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Cosmological hydrodynamical simulations are a valuable tool for understanding the growth of large‐scale structure and the observables connected with this. Yet, comparably little attention has been given to validation studies of the properties of shocks and of the resulting thermal gas between different numerical methods – something of immediate importance as gravitational shocks are responsible for generating most of the entropy of the large‐scale structure in the Universe. Here, we present results for the statistics of thermal gas and the shock wave properties for a large volume simulated with three different cosmological numerical codes: the Eulerian total variations diminishing (TVD) code, the Eulerian piecewise parabolic method based code  enzo  and the Lagrangian smoothed particle hydrodynamics (SPH) code  gadget . Starting from a shared set of initial conditions, we present convergence tests for a cosmological volume of side‐length 100 Mpc  h  −1 , studying in detail the morphological and statistical properties of the thermal gas as a function of mass and spatial resolution in all codes. By applying shock‐finding methods to each code, we measure the statistics of shock waves and the related cosmic ray acceleration efficiencies, within the sample of simulations and for the results of the different approaches. We discuss the regimes of uncertainties and disagreement among codes, with a particular focus on the results at the scale of galaxy clusters. Even if the bulk of thermal and shock properties is reasonably in agreement among the three codes, yet some significant differences exist (especially between Eulerian methods and SPH). In particular, we report (a) differences of huge factors (∼10–100) in the values of average gas density, temperature, entropy, Mach number and shock thermal energy flux in the most rarefied regions of the simulations (ρ/ρ cr  &lt; 1) between grid and SPH methods; (b) the hint of an entropy core inside clusters simulated in grid codes; (c) significantly different phase diagrams of shocked cells in grid codes compared to SPH and (d) sizable differences in the morphologies of accretion shocks between grid and SPH methods.

A comparison of cosmological codes: properties of thermal gas and shock waves in large‐scale structures