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We present two numerical schemes for passive tracer particles in thehydrodynamical moving-mesh code AREPO, and compare their performance forvarious problems, from simple setups to cosmological simulations. The purposeof 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 thermodynamicalhistory of individual fluid parcels to be recorded. We find that thecommonly-used `velocity field tracers', which are advected using the fluidvelocity field, do not in general follow the mass flow correctly, and explainwhy this is the case. This method can result in orders-of-magnitude biases insimulations of driven turbulence and in cosmological simulations, rendering thevelocity field tracers inappropriate for following these flows. We then discussa novel implementation of `Monte Carlo tracers', which are moved along withfluid cells, and are exchanged probabilistically between them following themass flux. This method reproduces the mass distribution of the fluid correctly.The main limitation of this approach is that it is more diffusive than thefluid itself. Nonetheless, we show that this novel approach is more reliablethan what has been employed previously and demonstrate that it is appropriatefor following hydrodynamical flows in mesh-based codes. The Monte Carlo tracerscan also naturally be transferred between fluid cells and other types ofparticles, such as stellar particles, so that the mass flow in cosmologicalsimulations can be followed in its entirety.

Following the flow: tracer particles in astrophysical fluid simulations