  In many natural and industrial applications, turbulent flows encompass some
form of dispersed particles. Although this type of multiphase turbulent flow is
omnipresent, its numerical modeling has proven to be a remarkably challenging
problem. Models that fully resolve the particle phase are computationally very
expensive, strongly limiting the number of particles that can be considered in
practice. This warrants the need for efficient reduced order modeling of the
complex system of particles in turbulence that can handle high number densities
of particles. Here, we present an efficient method for point-based simulation
of particles in turbulence that are four-way coupled. In contrast with
traditional one-way coupled simulations, where only the effect of the fluid
phase on the particle phase is modeled, this method additionally captures the
back-reaction of the particle phase on the fluid phase, as well as the
interactions between particles themselves. We focus on the most challenging
case of very light particles or bubbles, which show strong clustering in the
high-vorticity regions of the fluid. This strong clustering poses numerical
difficulties which are systematically treated in our work. Our method is valid
in the limit of small particles with respect to the Kolmogorov scales of the
flow and is able to handle very large number densities of particles. This
methods paves the way for comprehensive studies of the collective effect of
small particles in fluid turbulence for a multitude of applications.
