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

Abstract

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.