Kelvin-Helmholtz不稳定性的一个适定性检验和比较
A Well-Posed Kelvin-Helmholtz Instability Test and Comparison
摘要：
最近，在天体物理学界对正确处理开尔文-亥姆霍兹不稳定性进行了大量的讨论。这个讨论很大程度上依赖于如何提出和分析KHI测试。我们对不稳定性的初始增长提出了严格的检验。我们的目标是提供一个严格的方法来验证二维开尔文-亥姆霍兹不稳定性的代码。我们在Apache Code、Athena、Enzo、NDSPHMHD和Phurbas中运行了这个问题。严格的比较，判断，或排名，代码之间超出了这项工作的范围，虽然这项工作提供了这样的研究所需的数学框架。尽管如此，如何提出的测试，规避了从一个尖锐的接触不连续性开始的测试所提出的问题，但它仍然显示了光滑粒子流体动力学的性能差。然后，我们评论这种行为之间的连接，基本缺乏零阶一致性光滑粒子流体动力学插值。我们评论的趋势，一些方法，特别是那些非常低的数值扩散，产生二次开尔文-亥姆霍兹波涛在类似的测试。虽然缺乏一个固定的，在欧拉方程的物理扩散尺度是问题的根源，我们建议，在某些方法中，一个额外的扩散算子应被用来阻尼网格噪声所产生的不稳定性的增长。这种说法特别适用于移动网格镶嵌代码，但也适用于固定网格Goddom计划。
英文摘要：
Recently, there has been a significant level of discussion of the correct treatment of Kelvin-Helmholtz instability 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 Kelvin-Helmholtz instability. We ran the problem in the Pencil Code, Athena, Enzo, NDSPHMHD, 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. We then comment on the connection between this behavior to the underlying lack of zeroth-order consistency in Smoothed Particle Hydrodynamics 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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