宇宙学$N$ -体模拟预初始条件的一种生成方法
An alternative method to generate pre-initial conditions for cosmological $N$-body simulations
摘要：
目前，网格和玻璃方法是产生均匀颗粒分布（即，前初始条件）的宇宙学$N$体模拟。在这篇文章中，我们介绍了一种替代方法，称为容量约束Voronoi曲面细分（CCVT），它起源于计算机图形学。作为几何平衡态，CCVT粒子构型满足两个约束：（i）与每个粒子相关联的Voronoi胞的体积相等;（ii）每个粒子处于其Voronoi胞的质心位置。我们发现CCVT组态是均匀的和各向同性的，完全遵循最小功率谱$P(k)\propto k^4$，并且在引力相互作用下是相当稳定的。在制作CCVT的过程中加入周期性边界条件是很自然的，因此，我们可以通过平铺小的周期性CCVT来获得更大的CCVT。当应用CCVT预初始条件的宇宙学$N$体模拟，我们表明，它起到良好的网格和玻璃方案。CCVT方法将有助于研究宇宙学模拟中预初始条件的数值收敛性。它也可以用来设置预初始条件的光滑粒子流体动力学模拟。
英文摘要：
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.
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