A generalized moving least squares-enhanced Lagrangian particle method for anisotropic dispersion in heterogeneous porous media

Abstract

The Lagrangian particle method (LPM) is a promising alternative to Eulerian grid-based methods for modeling advection-dominant transport, as it avoids numerical diffusion and oscillation. However, the most widely used LPM for subsurface solute transport—Smooth Particle Hydrodynamics (SPH)—typically requires a large number of particles for local numerical approximation due to its low order of consistency, making it computationally expensive. In addition, the conventional SPH method is prone to producing negative concentrations under anisotropic dispersion because of the unphysical dispersive flux computed by the model. To address these two issues, this study proposes a new LPM for solute transport simulation based on the generalized moving least squares (GMLS) method. In this approach, a GMLS-based finite difference method is developed for conservative solute transport, enabling efficient and accurate computation of the required higher-order derivatives. As a result, the proposed GMLS-LPM achieves improved representation of anisotropic dispersion and enhanced robustness in long-term predictions of complex subsurface solute transport. The effectiveness of GMLS-LPM is demonstrated through comparisons with two existing LPMs that employ the conventional SPH method and the finite particle method (FPM) in two anisotropic dispersion scenarios: one in homogeneous porous media and the other in heterogeneous porous media. Under similar CPU time, the GMLS-LPM significantly outperforms both SPH and FPM models. Even with randomly distributed particles, the GMLS-LPM maintains high accuracy and avoids unphysical negative concentrations, highlighting its strong potential as a particle-based model for solute transport.