  The purpose of this paper is to examine the Lagrangian stochastic modeling of
the fluid velocity seen by inertial particles in a nonhomogeneous turbulent
flow. A new Langevin-type model, compatible with the transport equation of the
drift velocity in the limits of low and high particle inertia, is derived. It
is also shown that some previously proposed stochastic models are not
compatible with this transport equation in the limit of high particle inertia.
The drift and diffusion parameters of these stochastic differential equations
are then estimated using direct numerical simulation (DNS) data. It is observed
that, contrary to the conventional modeling, they are highly space dependent
and anisotropic. To investigate the performance of the present stochastic
model, a comparison is made with DNS data as well as with two different
stochastic models. A good prediction of the first and second order statistical
moments of the particle and fluid seen velocities is obtained with the three
models considered. Even for some components of the triple particle velocity
correlations, an acceptable accordance is noticed. The performance of the three
different models mainly diverges for the particle concentration and the drift
velocity. The proposed model is seen to be the only one which succeeds in
predicting the good evolution of these latter statistical quantities for the
range of particle inertia studied.
