Journal
ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES
Volume 201, Issue 2, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0067-0049/201/2/18
Keywords
hydrodynamics; instabilities; methods: numerical
Categories
Funding
- National Science Foundation (NSF) [AST-0835734, AST-0607111, AST-1009802, OCI-1053575]
- Division Of Astronomical Sciences
- Direct For Mathematical & Physical Scien [1009802] Funding Source: National Science Foundation
- Division Of Astronomical Sciences
- Direct For Mathematical & Physical Scien [0835734] Funding Source: National Science Foundation
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Recently, there has been a significant level of discussion of the correct treatment of Kelvin-Helmholtz instability (KHI) in the astrophysical community. This discussion relies largely on how the KHI 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 KHI. 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 tests starting from a sharp contact discontinuity yet it still shows the poor performance of smoothed particle hydrodynamics (SPH). We then comment on the connection between 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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