An Interactively Corrected Smoothed Particle Hydrodynamics (IC‐SPH) for Simulating Solute Transport in a Nonuniform Velocity Field

Abstract

AbstractThe Smoothed Particle Hydrodynamics (SPH) method is a Lagrangian approach that has been widely used to eliminate numerical dispersion for solving advection‐dispersion equation (ADE) of groundwater solute transport under advection‐dominated situations. It has been found that accuracy of SPH results is severely deteriorated, when particles are irregularly distributed in a model domain with heterogeneous hydraulic conductivity. To resolve this problem, we developed a new approach called Interactively Corrected SPH (IC‐SPH), which is an improved version of the Corrected SPH (C‐SPH) method. IC‐SPH uses an interactively corrected kernel gradient to construct concentration gradients used to solve ADE. This correction is made for each particle by using not only the particle's neighbor particles within the particle's support domain but also the particles within each neighbor particle's 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, while IC‐SPH is more computationally expensive than SPH and C‐SPH, IC‐SPH produces more accurate ADE solutions, and converges faster to the analytical solution. IC‐SPH is mathematically general, and can be applied to a wide range of problems that require solving ADE.