The Eulerian description of dilute collisionless suspension

We analyze the statistical properties of an Eulerian fluid model describing the evolution of a suspension of inertial particles in an incompressible flow. Regularity and compressibility of the velocity field for the inertial phase are investigated in the limit of heavy particles by means of numerical simulations in two- and three-dimensional flows. We show that in the small Stokes number regime the Eulerian fluid model is able to capture fine details of the clustering dynamics, and exhibits good agreement with fully Lagrangian simulations of inertial particle trajectories. The fluid description breaks down due to collisions at Stokes numbers $\gtrsim 0.1$, the actual value depending on the carrier flow characteristics.