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

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.

References in corpus (2)

• Dislocation dynamics simulations with climb: kinetics of dislocation loop coarsening controlled by bulk diffusion
• Hybrid deterministic/stochastic algorithm for large sets of rate equations

Cited by in corpus (4)

• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The $O(N)$ model
• Cluster dynamics modelling of materials: a new hybrid deterministic/stochastic coupling approach
• New insight into the diffusion of hydrogen and helium atoms in tungsten
• A mathematical justification of the finite time approximation of Becker-Döring equations by a Fokker-Planck dynamics