Studying ballistic aggregation phenomena through efficient Time Stepping approaches

Abstract

This paper deals with the problem of simulating dense dispersed systems composed by large numbers of particles undergoing ballistic aggregation. The most classical approaches for dealing with such problems are represented by the so-called event-driven methods. Despite being more accurate, these methods become computationally very expensive as the number of particles increases. Typically, their computational cost is proportional to the square of the number of particles and thus they become extremely demanding as soon as this number becomes sufficiently large. An alternative approach, called time-stepping, consists in evolving the problem over small time-intervals and to handle all collisions occurring during each time interval simultaneously. In this work, we follow this second direction and we introduce a new time stepping method which recasts the problem of the multiple collisions in a minimization framework. The objective of this work is twofold, first to show that the statistical description of the resulting aggregates obtained with this new time stepping method is sufficiently close to that of the event driven methods. The second goal consists in showing that the computational performance considerably improve when the number of particles becomes sufficiently large. Numerical results obtained in the case of spherical particles moving in a two dimensional box show that these two properties are indeed satisfied by this new method.