An Adaptive SPH Method (ADP‐SPH) for Simulating Solute Transport in Heterogeneous Aquifers

Smoothed Particle Hydrodynamics (SPH) is a meshfree, Lagrangian‐based approach used to solve the advection‐dispersion equation (ADE) of groundwater solute transport. It is well known that the accuracy of SPH deteriorates significantly when particles become irregularly distributed, often occurring in heterogeneous aquifers. To address this issue, we develop a new approach, Adaptive Smoothed Particle Hydrodynamics (ADP‐SPH), grounded in the kernel density estimation (KDE) theory. ADP‐SPH employs an adaptive smoothing length, which is a critical factor in SPH approximations to determine the size of the support domain within which particles contribute to the approximations. Unlike traditional adaptive SPH approaches that scale smoothing length solely with particle number density using a fixed empirical factor, the new ADP‐SPH method determines the smoothing length by minimizing KDE‐based estimation error, incorporating particle irregularity into the optimal support domain selection. This enables the smoothing length to dynamically adjust over simulation time in response to both particle density and spatial irregularity, thereby improving the accuracy of SPH‐simulated concentration and concentration gradient approximations. The performance of ADP‐SPH is evaluated through two numerical experiments: diffusion with an analytical solution and advection–dispersion transport in heterogeneous hydraulic conductivity fields. Results demonstrate that ADP‐SPH effectively identifies the optimal smoothing length in the two cases, achieving high accuracy in ADE solutions for both isotropic and anisotropic dispersion scenarios.