An alternative method to generate pre-initial conditions for cosmological $N$-body simulations

TL;DR

This paper introduces the capacity constrained Voronoi tessellation (CCVT) as a new method for generating initial particle distributions in cosmological N-body simulations, demonstrating its uniformity, stability, and comparable performance to existing methods.

Contribution

The paper presents CCVT, a novel geometrical method from computer graphics, for creating uniform, isotropic initial conditions in cosmological simulations, with advantages in stability and flexibility.

Findings

CCVT produces uniform, isotropic particle distributions.

CCVT configurations follow the minimal power spectrum $P(k) \\propto k^4$.

CCVT performs as well as grid and glass methods in simulations.

Abstract

Currently, grid and glass methods are the two most popular choices to generate uniform particle distributions (i.e., pre-initial conditions) for cosmological $N$-body simulations. In this article, we introduce an alternative method called the capacity constrained Voronoi tessellation (CCVT), which originates from computer graphics. As a geometrical equilibrium state, a CCVT particle configuration satisfies two constraints: (i) the volume of the Voronoi cell associated with each particle is equal; (ii) every particle is in the center-of-mass position of its Voronoi cell. We show that the CCVT configuration is uniform and isotropic, follows perfectly the minimal power spectrum, $P(k)\propto k^4$, and is quite stable under gravitational interactions. It is natural to incorporate periodic boundary conditions during CCVT making, therefore, we can obtain a larger CCVT by tiling with a small periodic CCVT. When applying the CCVT pre-initial condition to cosmological $N$-body simulations, we show that it plays as good as grid and glass schemes. The CCVT method will be helpful in studying the numerical convergence of pre-initial conditions in cosmological simulations. It can also be used to set up pre-initial conditions in smoothed-particle hydrodynamics simulations.