论文标题
放松时间近似中二阶相对论流体动力学的转运系数
Transport coefficients of second-order relativistic fluid dynamics in the relaxation-time approximation
论文作者
论文摘要
我们使用矩的方法和Chapman-Enskog方法在放松时近似中得出了二阶流体动力学的传输系数，以$ 14 $的动力学力矩来得出相对论鲍尔茨曼方程的碰撞积分的放松时间近似。与先前在文献中报道的结果相反，我们发现使用两种方法得出的二阶传输系数是完全一致的。此外，我们表明，与二进制硬球相互作用不同，扩散剪切耦合系数$ \ ell_ {vπ} $，$λ_{vπ} $和$τ_{vπ} $实际上是在扩展订单$ n _ _ el el frircorl \ right \ righorl \ righorl \ firs offty $ fty fty ftty时实际上取消的。在这里，我们展示了如何以多种方式解决此类问题，并以$ 14 $的动态矩恢复了正确的二阶流体动力学传输系数。我们还通过与Boltzmann方程的数值解相比，验证了扩散剪切耦合的结果，以在超层压理想的理想气体中传播声波。
We derive the transport coefficients of second-order fluid dynamics with $14$ dynamical moments using the method of moments and the Chapman-Enskog method in the relaxation-time approximation for the collision integral of the relativistic Boltzmann equation. Contrary to results previously reported in the literature, we find that the second-order transport coefficients derived using the two methods are in perfect agreement. Furthermore, we show that, unlike in the case of binary hard-sphere interactions, the diffusion-shear coupling coefficients $\ell_{Vπ}$, $λ_{Vπ}$, and $τ_{Vπ}$ actually diverge in some approximations when the expansion order $N_\ell \rightarrow \infty$. Here we show how to circumvent such a problem in multiple ways, recovering the correct transport coefficients of second-order fluid dynamics with $14$ dynamical moments. We also validate our results for the diffusion-shear coupling by comparison to a numerical solution of the Boltzmann equation for the propagation of sound waves in an ultrarelativistic ideal gas.
