Modelling Shear Flows with SPH and Grid Based Methods
  Given the importance of shear flows for astrophysical gas dynamics, we study
the evolution of the Kelvin-Helmholtz instability (KHI) analytically and
numerically. We derive the dispersion relation for the two-dimensional KHI
including viscous dissipation. The resulting expression for the growth rate is
then used to estimate the intrinsic viscosity of four numerical schemes
depending on code-specific as well as on physical parameters. Our set of
numerical schemes includes the Tree-SPH code VINE, an alternative SPH
formulation developed by Price (2008), and the finite-volume grid codes FLASH
and PLUTO. In the first part, we explicitly demonstrate the effect of
dissipation-inhibiting mechanisms such as the Balsara viscosity on the
evolution of the KHI. With VINE, increasing density contrasts lead to a
continuously increasing suppression of the KHI (with complete suppression from
a contrast of 6:1 or higher). The alternative SPH formulation including an
artificial thermal conductivity reproduces the analytically expected growth
rates up to a density contrast of 10:1. The second part addresses the shear
flow evolution with FLASH and PLUTO. Both codes result in a consistent
non-viscous evolution (in the equal as well as in the different density case)
in agreement with the analytical prediction. The viscous evolution studied with
FLASH shows minor deviations from the analytical prediction.
