  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.
