We introduce a strategy for the simulation a particulate flow in a 3– dimensional domain. The particles are assumed to be rigid, and the homogeneous fluid flow to be governed by the incompressible Navier–Stokes equations. The system is solved using a predictor-corrector scheme for the Navier–Stokes equations with variable density. The latter scheme is adapted to take into account the solid 10 domain by adopting a volume penalization method. In order to advect efficiently the particles, the approximation of the mass balance equation is carried out by an antidissipative scheme similar to the Ultra-Bee scheme. We conclude with numerical tests in the context of particulate flows.