New particle tracking method for 2D steady-state groundwater flow around wells: A modified algorithm using the stream function

Abstract

Particle tracking is an essential process in analyzing groundwater flow and solute transport in aquifers. A drawback of existing particle tracking methods, which are based on approximate estimations of the velocity in a time step, is the accumulative errors of numerous time steps would lead to deviation of particles away from the exact streamlines, especially when pumping and injecting wells exist. In this study, to improve the accuracy of particle tracking for the two-dimensional (2D) steady-state flow around wells, we propose a stream-function-based (SFB) particle tracking method in which a particle is traced along the exact streamline with a given value of the stream function, and the branch cut effect caused by the multivalued stream function around a well is eliminated. Three synthetic cases are used to demonstrate the advantages of the SFB method over the existing Pollock method and the fourth-order Runge-Kutta method. In the cases of a single pumping well and an injecting-pumping well pair, the Pollock and Runge-Kutta methods yield pathways that may be far away from the exact streamline, but the SFB method performs much better. In the case with a pumping well and two injecting wells, the SFB method successfully delineated a narrow capture zone of the pumping well, which requires a high accuracy particle tracking process. Moreover, the accuracy of particle positions obtained by the SFB method is insensitive to the step-travel distance. The study would be useful for accurate investigation of flow fields in aquifers disturbed by wells.