Development of particle tracking algorithms for various types of finite elements in multi-dimensions

摘要

Particle tracking techniques are popular methods for generating pathlines and travel time information, which can be incorporated into solute transport models to account for the advective component of transport. In particular, the accuracy in determining the Lagrangian concentration in the Eulerian-Lagrangian methods (ELMs) depends on both the particle tracking algorithm and concentration interpolation. In the Eulerian-Lagrangian framework, the Lagrangian concentration will also have a large error if the particle tracking algorithm produces a large error in the final location and travel time of a particle because the Lagrangian concentration is obtained by interpolating the concentration of the global nodes surrounding the target point. Oliveira and Baptista (1998) reported that even moderate tracking errors can affect substantially the accuracy and stability of ELMs when solving transport equations, which can lead to the instability of otherwise stable and very accurate ELMs.