Kelvin-Helmholtz instabilities in Smoothed Particle Hydrodynamics

TL;DR

This paper assesses Smoothed Particle Hydrodynamics (SPH) with artificial conductivity for modeling Kelvin-Helmholtz instabilities, identifying key issues like shock waves and particle noise, and proposing improved signal velocities to enhance simulation accuracy.

Contribution

It demonstrates the importance of artificial conductivity and introduces new signal velocities to reduce energy diffusion in SPH simulations of KH instabilities.

Findings

Artificial conductivity is essential for long-term KH roll development.

Default AC signal velocity causes excessive energy diffusion.

Particle noise and shock waves are main causes of KH roll failure.

Abstract

In this paper we investigate whether Smoothed Particle Hydrodynamics (SPH), equipped with artificial conductivity, is able to capture the physics of density/energy discontinuities in the case of the so-called shearing layers test, a test for examining Kelvin-Helmholtz (KH) instabilities. We can trace back each failure of SPH to show KH rolls to two causes: i) shock waves travelling in the simulation box and ii) particle clumping, or more generally, particle noise. The probable cause of shock waves is the Local Mixing Instability (LMI), previously identified in the literature. Particle noise on the other hand is a problem because it introduces a large error in the SPH momentum equation. We also investigate the role of artificial conductivity (AC). Including AC is necessary for the long-term behavior of the simulation (e.g. to get $\lambda=1/2, 1$ KH rolls). In sensitive hydrodynamical simulations great care is however needed in selecting the AC signal velocity, with the default formulation leading to too much energy diffusion. We present new signal velocities that lead to less diffusion. The effects of the shock waves and of particle disorder become less important as the time-scale of the physical problem (for the shearing layers problem: lower density contrast and higher Mach numbers) decreases. At the resolution of current galaxy formation simulations mixing is probably not important. However, mixing could become crucial for next-generation simulations.