Fast and accurate Voronoi density gridding from Lagrangian hydrodynamics data

TL;DR

This paper introduces a fast, accurate analytic method for calculating Voronoi cell densities from SPH data, improving speed and accuracy over traditional numerical approaches.

Contribution

It derives an explicit integral expression for cubic spline kernels over Voronoi cells, ensuring mass conservation and broad applicability.

Findings

Method significantly speeds up density calculations.

Achieves higher accuracy than numerical methods.

Ensures rigorous mass conservation.

Abstract

Voronoi grids have been successfully used to represent density structures of gas in astronomical hydrodynamics simulations. While some codes are explicitly built around using a Voronoi grid, others, such as Smoothed Particle Hydrodynamics (SPH), use particle-based representations and can benefit from constructing a Voronoi grid for post-processing their output. So far, calculating the density of each Voronoi cell from SPH data has been done numerically, which is both slow and potentially inaccurate. This paper proposes an alternative analytic method, which is fast and accurate. We derive an expression for the integral of a cubic spline kernel over the volume of a Voronoi cell and link it to the density of the cell. Mass conservation is ensured rigorously by the procedure. The method can be applied more broadly to integrate a spherically symmetric polynomial function over the volume of a random polyhedron.