Solving Time-Fractional Advection–Dispersion Equation by Variable Weights Particle Tracking Method

Particle tracking method is an efficient and reliable method to solve time-fractional advection-dispersion equation, which can describe anomalous transport in heterogeneous porous media. However, this method will lead to severe fluctuation or disappearance of solutions if the concentration value is...

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Bibliographic Details
Published in:Journal of statistical physics 2017-09, Vol.168 (6), p.1248-1258
Main Authors: Cao, Shaohua, Jiang, Jianguo, Wu, Jichun
Format: Article
Language:English
Subjects:
Advection
Advection (Earth sciences)
Analysis
Dispersions
Mathematical and Computational Physics
Methods
Particle tracking
Physical Chemistry
Physics
Physics and Astronomy
Porous media
Predation
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Variation
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Summary:Particle tracking method is an efficient and reliable method to solve time-fractional advection-dispersion equation, which can describe anomalous transport in heterogeneous porous media. However, this method will lead to severe fluctuation or disappearance of solutions if the concentration value is small. A variable weights method is developed to conquer the shortcoming of particle tracking method. Then, one-dimensional and two-dimensional time-fractional advection-dispersion equations are solved by the variable weights particle tracking method. Compared to traditional particle tracking method, the variable weights version may eliminate the fluctuation and improve the accuracy by orders of magnitude without more computational cost.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-017-1849-0