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 10 10 dark matter particles, reaching a homogeneous spatial dynamic range of 10 5 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. Ke yw ords: methods: numerical ‐ galaxies: interactions ‐ dark matter.

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The Cosmological simulation code GADGET-2

In this review the theory and application of Smoothed particle hydrodynamics (SPH) since its inception in 1977 are discussed. Emphasis is placed on the strengths and weaknesses, the analogy with particle dynamics and the numerous areas where SPH has been successfully applied.

https://iopscience.iop.org/article/10.1088/0034-4885/68/8/R01/pdf

Smoothed particle hydrodynamics

Stellar physics and evolution calculations enable a broad range of research in astrophysics. Modules for Experiments in Stellar Astrophysics (MESA) is a suite of open source, robust, efficient, thread-safe libraries for a wide range of applications in computational stellar astrophysics. A one-dimensional stellar evolution module, MESAstar, combines many of the numerical and physics modules for simulations of a wide range of stellar evolution scenarios ranging from very low mass to massive stars, including advanced evolutionary phases. MESAstar solves the fully coupled structure and composition equations simultaneously. It uses adaptive mesh refinement and sophisticated timestep controls, and supports shared memory parallelism based on OpenMP. State-of-the-art modules provide equation of state, opacity, nuclear reaction rates, element diffusion data, and atmosphere boundary conditions. Each module is constructed as a separate Fortran 95 library with its own explicitly defined public interface to facilitate independent development. Several detailed examples indicate the extensive verification and testing that is continuously performed and demonstrate the wide range of capabilities that MESA possesses. These examples include evolutionary tracks of very low mass stars, brown dwarfs, and gas giant planets to very old ages; the complete evolutionary track of a 1 M ☉ star from the pre-main sequence (PMS) to a cooling white dwarf; the solar sound speed profile; the evolution of intermediate-mass stars through the He-core burning phase and thermal pulses on the He-shell burning asymptotic giant branch phase; the interior structure of slowly pulsating B Stars and Beta Cepheids; the complete evolutionary tracks of massive stars from the PMS to the onset of core collapse; mass transfer from stars undergoing Roche lobe overflow; and the evolution of helium accretion onto a neutron star. MESA can be downloaded from the project Web site (http://mesa.sourceforge.net/).

https://iopscience.iop.org/article/10.1088/0067-0049/192/1/3/pdf

Modules for Experiments in Stellar Astrophysics (MESA)

amount of energy, a tiny fraction of which is sufficient to explode the star as a supernova. The authors examine our current understanding of the lives and deaths of massive stars, with special attention to the relevant nuclear and stellar physics. Emphasis is placed upon their post-helium-burning evolution. Current views regarding the supernova explosion mechanism are reviewed, and the hydrodynamics of supernova shock propagation and ‘‘fallback’’ is discussed. The calculated neutron star masses, supernova light curves, and spectra from these model stars are shown to be consistent with observations. During all phases, particular attention is paid to the nucleosynthesis of heavy elements. Such stars are capable of producing, with few exceptions, the isotopes between mass 16 and 88 as well as a large fraction of still heavier elements made by the r and p processes.

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The evolution and explosion of massive stars

http://staff.ustc.edu.cn/~wzhao7/c_index_files/main.files/lss.pdf

Large scale structure of the universe and cosmological perturbation theory

A processor has been constructed using a 'pipeline' architecture to simulate many-body systems with long-range forces. It has a speed equivalent to 120 megaflops, and the architecture can be readily parallelized to make teraflop machines a feasible possibility. The machine can be adapted to study molecular dynamics, plasma dynamics and astrophysical hydrodynamics with only minor modifications.

A special-purpose computer for gravitational many-body problems

In this paper, we describe the architecture and performance of the GRAPE-4 system, a massively parallel special-purpose computer for N-body simulation of gravitational collisional systems. The calculation cost of N-body simulation of collisional self-gravitating system is O(N3). Thus, even with present-day supercomputers, the number of particles one can handle is still around 10,000. In N-body simulations, almost all computing time is spent calculating the force between particles, since the number of interactions is proportional to the square of the number of particles. Computational cost of the rest of the simulation, such as the time integration and the reduction of the result, is generally proportional to the number of particles. The calculation of the force between particles can be greatly accelerated by means of a dedicated special-purpose hardware. We have developed a series of hardware systems, the GRAPE (GRAvity PipE) systems, which perform the force calculation. They are used with a general-purpose host computer which performs the rest of the calculation. The GRAPE-4 system is our newest hardware, completed in 1995 summer. Its peak speed is 1.08 TFLOPS. This speed is achieved by running 1692 pipeline large-scale integrated circuits (LSIs), each providing 640 MFLOPS, in parallel.

/pdf/grape-4-a-massively-parallel-special-purpose-computer-for-1irvx1u5n0.pdf

GRAPE-4: A Massively Parallel Special-Purpose Computer for Collisional N-Body Simulations

As an alternative to the carbon detonation, we present a carbondeflagration supernova model by a full hydrodynamic computation. A deflagration wave, which propagates through the core due to convective heat transport, does not grow into detonation. Though it results in a complete disruption of the star, the difficulty of overproduction of iron peak elements can be avoided if the deflagration is relatively slow.

Carbon Deflagration Supernova, an Alternative to Carbon Detonation

Modern theories on the evolution of stars are extended to the phases of helium burning, carbon burning, and later burnings as far as possible, and the theoretical results are compared wth the Hertzsprung-Russell diagrams of star clusters. The topics discussed include nuclear generation and energy loss by neutrinos, quasi-static equilibrium, envelope,core, and surface solutions, stellar models with homogeneous chemical composition, hydrogen burning phase, helium burning phase, advanced phases of nuclear burning, iinal phase toward white dwarfs, and pre-mainsequence contricting phase. (C.E.S.)

Evolution of the stars

The initial mass of the Crab Nebula's progenitor star is estimated by comparing the observed nebular chemical abundances with detailed evolutionary calculations for 2.4- and 2.6-solar-mass helium cores of stars with masses of 8 to 10 solar masses. The results indicate that the mass of the Crab's progenitor was between the upper limit of about 8 solar masses for carbon deflagration and the lower limit of about 9.5 solar masses set by the dredge-up of the helium layer before the development of the helium-burning convective region. A scenario is outlined for the evolution of the progenitor star. It is suggested that the Crab Nebula was probably the product of an electron-capture supernova.

Daiichiro Sugimoto

Papers

A special-purpose computer for gravitational many-body problems

GRAPE-4: A Massively Parallel Special-Purpose Computer for Collisional N-Body Simulations

Carbon Deflagration Supernova, an Alternative to Carbon Detonation

Evolution of the stars

The Crab Nebula's progenitor