Simulating multi-dimensional anomalous diffusion in nonstationary media using variable-order vector fractional-derivative models with Kansa solver

Liu, Xiaoting1; Sun, HongGuang1; Zhang, Yong2; Zheng, Chunmiao3; Yu, Zhongbo4

2019-11

10.1016/j.advwatres.2019.103423

ADVANCES IN WATER RESOURCES   影响因子和分区

0309-1708

1872-9657

Anomalous diffusion can be multiple dimensional and space dependent in large-scale natural media with evolving nonstationary heterogeneity, whose quantification requires an efficient technique. This research paper develops, evaluates, and applies variable-order, vector, spatial fractional-derivative equation (FDE) models with a Kansa solver, to capture spatiotemporal variation of super-diffusion along arbitrary angles (i.e., preferential pathways) in complex geological media. The Kansa approach is superior to the traditional Eulerian solvers in solving the vector FDE models, because it is meshless and can be conveniently extended to mull-dimensional transport processes. Numerical experiments show that the shape parameter, one critical parameter used in the Kansa solver, significantly affects the accuracy and convergence of the numerical solutions. In addition, the collocation nodes need to be assigned uniformly in the model domain to improve the numerical accuracy. Real-world applications also test the feasibility of this novel technique. Hence, the variable-order vector FDE model and the Kansa numerical solver developed in this study can provide a convenient tool to quantify complex anomalous transport in mull-dimensional and non-stationary media with continuously or abruptly changing heterogeneity, filling the knowledge gap in parsimonious non-local transport models developed in the last decades.

Heterogeneity Kansa method Numerical accuracy Shape parameter Variable-order space FDE

SCI ; EI

英语

其他

National Natural Science Foundation of China[11972148] ; National Natural Science Foundation of China[41931292] ; National Natural Science Foundation of China[41831289] ; National Natural Science Foundation of China[11528205]

Water Resources

Water Resources

WOS:000490423900010

ELSEVIER SCI LTD

20193907483763

Numerical methods ; Vectors

Algebra:921.1 ; Numerical Methods:921.6

ENGINEERING

Web of Science

1.Hohai Univ, Coll Mech & Mat, State Key Lab Hydrol Water Resources & Hydraul En, 9 Focheng Xi Rd, Nanjing 210098, Jiangsu, Peoples R China
2.Univ Alabama, Dept Geol Sci, Tuscaloosa, AL 35487 USA
3.Southern Univ Sci & Technol, Sch Environm Sci & Engn, Guangdong Prov Key Lab Soil & Groundwater Pollut, Shenzhen 518055, Peoples R China
4.Hohai Univ, State Key Lab Hydrol Water Resources & Hydraul En, Nanjing 210098, Jiangsu, Peoples R China

Liu, Xiaoting,Sun, HongGuang,Zhang, Yong,et al. Simulating multi-dimensional anomalous diffusion in nonstationary media using variable-order vector fractional-derivative models with Kansa solver[J]. ADVANCES IN WATER RESOURCES,2019,133.

Liu, Xiaoting,Sun, HongGuang,Zhang, Yong,Zheng, Chunmiao,&Yu, Zhongbo.(2019).Simulating multi-dimensional anomalous diffusion in nonstationary media using variable-order vector fractional-derivative models with Kansa solver.ADVANCES IN WATER RESOURCES,133.

Liu, Xiaoting,et al."Simulating multi-dimensional anomalous diffusion in nonstationary media using variable-order vector fractional-derivative models with Kansa solver".ADVANCES IN WATER RESOURCES 133(2019).