远离平衡态流动中的各向异性热化
Anisotropic Thermalization in Far-from-Equilibrium Flows
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中文总结 AI 辅助
该研究针对四类典型远离平衡态流动，采用间断伽辽金方法求解无矩闭合近似的玻尔兹曼方程，发现速度分布可由各向异性高斯近似，其协方差张量演化在短时间内符合自由流极限预测，长时间偏离反映碰撞影响。
中文摘要 AI 辅助
我们针对一类远离平衡态的变形条件，给出了玻尔兹曼方程的确定性间断伽辽金（DG）有限元解，未采用矩闭合近似。具体而言，我们考虑仿射流动，这类流动可将玻尔兹曼方程简化为约化速度场中约化分布函数的纯速度空间问题。我们采用张量积拉格朗日DG离散化方法，求解了四种典型流动的约化方程：简单剪切流、压力剪切流、双向剪切流以及涡旋流。我们的主要发现是，尽管处于非平衡条件下，速度分布在整个演化过程中可由各向异性高斯分布很好地近似。此外，我们证明，在无碰撞的自由流极限下，高斯分布协方差张量的演化等于右柯西-格林张量的逆。该预测与短时间内的数值解吻合度极高；而在更长时间尺度上，两者出现偏离，这反映了粒子碰撞的影响。
英文摘要
We present a deterministic discontinuous Galerkin (DG) finite-element solution of the Boltzmann equation, without moment-closure approximations, under a class of far-from-equilibrium deformations. Specifically, we consider affine flows which reduce the Boltzmann equation to a purely velocity-space problem for the reduced distribution function in a reduced velocity field. We solve the reduced equation using a tensor-product Lagrange DG discretization for four representative flows: simple shear, pressure shear, bi-directional shear, and a vortex flow. Our principal finding is that the velocity distribution is well-approximated by an anisotropic Gaussian throughout the evolution, despite the non-equilibrium conditions. Further, we show the evolution of the covariance tensor of the Gaussian distribution is equal to the inverse of the right Cauchy-Green tensor in the free-streaming limit without collisions. This prediction compares very well with the numerical solution at short times; at longer times, they grow apart, reflecting the influence of particle collisions.
