Shock finding on a moving-mesh: I. Shock statistics in non-radiative
  cosmological simulations
  Cosmological shock waves play an important role in hierarchical structure
formation by dissipating and thermalizing kinetic energy of gas flows, thereby
heating the universe. Furthermore, identifying shocks in hydrodynamical
simulations and measuring their Mach number accurately is critical for
calculating the production of non-thermal particle components through diffusive
shock acceleration. However, shocks are often significantly broadened in
numerical simulations, making it challenging to implement an accurate shock
finder. We here introduce a refined methodology for detecting shocks in the
moving-mesh code AREPO, and show that results for shock statistics can be
sensitive to implementation details. We put special emphasis on filtering
against spurious shock detections due to tangential discontinuities and
contacts. Both of them are omnipresent in cosmological simulations, for example
in the form of shear-induced Kelvin-Helmholtz instabilities and cold fronts. As
an initial application of our new implementation, we analyse shock statistics
in non-radiative cosmological simulations of dark matter and baryons. We find
that the bulk of energy dissipation at redshift zero occurs in shocks with Mach
numbers around ${\cal M}\approx2.7$. Furthermore, almost $40\%$ of the
thermalization is contributed by shocks in the warm hot intergalactic medium
(WHIM), whereas $\approx60\%$ occurs in clusters, groups and smaller halos.
Compared to previous studies, these findings revise the characterization of the
most important shocks towards higher Mach numbers and lower density structures.
Our results also suggest that regions with densities above and below
$\delta_b=100$ should be roughly equally important for the energetics of cosmic
ray acceleration through large-scale structure shocks.
