Colin P. McNally, Wladimir Lyra, Jean-Claude Passy
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.
View original:
http://arxiv.org/abs/1111.1764
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