  We investigate the nature of gas accretion onto haloes and galaxies at z=2
using cosmological hydrodynamic simulations run with the moving mesh code
AREPO. Implementing a Monte Carlo tracer particle scheme to determine the
origin and thermodynamic history of accreting gas, we make quantitative
comparisons to an otherwise identical simulation run with the smoothed particle
hydrodynamics (SPH) code GADGET-3. Contrasting these two numerical approaches,
we find significant physical differences in the thermodynamic history of
accreted gas in haloes above 10^10.5 solar masses. In agreement with previous
work, GADGET simulations show a cold fraction near unity for galaxies forming
in massive haloes, implying that only a small percentage of accreted gas heats
to an appreciable fraction of the virial temperature during accretion. The same
galaxies in AREPO show a much lower cold fraction, <20% in haloes above 10^11
solar masses. This results from a hot gas accretion rate which, at this same
halo mass, is an order of magnitude larger than with GADGET, while the cold
accretion rate is also lower. These discrepancies increase for more massive
systems, and we explain both as due to numerical inaccuracies in the standard
formulation of SPH. We also observe that the relatively sharp transition from
cold to hot mode dominated accretion, at a halo mass of ~10^11, is a
consequence of comparing past gas temperatures to a constant threshold value
independent of virial temperature. Examining the spatial distribution of
accreting gas, we find that gas filaments in GADGET tend to remain collimated
and flow coherently to small radii, or artificially fragment and form a large
number of purely numerical "blobs". Similar gas streams in AREPO show increased
heating and disruption at 0.25-0.5 virial radii and contribute to the hot gas
accretion rate in a manner distinct from classical cooling flows.
