  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.
