  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.
