Decoupled Finite Particle Method With Normalized Kernel (DFPM‐NK): A Computationally Efficient Method for Simulating Solute Transport in Heterogeneous Porous Media

Abstract

AbstractPrevious studies found that Finite Particle Method (FPM), an improved Smoothed Particle Hydrodynamics (SPH) method, yields more accurate solutions of the advection‐dispersion equation (ADE) than SPH method does when simulating solute transport in heterogeneous porous media. FPM however is computationally more expensive than SPH because FPM needs to solve a correction matrix equation for each particle. While decoupled FPM (DFPM) can reduce computational cost of FPM by using diagonal terms of the matrix equation, DFPM is less accurate than FPM due to discarding off‐diagonal terms of the matrix equation. This study develops the Decoupled Finite Particle Method with Normalized Kernel (DFPM‐NK) to improve computational accuracy of DFPM by using normalized kernels in DFPM. We evaluate computational performance of SPH, FPM, DFPM, and DFPM‐NK using two numerical experiments of ADE with non‐reactive and reactive solute transport in a heterogeneous aquifer. Results of the two experiments indicate that, among the four methods, SPH has the least computational time, but has the worst computational accuracy. DFPM‐NK is substantially more efficient than FPM, and has similar accuracy of FPM. On the other hand, DFPM‐NK and DFPM have similar computational cost, but DFMP‐NK is significantly more accurate than DFPM, especially for heterogeneous hydraulic conductivity fields. We thus recommend to use DFPM‐NK for computationally expensive ADE problems without sacrificing computational accuracy.