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Relativistic lattice Boltzmann methods: Theory and applications
Physics Reports ( IF 23.9 ) Pub Date : 2020-06-01 , DOI: 10.1016/j.physrep.2020.03.004
A. Gabbana , D. Simeoni , S. Succi , R. Tripiccione

We present a systematic account of recent developments of the relativistic Lattice Boltzmann method (RLBM) for dissipative hydrodynamics. We describe in full detail a unified, compact and dimension-independent procedure to design relativistic LB schemes capable of bridging the gap between the ultra-relativistic regime, $k_{\rm B} T \gg mc^2$, and the non-relativistic one, $k_{\rm B} T \ll mc^2$. We further develop a systematic derivation of the transport coefficients as a function of the kinetic relaxation time in $d=1,2,3$ spatial dimensions. The latter step allows to establish a quantitative bridge between the parameters of the kinetic model and the macroscopic transport coefficients. This leads to accurate calibrations of simulation parameters and is also relevant at the theoretical level, as it provides neat numerical evidence of the correctness of the Chapman-Enskog procedure. We present an extended set of validation tests, in which simulation results based on the RLBMs are compared with existing analytic or semi-analytic results in the mildly-relativistic ($k_{\rm B} T \sim mc^2$) regime for the case of shock propagations in quark-gluon plasmas and laminar electronic flows in ultra-clean graphene samples. It is hoped and expected that the material collected in this paper may allow the interested readers to reproduce the present results and generate new applications of the RLBM scheme.

中文翻译:

相对论格子玻尔兹曼方法:理论与应用

我们系统地介绍了用于耗散流体动力学的相对论格子玻尔兹曼方法 (RLBM) 的最新发展。我们详细描述了一个统一、紧凑且与维度无关的程序来设计相对论 LB 方案,该方案能够弥合超相对论机制 $k_{\rm B} T \gg mc^2$ 和非-相对论,$k_{\rm B} T \ll mc^2$。我们进一步开发了传输系数的系统推导,作为 $d=1,2,3$ 空间维度中动力学弛豫时间的函数。后一步允许在动力学模型的参数和宏观传输系数之间建立定量桥梁。这导致模拟参数的准确校准,并且在理论水平上也是相关的,因为它为 Chapman-Enskog 过程的正确性提供了简洁的数字证据。我们提出了一组扩展的验证测试,其中将基于 RLBM 的模拟结果与温和相对论 ($k_{\rm B} T \sim mc^2$) 机制中的现有分析或半分析结果进行比较夸克-胶子等离子体中的冲击传播和超洁净石墨烯样品中的层流电子流。希望并期望本文收集的材料可以让感兴趣的读者重现目前的结果并产生 RLBM 方案的新应用。其中,在夸克胶子中激波传播的情况下,将基于 RLBM 的模拟结果与温和相对论 ($k_{\rm B} T \sim mc^2$) 机制中现有的解析或半解析结果进行比较超净石墨烯样品中的等离子体和层流电子流。希望并期望本文收集的材料可以让感兴趣的读者重现目前的结果并产生 RLBM 方案的新应用。其中,在夸克胶子中激波传播的情况下,将基于 RLBM 的模拟结果与温和相对论 ($k_{\rm B} T \sim mc^2$) 机制中现有的解析或半解析结果进行比较超净石墨烯样品中的等离子体和层流电子流。希望并期望本文收集的材料可以让感兴趣的读者重现目前的结果并产生 RLBM 方案的新应用。
更新日期:2020-06-01
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