In this paper, we develop and characterize the fully dissipative Lattice Boltzmann method for ultra-relativistic fluids in two dimensions using three equilibrium distribution functions: Maxwell-Jüttner, Fermi-Dirac and Bose-Einstein. Our results stem from the expansion of these distribution functions up to fifth order in relativistic polynomials. We also obtain new Gaussian quadratures for square lattices that preserve the spatial resolution. Our models are validated with the Riemann problem and the limitations of lower order expansions to calculate higher order moments are shown. The kinematic viscosity and the thermal conductivity are numerically obtained using the Taylor-Green vortex and the Fourier flow respectively and these transport coefficients are compared with the theoretical prediction from Grad's theory. In order to compare different expansion orders, we analyze the temperature and heat flux fields on the time evolution of a hot spot.
Resistive dissipative magnetohydrodynamics from the Boltzmann-Vlasov equation
从Boltzmann-Vlasov方程出发，利用矩量法导出了相对论性、电阻性、二阶耗散磁流体力学的运动方程。因此，我们将之前的工作[Phys. Rev. D 98，076009（2018）]扩展到有限电导率的情况，其中我们只考虑了非电阻极限。这需要在运动方程中保持与电场$E^μ$成比例的项，并且由于电场与耗散量的耦合而导致新的输运系数。我们还表明，电荷扩散电流的纳维尔-斯托克斯极限对应于欧姆定律，而电导率系数和电荷扩散系数则与一种类型的维德曼-弗朗茨定律相关。
A Lattice Boltzmann Method for Relativistic Rarefied Flows in (2 + 1) Dimensions
我们提出了一个扩展最近开发的相对论格子玻尔兹曼解算器（RLBM），它允许模拟接近自由流动的限制。根据以前的工作[Phys. Rev. C 98（2018）035201]，我们使用积求积规则，并通过分别离散径向和角度分量来选择权重和节点。这个过程有利于发展的正交为基础的RLBM增加各向同性的水平，从而提高了精度的方法模拟超出流体动力学制度的流动。为了量化改进现有的方法，这种离散化过程中，我们进行数值测试的冲击波在一个和两个空间维度在各种动力学制度的流体动力学和自由流动的限制。
