A numerical approach to the non-uniqueness problem of cosmic ray two-fluid equations at shocks
A numerical approach to the non-uniqueness problem of cosmic ray two-fluid equations at shocks
复制标题
冲击时宇宙线二流体方程非唯一性问题的数值方法
DOI：
10.1093/mnras/stab142
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发表时间：
2021
影响因子：
4.8
通讯作者：
A. Mignone
中科院分区：
文献类型：
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作者：
Siddhartha Gupta;P. Sharma;A. Mignone
在天体物理流动的流体动力学（HD）和磁流体动力学（MHD）模拟中，宇宙线（CR）经常被模拟为附加流体。标准的CR双流体模型描述的三个守恒定律（表示质量，动量和总能量守恒）和一个额外的方程（CR压力），不能在一个令人满意的保守形式铸造。模型方程中含有空间导数的非保守项的存在阻止了激波后面的唯一弱解。我们调查了一些方法的数值解的两流体方程，并发现，在存在冲击波，结果通常取决于数值的细节（空间重建，时间步进，CFL数，和所采用的离散化）。所有的方法收敛到一个独特的结果，如果在冲击的热流体和非热流体之间的能量分配是规定使用亚网格处方。这突出了双流体方程在冲击时的非唯一性问题。从我们的数值研究，我们报告了一个强大的方法，解决方案是不敏感的数值细节，即使在没有一个亚网格处方，虽然我们建议使用动力学理论的结果在冲击的亚网格关闭。次网格闭合对于一个可靠的激波后解及其对大尺度流动的影响是至关重要的，因为确定CR加速度的激波微物理在流体近似中没有被准确地捕获。关键的测试问题，流体建模的局限性，和未来的发展方向进行了讨论。
Cosmic rays (CRs) are frequently modeled as an additional fluid in hydrodynamic (HD) and magnetohydrodynamic (MHD) simulations of astrophysical flows. The standard CR two-fluid model is described in terms of three conservation laws (expressing conservation of mass, momentum and total energy) and one additional equation (for the CR pressure) that cannot be cast in a satisfactory conservative form. The presence of non-conservative terms with spatial derivatives in the model equations prevents a unique weak solution behind a shock. We investigate a number of methods for the numerical solution of the two-fluid equations and find that, in the presence of shock waves, the results generally depend on the numerical details (spatial reconstruction, time stepping, the CFL number, and the adopted discretization). All methods converge to a unique result if the energy partition between the thermal and non-thermal fluids at the shock is prescribed using a subgrid prescription. This highlights the non-uniqueness problem of the two-fluid equations at shocks. From our numerical investigations, we report a robust method for which the solutions are insensitive to the numerical details even in absence of a subgrid prescription, although we recommend a subgrid closure at shocks using results from kinetic theory. The subgrid closure is crucial for a reliable post-shock solution and also its impact on large scale flows because the shock microphysics that determines CR acceleration is not accurately captured in a fluid approximation. Critical test problems, limitations of fluid modeling, and future directions are discussed.