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Register a new userA Hybrid Cosmological Hydrodynamic/N-body Code Based on the Weighted Essentially Non-Oscillatory Scheme
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We describe a newly developed cosmological hydrodynamics code based on the weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws. High order finite difference WENO schemes are designed for problems with piecewise smooth solutions containing discontinuities, and have been successful in applications for problems involving both shocks and complicated smooth solution structures. We couple hydrodynamics based on the WENO scheme with standard Poisson solver - particle-mesh (PM) algorithm for evolving the self-gravitating system. A third order total variation diminishing (TVD) Runge-Kutta scheme has been used for time-integration of the system. We brief the implementation of numerical technique. The cosmological applications in simulating intergalactic medium and Ly$alpha$ forest in the CDM scenario are also presented.
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We present a newly developed cosmological hydrodynamics code based on weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws. WENO is a higher order accurate finite difference scheme designed for problems with piecewise smooth solutions containing discontinuities, and has been successfully applied for problems involving both shocks and complicated smooth solution structures. We couple hydrodynamics based on the WENO scheme with standard Poisson solver - particle-mesh (PM) algorithm for evolving the self-gravitating system. The third order low storage total variation diminishing (TVD) Runge-Kutta scheme has been used for the time integration of the system. To test accuracy and convergence rate of the code, we subject it to a number of typical tests including the Sod shock tube in multidimensions, the Sedov blast wave and formation of the Zeldovich pancake. These tests validate the WENO hydrodynamics with fast convergence rate and high accuracy. We also evolve a low density flat cosmological model ($Lambda$CDM) to explore the validity of the code in practical simulations.
We describe a new hybrid N-body/hydrodynamical code based on the particle-mesh (PM) method and the piecewise-parabolic method (PPM) for use in solving problems related to the evolution of large-scale structure, galaxy clusters, and individual galaxies. The code, named COSMOS, possesses several new features which distinguish it from other PM-PPM codes. In particular, to solve the Poisson equation we have written a new multigrid solver which can determine the gravitational potential of isolated matter distributions and which properly takes into account the finite-volume discretization required by PPM. All components of the code are constructed to work with a nonuniform mesh, preserving second-order spatial differences. The PPM code uses vacuum boundary conditions for isolated problems, preventing inflows when appropriate. The PM code uses a second-order variable-timestep time integration scheme. Radiative cooling and cosmological expansion terms are included. COSMOS has been implemented for parallel computers using the Parallel Virtual Machine (PVM) library, and it features a modular design which simplifies the addition of new physics and the configuration of the code for different types of problems. We discuss the equations solved by COSMOS and describe the algorithms used, with emphasis on these features. We also discuss the results of tests we have performed to establish that COSMOS works and to determine its range of validity.
We describe a novel N-body code designed for simulations of the central regions of galaxies containing massive black holes. The code incorporates Mikkolas algorithmic chain regularization scheme including post-Newtonian terms up to PN2.5 order. Stars moving beyond the chain are advanced using a fourth-order integrator with forces computed on a GRAPE board. Performance tests confirm that the hybrid code achieves better energy conservation, in less elapsed time, than the standard scheme and that it reproduces the orbits of stars tightly bound to the black hole with high precision. The hybrid code is applied to two sample problems: the effect of finite-N gravitational fluctuations on the orbits of the S-stars; and inspiral of an intermediate-mass black hole into the galactic center.
Cosmology is entering an era of percent level precision due to current large observational surveys. This precision in observation is now demanding more accuracy from numerical methods and cosmological simulations. In this paper, we study the accuracy of $N$-body numerical simulations and their dependence on changes in the initial conditions and in the simulation algorithms. For this purpose, we use a series of cosmological $N$-body simulations with varying initial conditions. We test the influence of the initial conditions, namely the pre-initial configuration (preIC), the order of the Lagrangian perturbation theory (LPT), and the initial redshift, on the statistics associated with the large scale structures of the universe such as the halo mass function, the density power spectrum, and the maximal extent of the large scale structures. We find that glass or grid pre-initial conditions give similar results at $zlesssim 2$. However, the initial excess of power in the glass initial conditions yields a subtle difference in the power spectra and the mass function at high redshifts. The LPT order used to generate the ICs of the simulations is found to play a crucial role. First-order LPT (1LPT) simulations underestimate the number of massive haloes with respect to second-order (2LPT) ones, typically by 2% at $10^{14} h^{-1} M_odot$ for an initial redshift of 23, and the small-scale power with an underestimation of 6% near the Nyquist frequency for $z_mathrm{ini} = 23$. Moreover, at higher redshifts, the high-mass end of the mass function is significantly underestimated in 1LPT simulations. On the other hand, when the LPT order is fixed, the starting redshift has a systematic impact on the low-mass end of the halo mass function.
This work arises on the environment of the ExaNeSt project aiming at design and development of an exascale ready supercomputer with low energy consumption profile but able to support the most demanding scientific and technical applications. The ExaNeSt compute unit consists of densely-packed low-power 64-bit ARM processors, embedded within Xilinx FPGA SoCs. SoC boards are heterogeneous architecture where computing power is supplied both by CPUs and GPUs, and are emerging as a possible low-power and low-cost alternative to clusters based on traditional CPUs. A state-of-the-art direct $N$-body code suitable for astrophysical simulations has been re-engineered in order to exploit SoC heterogeneous platforms based on ARM CPUs and embedded GPUs. Performance tests show that embedded GPUs can be effectively used to accelerate real-life scientific calculations, and that are promising also because of their energy efficiency, which is a crucial design in future exascale platforms.
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