A Comparison of Cosmological Codes: Properties of Thermal Gas and Shock Waves in Large Scale Structures
📝 Abstract
[…] 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 code TVD, the Eulerian piecewise parabolic method-based code ENZO, and the Lagrangian smoothed-particle hydrodynamics code GADGET. Starting from a shared set of initial conditions, we present convergence tests for a cosmological volume of side-length 100 Mpc/h, 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 are reasonably in agreement among the three codes, yet some significant differences exist (especially between Eulerian methods and smoothed particle hydrodynamics). 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 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; d) sizable differences in the morphologies of accretion shocks between grid and SPH methods.
💡 Analysis
[…] 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 code TVD, the Eulerian piecewise parabolic method-based code ENZO, and the Lagrangian smoothed-particle hydrodynamics code GADGET. Starting from a shared set of initial conditions, we present convergence tests for a cosmological volume of side-length 100 Mpc/h, 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 are reasonably in agreement among the three codes, yet some significant differences exist (especially between Eulerian methods and smoothed particle hydrodynamics). 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 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; d) sizable differences in the morphologies of accretion shocks between grid and SPH methods.
📄 Content
arXiv:1106.2159v2 [astro-ph.CO] 3 Aug 2011 Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 14 July 2018 (MN LATEX style file v2.2) A Comparison of Cosmological Codes: Properties of Thermal Gas and Shock Waves in Large Scale Structures F.Vazza1,2⋆, K.Dolag 3,4, D.Ryu5, G.Brunetti2, C.Gheller6, H.Kang7, C.Pfrommer8 1 Jacobs University Bremen, Campus Ring 1, 28759 Germany 2 INAF-Istituto di Radioastronomia, via Gobetti 101, I-40129 Bologna, Italy 3 University Observatory Munich, Scheinerstr. 1, D-81679 Munich, Germany 4 Max-Planck Institut fur Astrophisik, P.O. Box 1317,D-85741,Garching,Germany 5 Department of Astronomy and Space Science, Chungnam National University, Daejeon 305-764, Korea Italy 6 CINECA, High Performance System Division, Casalecchio di Reno–Bologna, Italy 7 Department of Earth Sciences, Pusan National University, Busan 609-735, Korea 8 Heidelberg Institute for Theoretical Studies, Schloss-Wolfsbrunnenweg 35, D-69118 Heidelberg, Germany Accepted ???. Received ???; in original form ??? ABSTRACT 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 result- ing 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 nu- merical codes: the Eulerian total variations diminishing code TVD, the Eulerian piecewise parabolic method-based code ENZO, and the Lagrangian smoothed-particle hydrodynamics code GADGET. Starting from a shared set of initial conditions, we present convergence tests for a cosmological volume of side-length 100Mpc/h, 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 clus- ters. Even if the bulk of thermal and shock properties are reasonably in agreement among the three codes, yet some significant differences exist (especially between Eulerian methods and smoothed particle hydrodynamics). 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/ρcr < 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; d) sizable differences in the morphologies of accretion shocks between grid and SPH methods. Key words: galaxy: clusters, general – methods: numerical – intergalactic medium – large- scale structure of Universe 1 INTRODUCTION Cosmological numerical simulations are a powerful tool to investigate the properties of the Universe at the largest scales. From galaxy formation to the precise measurement of cosmological parameters, from the ⋆E-mail: f.vazza@jacobs-university.de propagation of ultra high cosmic rays to the growth of the non-thermal energy components of the intra clus- ter medium (e.g. magnetic field, relativistic particles), cosmological simulations represent an effective com- plement to theoretical models and observations (e.g. Borgani et al. 2008; Borgani & Kravtsov 2009 and Norman 2010 for recent reviews). In order to model the evolution of cosmic structures in the most reliable 2 F.Vazza, K.Dolag, D.Ryu, G.Brunetti, C.Gheller, H.Kang, C.Pfrommer way, numerical methods must follow the non-linear dynamics of the gas and dark matter (DM) assembly across a very large dynamical range (e.g. from scales of ∼(102 −103)Mpc to ∼(1 −10)kpc), over the age of the Universe. To accomplish this task, a number of finite differ- ence methods have been developed in the past, which can be broadly divided into 2 classes (e.g. Dolag et al. 2008 for a modern review). “Lagrangian” methods dis- cretize baryon gas by mass, using a finite number of particles, and the equation of fluid-dynamics are solved with the approach of smoothed particle hydrodynamics (SPH, see Price 2008 and Springel 2010 for recent re- views). Further details of the SPH method investigated in this project will be discussed in Sec.2.3. Contrarily, “Eulerian” methods discretize space, by dividing the computational domain into regular cells (with fixed or variable size), and the gas-dynamics
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