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

Abstract

We compare two cosmological hydrodynamic simulation codes in the context of hierarchical galaxy formation: the Lagrangian 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. The SPH method in GADGET uses a recently developed 'entropy conserving' formulation of SPH, while for the mesh-based Enzo two different formulations of Eulerian hydrodynamics are employed: the piecewise parabolic method (PPM) extended with a dual energy formulation for cosmology, 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 early times before any adaptive mesh refinement takes place. 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 log T > 0.5 is ∼ 80% for both Enzo/ZEUS and GADGET, while it is 40 − 60% for Enzo/PPM. We argue that these discrepancies are due 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 significantly 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.

Subhalo demographics in the Illustris simulation: effects of baryons and halo-to-halo variation

“…Importantly, the combination of the particle-mesh method with the tree algorithm delivers much higher accuracy than the pure particle-mesh methods usually adopted within adaptive mesh refinement (AMR) codes. This makes the Tree-PM a superior choice particularly in the case of cosmological simulations, where mesh-based Poisson solvers typically implemented in AMR codes have been shown to underestimate structure formation at the low-mass end of the dark-matter halo mass function (O'Shea et al 2005;Heitmann et al 2008).…”

The impact of numerical viscosity in SPH simulations of galaxy clusters

“…Moreover, a long-standing problem between the two numerical approaches occurs in non-radiative simulations of a galaxy cluster, where a discrepancy occurs at the cluster core between the two codes in the radial entropy profile of the gas (Frenk et al 1999;O'Shea et al 2005b;Wadsley et al 2008;Mitchell et al 2009). To investigate the origin of this discrepancy, Mitchell et al (2009) compared the final entropy profiles extracted from simulation runs of idealized binary merger cluster simulations.…”

Direct collapse to supermassive black hole seeds: comparing the AMR and SPH approaches

“…In the present work, the context and the spatial scale of the problem is very different from that of O'Shea et al (2005). Enzo's main advantage is the refinement method which allows it to obtain a superior hydrodynamic or gravitational force resolution, albeit toward the end of the cosmological simulation and in a very small volume.…”