标题： 相对论动理论中松弛时间近似的高阶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： 在本文中，我们提出了一种相对论性的Shakhov型广义模型，用于对Anderson-Witting弛豫时间模型进行改进，以处理玻尔兹曼碰撞积分。该扩展是通过修改分布函数$f_{\mathbf{k}}$趋向于局部平衡$f_{0\mathbf{k}}$的路径，将$f_{\mathbf{k}} - f_{0\mathbf{k}}$替换为$f_{\mathbf{k}} - f_{{\rm S}\mathbf{k}}$。 类似于Shakhov的分布$f_{{\rm S} \mathbf{k}}$是使用$f_{0\mathbf{k}}$和$\rho_r^{\mu_1 \cdots \mu_\ell}$的不可约矩$f_\mathbf{k}$构造的，并在局部平衡中简化为$f_{0\mathbf{k}}$。采用矩方法，我们推导出系统高阶Shakhov扩展，使得一阶和二阶输运系数可以相互独立控制。 我们通过调整质量粒子的Bjorken流框架中的剪切-体积耦合系数$\lambda_{\Pi \pi}$，以及超相对论性气体中声波传播框架中的扩散-剪切输运系数$\ell_{V\pi}$，$\ell_{\pi V}$，来展示该形式体系的能力。最后，我们通过与一维Riemann问题背景下随机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.