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Hydrodynamic cosmological simulations at present usually employ either the Lagrangian smoothed particle hydrodynamics (SPH) technique or Eulerian hydrodynamics on a Cartesian mesh with (optional) adaptive mesh refinement (AMR). Both of these methods have disadvantages that negatively impact their accuracy in certain situations, for example the suppression of fluid instabilities in the case of SPH, and the lack of Galilean invariance and the presence of overmixing in the case of AMR. We here propose a novel scheme which largely eliminates these weaknesses. It is based on a moving unstructured mesh defined by the Voronoi tessellation of a set of discrete points. The mesh is used to solve the hyperbolic conservation laws of ideal hydrodynamics with a finite-volume approach, based on a second-order unsplit Godunov scheme with an exact Riemann solver. The mesh-generating points can in principle be moved arbitrarily. If they are chosen to be stationary, the scheme is equivalent to an ordinary Eulerian method with second-order accuracy. If they instead move with the velocity of the local flow, one obtains a Lagrangian formulation of continuum hydrodynamics that does not suffer from the mesh distortion limitations inherent in other mesh-based Lagrangian schemes. In this mode, our new method is fully Galilean invariant, unlike ordinary Eulerian codes, a property that is of significant importance for cosmological simulations where highly supersonic bulk flows are common. In addition, the new scheme can adjust its spatial resolution automatically and continuously, and hence inherits the principal advantage of SPH for simulations of cosmological structure growth. The high accuracy of Eulerian methods in the treatment of shocks is also retained, while the treatment of contact discontinuities improves. We discuss how this approach is implemented in our new codearepo, both in 2D and in 3D, and is parallelized for distributed memory computers. We also discuss techniques for adaptive refinement or de-refinement of the unstructured mesh. We introduce an individual time-step approach for finite-volume hydrodynamics, and present a high-accuracy treatment of self-gravity for the gas that allows the new method to be seamlessly combined with a high-resolution treatment of collisionless dark matter. We use a suite of test problems to examine the performance of the new code and argue that the hydrodynamic moving-mesh scheme proposed here provides an attractive and competitive alternative to current SPH and Eulerian techniques. [ABSTRACT FROM AUTHOR]

We discuss the cosmological simulation code gadget-2, a new massively parallel TreeSPH code, capable of following a collisionless fluid with the N-body method, and an ideal gas by means of smoothed particle hydrodynamics (SPH). Our implementation of SPH manifestly conserves energy and entropy in regions free of dissipation, while allowing for fully adaptive smoothing lengths. Gravitational forces are computed with a hierarchical multipole expansion, which can optionally be applied in the form of a TreePM algorithm, where only short-range forces are computed with the ‘tree’ method while long-range forces are determined with Fourier techniques. Time integration is based on a quasi-symplectic scheme where long-range and short-range forces can be integrated with different time-steps. Individual and adaptive short-range time-steps may also be employed. The domain decomposition used in the parallelization algorithm is based on a space-filling curve, resulting in high flexibility and tree force errors that do not depend on the way the domains are cut. The code is efficient in terms of memory consumption and required communication bandwidth. It has been used to compute the first cosmological N-body simulation with more than 1010 dark matter particles, reaching a homogeneous spatial dynamic range of 105 per dimension in a three-dimensional box. It has also been used to carry out very large cosmological SPH simulations that account for radiative cooling and star formation, reaching total particle numbers of more than 250 million. We present the algorithms used by the code and discuss their accuracy and performance using a number of test problems. gadget-2 is publicly released to the research community. [ABSTRACT FROM AUTHOR]

The cold dark matter model has become the leading theoretical picture for the formation of structure in the Universe. This model, together with the theory of cosmic inflation, makes a clear prediction for the initial conditions for structure formation and predicts that structures grow hierarchically through gravitational instability. Testing this model requires that the precise measurements delivered by galaxy surveys can be compared to robust and equally precise theoretical calculations. Here we present a simulation of the growth of dark matter structure using 2,1603 particles, following them from redshift z= 127 to the present in a cube-shaped region 2.230 billion lightyears on a side. In postprocessing, we also follow the formation and evolution of the galaxies and quasars. We show that baryon-induced features in the initial conditions of the Universe are reflected in distorted form in the low-redshift galaxy distribution, an effect that can be used to constrain the nature of dark energy with future generations of observational surveys of galaxies. [ABSTRACT FROM AUTHOR]

We introduce a set of four very high resolution cosmological simulations exploring f (R) gravity, with 20483 particles in 768 and |$1536 \, h^{-1} \, {\rm Mpc}$| simulation boxes, for |$|\bar{f}_{R0}| = 10^{-5}$| and Λ cold dark matter (ΛCDM), making the set the largest simulations of f (R) gravity to date. To mimic real observations, the simulations include a continuous 2D- and 3D-light-cone output dedicated to study lensing and clustering statistics. We present a detailed analysis and resolution study for the matter power spectrum in f (R) gravity over a wide range of scales. We also analyse the angular matter power spectrum and lensing convergence on the light-cone. In addition, we investigate the impact of modified gravity on the halo mass function, matter, and halo autocorrelation functions, linear halo bias, and the concentration–mass relation. The impact of f (R) gravity is generally larger on smaller scales and smaller redshift. Comparing our simulations to state-of-the-art hydrodynamical simulations, we confirm a degeneracy between f (R) gravity and baryonic feedback in the matter power spectrum on small scales, but also find that scales around |$k = 1 \, h\, {\rm Mpc}^{-1}$| are promising to distinguish both effects. The lensing convergence power spectrum is increased in f (R) gravity. Numerical fits are in good agreement with our simulations for both standard and modified gravity, but tend to overestimate their relative difference on non-linear scales. The halo bias is lower in f (R) gravity, whereas halo concentrations are increased for unscreened haloes. [ABSTRACT FROM AUTHOR]