Comparing AMR and SPH Cosmological Simulations: I. Dark Matter & Adiabatic Simulations

We compare two cosmological hydrodynamic simulation codes in the context of hierarchical galaxy formation: the smoothed particle hydrodynamics (SPH) code ‘GADGET’, and the Eulerian adaptive mesh refinement (AMR) code ‘ENZO’. Both codes represent dark matter with the N-body method, but use different gravity solvers, and fundamentally different approaches for baryonic hydrodynamics. In the Lagrangian SPH-method of GADGET, a recently developed ‘entropy conserving’ formulation of SPH is used, while for the mesh-based ENZO, two different formulations of Eulerian hydrodynamics are employed: the piecewise parabolic method (PPM) and the artificial viscosity-based scheme used in the magnetohydrodynamics code ZEUS. In this paper, we focus on a comparison of cosmological simulations that follow either only dark matter, or also a non-radiative (‘adiabatic’) hydrodynamic gaseous component. We perform multiple simulations using both codes with varying spatial and mass resolution with identical initial conditions. The dark matter-only runs agree generally quite well, provided ENZO is run with a comparatively fine root grid and a low overdensity threshold for mesh refinement, otherwise the abundance of low-mass halos is suppressed. This can be readily understood as a consequence of the hierarchical particle-mesh algorithm used by ENZO to compute gravitational forces, which tends to deliver lower force resolution than the tree-algorithm of GADGET. At comparable force resolution, we find that the latter offers substantially better performance and lower memory consumption than the present gravity solver in ENZO. In simulations that include adiabatic gas dynamics, we find general agreement in the distribution functions of temperature, entropy, and density for gas of moderate to high overdensity, as found inside dark matter halos. However, there are also some significant differences in the same quantities for gas of lower overdensity. For example, at z = 3, the fraction of cosmic gas that has temperature logT > 0.5 is ∼ 80% for both ENZO/ZEUS and GADGET, while it is 40−60% for ENZO/PPM. We argue that these discrepancies are presumably owing to differences in the shock-capturing abilities of the different methods. In particular, we find that the ZEUS implementation of artificial viscosity in ENZO leads to some unphysical heating at early times in preshock regions. While this is apparently a much weaker effect in GADGET, its use of an artificial viscosity technique may also make it prone to some excess generation of entropy which should be absent in ENZO/PPM. Overall, the hydrodynamical results for GADGET are bracketed by those for ENZO/ZEUS and ENZO/PPM, but are closer to ENZO/ZEUS. Subject headings: galaxies: formation — cosmology: theory — methods: numerical Center for Astrophysics and Space Sciences, University of California at San Diego, La Jolla, CA 92093, U.S.A. Email: bwoshea, [email protected] Harvard-Smithsonian Center for Astrophysics 60 Garden St., Cambridge, MA 02138, U.S.A. Email: knagamin, [email protected] Max-Planck-Institut für Astrophysik Karl-Schwarzschild-Straße 1, 85740 Garching bei München,