标题： 相对论kinetic理论中relaxation时间近似的一种高阶Shakhov类似扩展 显示英文标题

标题： High-order Shakhov-like extension of the relaxation time approximation in relativistic kinetic theory

摘要： 本文中我们提出了 Boltzmann 碰撞积分的 Anderson-Witting 松弛时间模型的一种相对论性的 Shakhov 类型推广。通过修改分布函数 $f_{\mathbf{k}}$ 趋向局部平衡 $f_{0\mathbf{k}}$ 的路径，并用 $f_{\mathbf{k}} - f_{{\rm S}\mathbf{k}}$ 替换 $f_{\mathbf{k}} - f_{0\mathbf{k}}$，从而实现了这一扩展。 类似于Shakhov分布的分布$f_{{\rm S} \mathbf{k}}$使用$f_{0\mathbf{k}}$和$f_\mathbf{k}$的不可约矩$\rho_r^{\mu_1 \cdots \mu_\ell}$构造，并在局部平衡时退化为$f_{0\mathbf{k}}$。利用矩方法，我们推导出系统的高阶Shakhov扩展形式，这些形式允许第一和第二输运系数独立控制。 我们通过调整大质量粒子Bjorken流中的剪切-体积耦合系数$\lambda_{\Pi \pi}$以及声波传播于超相对论气体中的扩散-剪切输运系数$\ell_{V\pi}$、$\ell_{\pi V}$来展示这一形式主义的能力。最后，我们通过一维Riemann问题的随机BAMPS方法的结果比较来说明二阶输运系数的重要性。 显示英文摘要

摘要： In this paper we present a relativistic Shakhov-type generalization of the Anderson-Witting relaxation time model for the Boltzmann collision integral. The extension is performed by modifying the path on which the distribution function $f_{\mathbf{k}}$ is taken towards local equilibrium $f_{0\mathbf{k}}$, by replacing $f_{\mathbf{k}} - f_{0\mathbf{k}}$ via $f_{\mathbf{k}} - f_{{\rm S}\mathbf{k}}$. The Shakhov-like distribution $f_{{\rm S} \mathbf{k}}$ is constructed using $f_{0\mathbf{k}}$ and the irreducible moments $\rho_r^{\mu_1 \cdots \mu_\ell}$ of $f_\mathbf{k}$ and reduces to $f_{0\mathbf{k}}$ in local equilibrium. Employing the method of moments, we derive systematic high-order Shakhov extensions that allow both the first- and the second-order transport coefficients to be controlled independently of each other. We illustrate the capabilities of the formalism by tweaking the shear-bulk coupling coefficient $\lambda_{\Pi \pi}$ in the frame of the Bjorken flow of massive particles, as well as the diffusion-shear transport coefficients $\ell_{V\pi}$, $\ell_{\pi V}$ in the frame of sound wave propagation in an ultrarelativistic gas. Finally, we illustrate the importance of second-order transport coefficients by comparison with the results of the stochastic BAMPS method in the context of the one-dimensional Riemann problem.