  We present a detailed comparison between the well-known SPH code GADGET and
the new moving-mesh code AREPO on a number of hydrodynamical test problems.
Through a variety of numerical experiments we establish a clear link between
test problems and systematic numerical effects seen in cosmological simulations
of galaxy formation. Our tests demonstrate deficiencies of the SPH method in
several sectors. These accuracy problems not only manifest themselves in
idealized hydrodynamical tests, but also propagate to more realistic simulation
setups of galaxy formation, ultimately affecting gas properties in the full
cosmological framework, as highlighted in papers by Vogelsberger et al. (2011)
and Keres et al. (2011). We find that an inadequate treatment of fluid
instabilities in GADGET suppresses entropy generation by mixing, underestimates
vorticity generation in curved shocks and prevents efficient gas stripping from
infalling substructures. In idealized tests of inside-out disk formation, the
convergence rate of gas disk sizes is much slower in GADGET due to spurious
angular momentum transport. In simulations where we follow the interaction
between a forming central disk and orbiting substructures in a halo, the final
disk morphology is strikingly different. In AREPO, gas from infalling
substructures is readily depleted and incorporated into the host halo
atmosphere, facilitating the formation of an extended central disk. Conversely,
gaseous sub-clumps are more coherent in GADGET simulations, morphologically
transforming the disk as they impact it. The numerical artefacts of the SPH
solver are particularly severe for poorly resolved flows, and thus inevitably
affect cosmological simulations due to their hierarchical nature. Our numerical
experiments clearly demonstrate that AREPO delivers a physically more reliable
solution.
