  In this work, we discuss some points relevant for stochastic modelling of
one- and two-phase turbulent flows. In the framework of stochastic modelling,
also referred to PDF approach, we propose a new Langevin model including all
viscosity effects and thus that is consistent with viscous Navier-Stokes
equations. In the second part of the work, we show how to develop a
second-order unconditionally stable numerical scheme for the stochastic
equations proposed. Accuracy and consistency of the numerical scheme is
demonstrated analytically. In the last part of the work, we study the fluid
flow in a channel flow with the proposed viscous method. A peculiar approach is
chosen: the flow is solved with a Eulerian method and after with the Lagrangian
model proposed which uses some of the Eulerian quantities. In this way
attention is devoted to the issue of consistency in hybrid Eulerian/Lagrangian
methods. It is shown that the coupling is important indeed and that to couple
the Lagrangian model to an Eulerian one which is not consistent with the same
turbulence physics leads to large errors. This part of the work complements a
recent article [Chibbaro and Minier International Journal of Multiphase flows
submitted (arXiv:0912.2045)]
