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

Thomas Jourdan (1) , Gabriel Stoltz (2, 3) , Frédéric Legoll (4, 2) , Laurent Monasse (3)

1 SRMP - Service de recherches de métallurgie physique
2 MATHERIALS - MATHematics for MatERIALS
3 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
4 navier umr 8205 - Laboratoire Navier

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.

Keywords: Ostwald ripening; Fokker-Planck equation; Cluster dynamics; Rate equations

Domains: Materials Science [cond-mat.mtrl-sci]; Computational Physics [physics.comp-ph]

Thomas Jourdan, Gabriel Stoltz, Frédéric Legoll, Laurent Monasse. An accurate scheme to solve cluster dynamics equations using a Fokker-Planck approach. Computer Physics Communications, 2016, 207, pp.170. ⟨10.1016/j.cpc.2016.06.001⟩. ⟨cea-01302986v2⟩