A Comparison of Two Algorithms for Simulating Collisionless Systems
Abstract
Two completely different simulation algorithms are compared by applying them to the same stellar dynamical problems: one is a self consistent field (SCF) method for solving Poisson's equation and the other is a phasespace method for integrating the collisionless Boltzmann equation. We consider simulations of spherical stellar systems which are initially far from equilibrium and relax to their final states by gravitational collapse. The initial conditions consist of either uniform density spheres or nonequilibrium models having Plummer density profiles, in which velocity dispersions are assigned according to given virial ratios. If a few tens of radial expansion terms with hundreds of thousands of particles are used in the SCF code, excellent agreement is found between the results it generates and those obtained with the phase space solver, provided that a sufficiently large number of grid cells are employed with the latter. These findings imply that for simulating collisionless systems over many dynamical times, the SCF approach based on sampling phase space is competitive with the approach treating phase space as a continuous fluid. The results of our tests make it possible to estimate the number of particles and basis functions required in situations like those modeled. Limitations of the SCF method and the choice of an optimal set of basis functions are also discussed.
 Publication:

The Astrophysical Journal
 Pub Date:
 February 1995
 DOI:
 10.1086/175247
 Bibcode:
 1995ApJ...440...60H
 Keywords:

 Algorithms;
 Astronomical Models;
 Boltzmann Transport Equation;
 Gravitational Collapse;
 Poisson Equation;
 Self Consistent Fields;
 Stellar Motions;
 Stellar Systems;
 Computerized Simulation;
 Mathematical Models;
 Stellar Gravitation;
 Astrophysics;
 CELESTIAL MECHANICS;
 STELLAR DYNAMICS;
 GALAXIES: FORMATION;
 METHODS: NUMERICAL