Fast and accurate Voronoi density gridding from Lagrangian hydrodynamics data
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 particlebased representations and can benefit from constructing a Voronoi grid for postprocessing 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.
 Publication:

Journal of Computational Physics
 Pub Date:
 January 2018
 DOI:
 10.1016/j.jcp.2017.10.024
 arXiv:
 arXiv:1710.07108
 Bibcode:
 2018JCoPh.353..300P
 Keywords:

 Voronoi grid;
 SPH kernel;
 Density structure;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Astrophysics  Earth and Planetary Astrophysics;
 Astrophysics  Astrophysics of Galaxies;
 Astrophysics  Solar and Stellar Astrophysics
 EPrint:
 26 pages, 6 figures. Accepted for publication in Journal of Computational Physics. For a sample implementation of the described algorithm, see https://github.com/mapetkova/kernelintegration