Journal Article

Modelling shear flows with smoothed particle hydrodynamics and grid-based methods

Veronika Junk, Stefanie Walch, Fabian Heitsch, Andreas Burkert, Markus Wetzstein, Marc Schartmann and Daniel Price

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 407, issue 3, pages 1933-1945
Published in print September 2010 | ISSN: 0035-8711
Published online September 2010 | e-ISSN: 1365-2966 | DOI:
Modelling shear flows with smoothed particle hydrodynamics and grid-based methods

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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.

Keywords: hydrodynamics; instabilities; methods: analytical; methods: numerical; ISM: kinematics and dynamics

Journal Article.  7326 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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