Fokker--Planck Approach of Ostwald Ripening: Simulation of a Modified Lifshitz--Slyozov--Wagner System with a Diffusive Correction

Abstract

We propose a well-balanced scheme for the modified Lifshitz--Slyozov equation, which incorporates a size-diffusion term. The method uses the Fokker--Planck structure of the equation. In turn, large time simulations can be performed with a reduced computational cost, since the time-step constraints are relaxed. The simulations bring out the critical mass threshold and the relaxation to equilibrium, which can be expected from the formal analogies with the Becker--Döring system.