We propose an extension to recently developed Relativistic Lattice Boltzmann solvers (RLBM), which allows the simulation of flows close to the free streaming limit. Following previous works Ambruş and Blaga (2018), we use product quadrature rules and select weights and nodes by separately discretizing the radial and the angular components.

This procedure facilitates the development of quadrature-based RLBM with increased isotropy levels, thus improving the accuracy of the method for the simulation of flows beyond the hydrodynamic regime.

In order to quantify the improvement of this discretization procedure over existing methods, we perform numerical tests of shock waves in one and two spatial dimensions in various kinetic regimes across the hydrodynamic and the free-streaming limits.

我们建议对最近开发的相对论格玻尔兹曼解算器（RLBM）进行扩展，该模型可以模拟接近自由流限制的流。遵循先前的Ambruş和Blaga（2018）的著作，我们使用乘积正交规则并通过分别离散化径向分量和角度分量来选择权重和节点。

此过程有助于开发具有各向同性水平的基于正交的RLBM，从而提高了模拟超出流体力学状态的流量的方法的准确性。

为了量化该离散化程序相对于现有方法的改进，我们在流体动力学和自由流动极限的各种动力学范围内，在一个和两个空间维度上对冲击波进​​行了数值测试。