  We present a numerical method to deal efficiently with large numbers of
particles in incompressible fluids. The interactions between particles and
fluid are taken into account by a physically motivated ansatz based on locally
defined drag forces. We demonstrate the validity of our approach by performing
numerical simulations of sedimenting non-Brownian spheres in two spatial
dimensions and compare our results with experiments. Our method reproduces
essential aspects of the experimental findings, in particular the strong
anisotropy of the hydrodynamic bulk self-diffusivities.
