We have investigated 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 show that setting up initial conditions with a suitably smoothed density gradient dramatically improves results. Particle clumping is easy to overcome, the most straightforward method being the use of a suitable smoothing kernel with non-zero first central derivative. We present results to that effect using a new smoothing kernel: the LInear Quartic (LIQ) kernel. Furthermore, we present new Artificial Conductivity 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.