Università di Ferrara and INFN-Ferrara, Via Saragat 1, I-44122 Ferrara, Italy.
ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Schafmattstraße 6, HIF, CH-8093 Zürich, Switzerland.
Phys Rev E. 2017 May;95(5-1):053304. doi: 10.1103/PhysRevE.95.053304. Epub 2017 May 11.
We present a systematic derivation of relativistic lattice kinetic equations for finite-mass particles, reaching close to the zero-mass ultrarelativistic regime treated in the previous literature. Starting from an expansion of the Maxwell-Jüttner distribution on orthogonal polynomials, we perform a Gauss-type quadrature procedure and discretize the relativistic Boltzmann equation on space-filling Cartesian lattices. The model is validated through numerical comparison with standard tests and solvers in relativistic fluid dynamics such as Boltzmann approach multiparton scattering and previous relativistic lattice Boltzmann models. This work provides a significant step towards the formulation of a unified relativistic lattice kinetic scheme, covering both massive and near-massless particles regimes.
我们提出了一种有限质量粒子的相对论格子动力学方程的系统推导方法，该方法可以接近之前文献中处理的零质量超相对论极限。从麦克斯韦-朱特纳分布的正交多项式展开出发，我们进行了高斯型求积过程，并在空间填充笛卡尔格子上对相对论玻尔兹曼方程进行了离散化。通过与相对论流体动力学中的标准测试和求解器（如玻尔兹曼方法多粒子散射和以前的相对论格子玻尔兹曼模型）的数值比较，对该模型进行了验证。这项工作朝着建立一个统一的相对论格子动力学方案迈出了重要的一步，该方案涵盖了有质量和近无质量粒子的范围。
