  Our work is motivated by the analysis of ash plume dynamics, arising in the
study of volcanic eruptions. Such phenomena are characterized by large Reynolds
number (exceeding $10^7$) and a large number of polydispersed particles~[1].
Thus, the choice of the methodology to be used is straightforward: we need LES
of a multiphase gas-particles flow. Since the simulation of the behavior of a
large number of dispersed particles is very difficult with Lagrangian methods,
we model the particles as a continuum, Eulerian fluid (dust), by using reduced
models involving two fluids, as proposed in Ref.~[2,3,4]. Moreover, we need a
robust numerical scheme to simultaneously treat compressibility, buoyancy
effects and turbulent dispersal dynamics.
  We analyze the turbulence properties of such models in a homogeneous and
isotropic setting, with the aim of formulating a LES model. In particular, we
examine the development of freely decaying homogeneous and isotropic turbulence
in subsonic regime (the r.m.s. Mach number either 0.2 or 0.5) using
OpenFOAM\textsuperscript{\textregistered}, which is one of the best known CFD
open source software packages.
