相对论性大涡模拟的协变方法：纤维化图象
A covariant approach to relativistic large-eddy simulations: The fibration picture
摘要：
湍流模型需要大范围尺度的分辨率，从大涡旋到与耗散直接相关的小尺度特征。由于所需的分辨率不在大规模数值模拟的范围内，标准策略涉及通过时间平均或空间滤波来平滑流体动力学。这些策略在广义相对论中提出了形式上的问题，在广义相对论中，空间和时间的分裂取决于观察者。为了取得进展，我们开发了一个新的协变框架过滤/平均的基础上与流体元素和费米坐标的使用，以方便有意义的本地分析的时空纤维化。我们推导出解决的运动方程，演示如何“有效”耗散项出现，因为粗粒化，并特别注意解决量的物理解释。最后，作为平滑的流体动力学不可避免地导致一个封闭的问题，我们提出了一个新的封闭方案的灵感来自最近的进展，在建模耗散相对论性流体，至关重要的是，证明了线性稳定性的建议模型。
英文摘要：
Models of turbulent flows require the resolution of a vast range of scales, from large eddies to small-scale features directly associated with dissipation. As the required resolution is not within reach of large scale numerical simulations, standard strategies involve a smoothing of the fluid dynamics, either through time averaging or spatial filtering. These strategies raise formal issues in general relativity, where the split between space and time is observer dependent. To make progress, we develop a new covariant framework for filtering/averaging based on the fibration of spacetime associated with fluid elements and the use of Fermi coordinates to facilitate a meaningful local analysis. We derive the resolved equations of motion, demonstrating how "effective" dissipative terms arise because of the coarse-graining, and paying particular attention to the thermodynamical interpretation of the resolved quantities. Finally, as the smoothing of the fluid-dynamics inevitably leads to a closure problem, we propose a new closure scheme inspired by recent progress in the modelling of dissipative relativistic fluids, and crucially, demonstrate the linear stability of the proposed model.
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