  The purpose of this paper is to give an overview in the realm of numerical
computations of polydispersed turbulent two-phase flows, using a mean-field/PDF
approach. In this approach, the numerical solution is obtained by resorting to
a hybrid method where the mean fluid properties are computed by solving
mean-field (RANS) equations with a classical finite volume procedure whereas
the local instantaneous properties of the particles are determined by solving
stochastic differential equations (SDEs). The fundamentals of the general
formalism are recalled and particular attention is focused on a specific
theoretical issue: the treatment of the multiscale character of the dynamics of
the discrete particles, that is the consistency of the system of SDEs in
asymptotic cases. Then, the main lines of the particle/mesh algorithm are given
and some specific problems, related to the integration of the SDEs, are
discussed, for example, issues related to the specificity of the treatment of
the averaging and projection operators, the time integration of the SDEs (weak
numerical schemes consistent with all asymptotic cases), and the computation of
the source terms. Practical simulations, for three different flows, are
performed in order to demonstrate the ability of both the models and the
numerics to cope with the stringent specificities of polydispersed turbulent
two-phase flows.
