Particle hydrodynamics with tessellation techniques

TL;DR

This paper introduces Voronoi Particle Hydrodynamics, a novel fluid simulation method that improves accuracy in contact discontinuities and turbulence modeling by replacing smoothing kernels with Voronoi tessellations.

Contribution

The paper presents a new particle-based fluid simulation approach using Voronoi tessellations, reducing surface tension effects and enhancing turbulence modeling over traditional SPH.

Findings

Eliminates spurious surface tension effects in contact discontinuities.

Produces better results in turbulent regimes compared to SPH.

Maintains comparable shock results to SPH.

Abstract

Lagrangian smoothed particle hydrodynamics (SPH) is a well-established approach to model fluids in astrophysical problems, thanks to its geometric flexibility and ability to automatically adjust the spatial resolution to the clumping of matter. However, a number of recent studies have emphasized inaccuracies of SPH in the treatment of fluid instabilities. The origin of these numerical problems can be traced back to spurious surface effects across contact discontinuities, and to SPH's inherent prevention of mixing at the particle level. We here investigate a new fluid particle model where the density estimate is carried out with the help of an auxiliary mesh constructed as the Voronoi tessellation of the simulation particles instead of an adaptive smoothing kernel. This Voronoi-based approach improves the ability of the scheme to represent sharp contact discontinuities. We show that this eliminates spurious surface tension effects present in SPH and that play a role in suppressing certain fluid instabilities. We find that the new `Voronoi Particle Hydrodynamics' described here produces comparable results than SPH in shocks, and better ones in turbulent regimes of pure hydrodynamical simulations. We also discuss formulations of the artificial viscosity needed in this scheme and how judiciously chosen correction forces can be derived in order to maintain a high degree of particle order and hence a regular Voronoi mesh. This is especially helpful in simulating self-gravitating fluids with existing gravity solvers used for N-body simulations.