Following the flow: tracer particles in astrophysical fluid simulations

We present two numerical schemes for passive tracer particles in the hydrodynamical moving-mesh code arepo, and compare their performance for various problems, from simple set-ups to cosmological simulations. The purpose of tracer particles is to allow the flow to be followed in a Lagrangian way, tracing the evolution of the fluid with time, and allowing the thermodynamical history of individual fluid parcels to be recorded. We find that the commonly used 'velocity field tracers', which are advected using the fluid velocity field, do not in general follow the mass flow correctly, and explain why this is the case. This method can result in order-of-magnitude biases in simulations of driven turbulence and in cosmological simulations, rendering the velocity field tracers inappropriate for following these flows. We then discuss a novel implementation of 'Monte Carlo tracers', which are moved along with fluid cells and are exchanged probabilistically between them following the mass flux. This method reproduces the mass distribution of the fluid correctly. The main limitation of this approach is that it is more diffusive than the fluid itself. Nonetheless, we show that this novel approach is more reliable than that has been employed previously and demonstrate that it is appropriate for following hydrodynamical flows in mesh-based codes. The Monte Carlo tracers can also naturally be transferred between fluid cells and other types of particles, such as stellar particles, so that the mass flow in cosmological simulations can be followed in its entirety.