TY - JOUR
T1 - Modelling shear flows with smoothed particle hydrodynamics and grid-based methods
AU - Junk, Veronika
AU - Walch, Stefanie
AU - Heitsch, Fabian
AU - Burkert, Andreas
AU - Wetzstein, Markus
AU - Schartmann, Marc
AU - Price, Daniel James
PY - 2010
Y1 - 2010
N2 - 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 smoothed particle hydrodynamics (SPH) formulation developed by Price 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.
AB - 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 smoothed particle hydrodynamics (SPH) formulation developed by Price 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.
UR - http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2966.2010.17039.x/pdf
U2 - 10.1111/j.1365-2966.2010.17039.x
DO - 10.1111/j.1365-2966.2010.17039.x
M3 - Article
VL - 407
SP - 1933
EP - 1945
JO - Monthly Notices of the Royal Astronomical Society
JF - Monthly Notices of the Royal Astronomical Society
SN - 0035-8711
IS - 3
ER -