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

Currently, grid and glassmethods 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 centre-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) proportional to 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.