Kelvin-Helmholtz instabilities in Smoothed Particle Hydrodynamics
  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.
