An accurate scheme to solve cluster dynamics equations using a Fokker-Planck approach

TL;DR

This paper introduces a highly accurate numerical scheme based on a Fokker-Planck approach for solving cluster dynamics equations, emphasizing careful discretization to prevent numerical diffusion and demonstrating its effectiveness on aluminum loop coarsening.

Contribution

The paper develops a novel discretization method using the Kurganov-Noelle-Petrova scheme with MP5 reconstruction for improved accuracy in cluster dynamics simulations.

Findings

The method accurately simulates particle size distributions.

Model choice for energetics has minimal impact on distribution.

Absorption coefficient models significantly affect the results.

Abstract

We present a numerical method to accurately simulate particle size distributions within the formalism of rate equation cluster dynamics. This method is based on a discretization of the associated Fokker-Planck equation. We show that particular care has to be taken to discretize the advection part of the Fokker-Planck equation, in order to avoid distortions of the distribution due to numerical diffusion. For this purpose we use the Kurganov-Noelle-Petrova scheme coupled with the monotonicity-preserving reconstruction MP5, which leads to very accurate results. The interest of the method is highlighted on the case of loop coarsening in aluminum. We show that the choice of the models to describe the energetics of loops does not significantly change the normalized loop distribution, while the choice of the models for the absorption coefficients seems to have a significant impact on it.