Parallel algorithms for particle tracking are central to the modeling of a wide range of physical processes including cloud formation, spray combustion, flows of ash from wildfires and reactions in nuclear systems. Here we focus on tracking the motion of cloud droplets with radii in the range from 10 to 60
that are suspended in a turbulent flow field. The gravity and droplet inertia are simultaneously considered. Our codes for turbulent flow and droplet motion are fully parallelized in MPI (message passing interface), allowing efficient computation of dynamic and kinematic properties of a polydisperse suspension with more than 10
droplets. Previous direct numerical simulations (DNS) of turbulent collision, due to their numerical complexity, are typically limited to small Taylor microscale flow Reynolds numbers (~100), or equivalently to a small physical domain size at a given flow dissipation rate in a turbulent cloud. The difficulty lies in the necessity to treat simultaneously a field representation of the turbulent flow and free movement of particles. We demonstrate here how the particle tracking and collision can be handled within the framework of a specific domain decomposition. Our newly developed MPI code can be run on computers with distributed memory and as such can take full advantage of available computational resources. We discuss scalability of five major computational tasks in our code: collision detection, advancing particle position, fluid velocity interpolation at particle location, implementation of the periodic boundary condition, using up to 128 CPUs. In most tested cases we achieved parallel efficiency above 100 %, due to a reduction in effective memory usage. Finally, our MPI results of pair statistics are validated against a previous OpenMP implementation.