A Well-Posed Kelvin-Helmholtz Instability Test and Comparison

Details A Well-Posed Kelvin-Helmholtz Instability Test and Comparison A Well-Posed Kelvin-Helmholtz Instability Test and Comparison

2011-11-07

arxiv.org/abs/1111.1764v1

Astronomy and Astrophysics

Astrophysics

Instrumentation and Methods for Astrophysics

24 pages, 25 figures, submitted, Comments welcome

Scientific paper

Agertz et al. (2007) sparked a controversy about the correct treatment of Kelvin-Helmholtz instability (KH) in the astrophysical community. This discussion relies largely on how the KH test is posed and analyzed. We pose a stringent test of the initial growth of the instability. The goal is to provide a rigorous methodology for verifying a code on two dimensional Kelvin-Helmholtz instability. We ran the problem in the Pencil Code, Athena, Enzo, NDSPMHD, and Phurbas. A strict comparison, judgment, or ranking, between codes is beyond the scope of this work, though this work provides the mathematical framework needed for such a study. Nonetheless, how the test is posed circumvents the issues raised by Agertz et al. (2007) yet it still shows poor performance of Smoothed Particle Hydrodynamics (SPH). We are then to connect this behavior to the underlying lack of zeroth-order consistency in SPH interpolation. We comment on the tendency of some methods, particularly those with very low numerical diffusion, to produce secondary Kelvin-Helmholtz billows on similar tests. Though the lack of a fixed, physical diffusive scale in the Euler equations lies at the root of the issue, we suggest that in some methods an extra diffusion operator should be used to damp the growth of instabilities arising from grid noise. This statement applies particularly to moving-mesh tessellation codes, but also to fixed-grid Godunov schemes.

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