On the accuracy of simulating mixing by random-walk particle-based mass-transfer algorithms

TL;DR

This paper evaluates various particle-based mass transfer algorithms for simulating mixing, highlighting their accuracy, computational complexity, and practical applicability for different particle counts.

Contribution

It compares implicit, explicit, and mixed methods for particle mass transfer, analyzing their accuracy and computational efficiency in simulating mixing processes.

Findings

All algorithms are accurate to order Δt.

Implicit methods require O(N^3) calculations, explicit methods require O(N^2).

Explicit methods are more practical for simulations with more than 5,000 particles.

Abstract

Several algorithms have been used for mass transfer between particles undergoing advective and macro-dispersive random walks. The mass transfer between particles is required for general reactions on, and among, particles. The mass transfer is shown to be diffusive, and may be simulated using implicit, explicit, or mixed methods. All algorithms investigated are accurate to $\mathcal{O}(\Delta t)$. For $N$ particles, the implicit and semi-implicit methods require inverse matrix solutions and $\mathcal{O}(N^3)$ calculations. The explicit methods use forward matrix solves and require only $\mathcal{O}(N^2)$ calculations. Practically, this means that naive implementations with more than about 5,000 particles run more reliably using explicit methods