Particle splitting in smoothed particle hydrodynamics based on Voronoi diagram

TL;DR

This paper introduces a Voronoi diagram-based particle splitting method for smoothed particle hydrodynamics that improves density accuracy and resolution in astrophysical simulations, enabling detailed star formation modeling.

Contribution

The novel Voronoi-based splitting method reduces density deviations and better preserves anisotropic structures compared to conventional isotropic splitting techniques.

Findings

Density deviation reduced by a factor of two

Accurate thermal evolution up to 10^12 /cc

Protostellar disk structure well resolved

Abstract

We present a novel method for particle splitting in smoothed particle hydrodynamics simulations. Our method utilizes the Voronoi diagram for a given particle set to determine the position of fine daughter particles. We perform several test simulations to compare our method with a conventional splitting method in which the daughter particles are placed isotropically over the local smoothing length. We show that, with our method, the density deviation after splitting is reduced by a factor of about two compared with the conventional method. Splitting would smooth out the anisotropic density structure if the daughters are distributed isotropically, but our scheme allows the daughter particles to trace the original density distribution with length scales of the mean separation of their parent. We apply the particle splitting to simulations of the primordial gas cloud collapse. The thermal evolution is accurately followed to the hydrogen number density of 10^12 /cc. With the effective mass resolution of ~10^-4 Msun after the multi-step particle splitting, the protostellar disk structure is well resolved. We conclude that the method offers an efficient way to simulate the evolution of an interstellar gas and the formation of stars.