A Finite Particle Method for Simulating Solute Transport in Heterogeneous Porous Media

Abstract:

Numerical schemes for solving the advection-dispersion equation (ADE) are always subject to numerical dispersion. This problem can be potentially resolved by using the smoothed particle hydrodynamics (SPH) methods that are truly lagrangian and mesh free. However, SPH’s solution accuracy is sensitive to spatial distribution of the particles used in SPH implementation, and the accuracy may deteriorate for heterogeneous flow fields. We propose to resolve this problem by using a finite particle method (FPM), an improved SPH method with better accuracy, for modeling conservative solute transport in heterogeneous porous media. The performance of FPM is evaluated with two two-dimensional numerical experiments. One experiment is based on dispersion of a Gaussian contaminant plume in homogeneous flow field, and the other experiment considers an advection-dispersion process in heterogeneous flow field. We show that, while SPH only has first-order accuracy, the solution of FPM converges to second-order accuracy at different degrees of particle disorder with standard deviation of normally distributed perturbation increasing from 0.25Δx to Δx over a regular equispaced grid with spacing Δx. In addition, FPM achieves better accuracy than conventional SPH in moderately heterogeneous porous media with the standard deviation of log hydraulic conductivity being one. Although FPM’s solutions are more accurate and less sensitive to particle position and smoothing length than SPH solutions are, a convergence analysis shows that FPM is more computationally demanding. Therefore, FPM may be used for solving ADE when existing numerical schemes cannot produce solutions accurate enough.