (st-FADE) can be efficiently solved using a fully Lagrangian approach. Further simulations reveal important impacts of absorbing/reflective boundaries on non-Fickian diffusion. First, the "local" reflective boundary mainly affects the solute dynamics near the boundary for non-local super-diffusion, while the "nonlocal" reflective boundary changes the overall pattern of non-Fickian transport in the whole domain. Second, the total mass for solutes in absorbing boundaries declines non-linearly with respect to time. Third, the mobile and immobile phase plumes tend to respond differently to the boundary because of their different transport mechanisms. Fourth, a field application shows that both the s-FADE with a negative skewness and the t-FADE can be used to quantify bounded-domain sub-diffusion for fluorescein dye transport in the Red Cedar River with a large Peclet number, although the determination of the upstream boundary position contains high uncertainty. Evaluation of the boundary impact on sub-diffusion, super-diffusion, and their mixture may improve our understanding of the nature of non-Fickian transport in bounded domains.

Fractional advection-dispersion equation Non-Fickian diffusion Bounded domain Absorbing boundary Reflective boundary

SCI ; EI

英语

其他

US NSF[EAR-1344280]

Water Resources

Water Resources

WOS:000468138400011

ELSEVIER SCI LTD

20191806848453

Advection ; Dispersions ; Lagrange multipliers

Materials Science:951

ENGINEERING

Web of Science

1.Hohai Univ, Coll Mech & Mat, State Key Lab Hydrol Water Resources & Hydraul En, Nanjing 210098, Jiangsu, Peoples R China
2.Univ Alabama, Dept Geol Sci, Tuscaloosa, AL 35487 USA
3.Hohai Univ, Coll Mech & Mat, Dept Engn Mech, Nanjing 210098, Jiangsu, Peoples R China
4.Univ Jinan, Sch Math Sci, Jinan 250022, Shandong, Peoples R China
5.Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA
6.Naval Res Lab, Code 7600, Washington, DC 20375 USA
7.Southern Univ Sci & Technol, Sch Environm Sci & Engn, Guangdong Prov Key Lab Soil & Groundwater Pollut, Shenzhen 518055, Guangdong, Peoples R China

Zhang, Yong,Yu, Xiangnan,Li, Xicheng,et al. Impact of absorbing and reflective boundaries on fractional derivative models: Quantification, evaluation and application[J]. ADVANCES IN WATER RESOURCES,2019,128:129-144.

Zhang, Yong,Yu, Xiangnan,Li, Xicheng,Kelly, James F.,Sun, HongGuang,&Zheng, Chunmiao.(2019).Impact of absorbing and reflective boundaries on fractional derivative models: Quantification, evaluation and application.ADVANCES IN WATER RESOURCES,128,129-144.

Zhang, Yong,et al."Impact of absorbing and reflective boundaries on fractional derivative models: Quantification, evaluation and application".ADVANCES IN WATER RESOURCES 128(2019):129-144.