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, i.e. 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 numericals to cope with the stringent specificities of polydispersed turbulent two-phase flows. q

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This paper discusses stochastic approaches to dispersed two-phase flow modeling. A general probability density function ͑PDF͒ formalism is used since it provides a common and convenient framework to analyze the relations between different formulations. For two-phase flow PDF modeling, a key issue is the choice of the state variables. In a first formulation, they include only the position and velocity of the dispersed particles. The kinetic equation satisfied by the corresponding PDF is derived in a different way using tools from the theory of stochastic differential equations. The final expression is identical to an earlier proposal by Reeks ͓Phys. Fluids A 4, 1290 ͑1992͔͒ obtained with a different method. As the kinetic equation involves the instantaneous fluid velocity sampled along the particle trajectories, it is unclosed. Another, more general, formulation is then presented, where the fluid velocity ''seen'' by the solid particles along their paths is added to the state variables. A diffusion model, where trajectories of the process follow a Langevin type of equation, is proposed for the time evolution equation of the fluid velocity ''seen'' and is discussed. A general PDF formulation that includes both fluid and particle variables, and from which both fluid and particle mean equations can be obtained, is then put forward.