用拉格朗日流体动力学格式检验分辨率对引力碎裂的影响
Testing the effect of resolution on gravitational fragmentation with Lagrangian hydrodynamic schemes
摘要：
为了研究新开发的拉格朗日流体动力学方案，无网格有限体积法（MFV）和无网格有限质量法（MFM）模拟引力破碎所需的分辨率，我们进行了一些模拟的Jeans测试和比较的结果与预期的解析解和结果从更标准的拉格朗日方法：光滑粒子流体动力学（SPH）。我们发现，当流体元的直径小于Jeans波长的四分之一，$λ_\mathrm{J}$，不同的计划收敛到解析解。在这三种格式中，SPH/MFV显示出最快/最慢的收敛到解析解。与众所周知的行为的欧拉计划，没有拉格朗日计划调查显示人为的碎片时，扰动波长，$λ$，短于$λ_\mathrm{J}$，即使在低数值分辨率。对于较大的波长（$λ> λ_\mathrm{J}$），当扰动没有很好地分辨时，扰动的增长被延迟。此外，在分辨率较差的情况下，与收敛解决方案相比，MFV方案所见的碎片化进展非常不同。所有这些结果表明，当未分辨时，在亚分辨率尺度上的水动力与自重力的大小之比在MFV/SPH中是最大/最小的，我们详细讨论了原因。重复这些测试以研究比基准三次样条更高阶的核的效果。我们的结果表明，标准偏差的内核是一个更合适的定义的流体元素的大小比其紧凑的支持半径。
英文摘要：
To study the resolution required for simulating gravitational fragmentation with newly developed Lagrangian hydrodynamic schemes, Meshless Finite Volume method (MFV) and Meshless Finite Mass method (MFM), we have performed a number of simulations of the Jeans test and compared the results with both the expected analytic solution and results from the more standard Lagrangian approach: Smoothed Particle Hydrodynamics (SPH). We find that the different schemes converge to the analytic solution when the diameter of a fluid element is smaller than a quarter of the Jeans wavelength, $λ_\mathrm{J}$. Among the three schemes, SPH/MFV shows the fastest/slowest convergence to the analytic solution. Unlike the well-known behaviour of Eulerian schemes, none of the Lagrangian schemes investigated displays artificial fragmentation when the perturbation wavelength, $λ$, is shorter than $λ_\mathrm{J}$, even at low numerical resolution. For larger wavelengths ($λ> λ_\mathrm{J}$) the growth of the perturbation is delayed when it is not well resolved. Furthermore, with poor resolution, the fragmentation seen with the MFV scheme proceeds very differently compared to the converged solution. All these results suggest that, when unresolved, the ratio of the magnitude of hydrodynamic force to that of self-gravity at the sub-resolution scale is the largest/smallest in MFV/SPH, the reasons for which we discussed in detail. These tests are repeated to investigate the effect of kernels of higher-order than the fiducial cubic spline. Our results indicate that the standard deviation of the kernel is a more appropriate definition of the size of a fluid element than its compact support radius.
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