# The Kelvin-Helmholtz instability and smoothed particle hydrodynamics

## TL;DR

This paper demonstrates that standard smoothed particle hydrodynamics (SPH) can accurately model the Kelvin-Helmholtz instability and achieve convergence with reference solutions in both linear and non-linear regimes.

## Contribution

The study shows that with appropriate physical viscosity and conductivity, SPH solutions converge to reference results, confirming its validity for modeling this instability.

## Key findings

- SPH solutions converge to reference solutions in linear and non-linear regimes.
- Physical Navier-Stokes viscosity improves convergence in non-linear regime.
- Standard SPH with artificial viscosity can correctly model Kelvin-Helmholtz instability.

## Abstract

There has been interest in recent years to assess the ability of astrophysical hydrodynamics codes to correctly model the Kelvin-Helmholtz instability. Smoothed particle hydrodynamics (SPH), in particular, has received significant attention, though there has yet to be a clear demonstration that SPH yields converged solutions that are in agreement with other methods. We have performed SPH simulations of the Kelvin-Helmholtz instability using the test problem put forward by Lecoanet et al (2016). We demonstrate that the SPH solutions converge to the reference solution in both the linear and non-linear regimes. Quantitative convergence in the strongly non-linear regime is achieved by using a physical Navier-Stokes viscosity and thermal conductivity. We conclude that standard SPH with an artificial viscosity can correctly capture the Kelvin-Helmholtz instability.