Gravitational N-Body Simulations

  title={Gravitational N-Body Simulations},
  author={Sverre J. Aarseth},
  • S. Aarseth
  • Published 1 October 2003
  • Computer Science
Preface 1. The N-body problem 2. Predictor-corrector methods 3. Neighbour treatments 4. Two-body regularization 5. Multiple regularization 6. Tree codes 7. Program organization 8. Initial setup 9. Decision-making 10. Neighbour schemes 11. Two-body algorithms 12. Chain procedures 13. Accuracy and performance 14. Practical aspects 15. Star clusters 16. Galaxies 17. Planetary systems 18. Small-N experiments Appendix A. Global regularization algorithms Appendix B. Chain algorithms Appendix C. High… 

Tables from this paper

A hybrid N-body code incorporating algorithmic regularization and post-Newtonian forces

We describe a novel N-body code designed for simulations of the central regions of galaxies containing massive black holes. The code incorporates Mikkola's 'algorithmic' chain regularization scheme


We discuss the implementation of a new regular algorithm for simulation of the gravitational few-body problem. The algorithm uses components from earlier methods, including the chain structure, the

An optimum time-stepping scheme for N-body simulations

We present a new time-stepping criterion for N-body simulations that is based on the true dynamical time of a particle. This allows us to follow the orbits of particles correctly in all environments

Fast Multipole Methods for N-body Simulations of Collisional Star Systems

Taichi is demonstrated to be more efficient than other CPU-based direct N-body codes for simulating large systems, and to accurately model collisional effects, such as dynamical friction and the core-collapse time of idealized clusters, producing results in strong agreement with benchmarks from other collisional codes.

A hybrid SPH/N-body method for star cluster simulations

We present a new hybrid smoothed particle hydrodynamics (SPH)/N-body method for modelling the collisional stellar dynamics of young clusters in a live gas background. By deriving the equations of

Evolution of stellar orbits in the galactic centre

We describe a novel N-body code designed for simulations of the central regions of galaxies containing massive black holes. The code incorporates Mikkola's "algorithmic" chain regularization scheme

Particle-based sampling of N-body simulations

This paper introduces a novel approach for sampling the orbits of an N-body simulation. The gist of the method is to exploit individual phase-space coordinates acquired during integration of the

A Keplerian-based Hamiltonian splitting for gravitational N-body simulations

We developed a Keplerian-based Hamiltonian splitting for solving the gravitational $N$-body problem. This splitting allows us to approximate the solution of a general $N$-body problem by a

GANDALF - Graphical Astrophysics code for N-body Dynamics And Lagrangian Fluids

The details of its implementation, results from the test suite, serial and parallel performance results and the planned future development of GANDALF are presented.

How to build and use special purpose PC clusters in stellar dynamics

  • R. Spurzem
  • Physics
    Proceedings of the International Astronomical Union
  • 2006
Large scale, direct particle-particle, brute force N-body simulations are required to accurately resolve numerically transport processes of energy and angular momentum due to two-body relaxation, and



Direct methods for N-Body simulations

The new Hermite integration scheme is described; it is based on explicit evaluation of the force and its first derivative and it is shown that this scheme is particularly efficient when combined with hierarchical time-steps which reduce the amount of prediction.

Regularization tools for binary interactions

We first discuss two-body and chain regularization methods for direct N-body simulations on HARP-2 and GRAPE-6. The former is used for accurate integration of perturbed binaries and hierarchies,

Direct Integration Methods of the N-Body Problem

A fourth-order polynomial method for the integration of iV-body systems is described in detail together with the computational algorithm. Most particles are treated efficiently by an individual

Integration Methods for Small N-Body Systems

This review concentrates on integration methods for small N-body systems (N ≤ 25). First some relevant astronomical problems are defined. Then follows a discussion of standard integration methods for

Performance analysis of direct N-body calculations

A theoretical framework for analyzing the computational cost of gravitational N-body codes is introduced and applied to three different types of direct-summation codes, including the type of Aarseth

The gravitational million-body problem

We review what has been learned recently using N-body simulations about the evolution of globular clusters. While simulations of star clusters have become more realistic, and now include the

Round-off sensitivity in the N -body problem

The solutions to the equations of motion of the gravitational N-body problem are extremely sensitive to very small changes in initial conditions, resulting in a near-exponential growth of deviations

Direct N-Body Calculations

The main principles for direct integration of large point-mass systems are outlined. Most particles are advanced by the Ahmad-Cohen neighbour scheme, using fourth-order force polynomials and

An implementation ofN-body chain regularization

The chain regularization method (Mikkola and Aarseth 1990) for high accuracy computation of particle motions in smallN-body systems has been reformulated. We discuss the transformation formulae,