An Interactively Corrected Smoothed Particle Hydrodynamics (IC-SPH) for Simulating Solute Transport in Heterogeneous Porous Media

The Smoothed Particle Hydrodynamics (SPH) method is a Lagrangian approach that has been widely used to eliminate numerical dispersion for solving advection-dispersion equation of groundwater solute transport under advection-dominated situations. It has been found that accuracy of SPH results is severely deteriorated by irregular distribution of particles in a model domain with heterogeneous hydraulic conductivity. To resolve this problem, we developed a new approach, called Interactively Corrected Smoothed Particle Hydrodynamics (IC-SPH). As an improved version of SPH, IC-SPH uses an interactively corrected kernel gradient to construct concentration gradients used to solve the advection-dispersion equation. This correction considers distribution information of not only a particle of interest but also the particles neighbor particles within the particles support domain. We evaluated IC-SPH performance in two numerical studies. One considers diffusive transport with an analytical solution, and the other considers advection-dispersion transport in a heterogeneous field of hydraulic conductivity. For each numerical study, several numerical experiments were conducted using multiple sets of irregularly distributed particles with different levels of particle irregularity. The numerical experiments indicate that, in comparison with the standard SPH, IC-SPH is more computationally demanding, but can substantially increase accuracy of simulated solute concentrations. IC-SPH is mathematically general, and can be applied to a wide range of problems that require solving the advection-dispersion equation.