We present a tensor-decomposition method to solve the Boltzmann transport equation (BTE) in the Bhatnagar-Gross-Krook approximation. The method represents the six-dimensional BTE as a set of six one-dimensional problems, which are solved with the alternating least-squares algorithm and the discrete Fourier transform at N collocation points. We use this method to predict the equilibrium distribution (steady-state simulation) and a non-equilibrium distribution returning to the equilibrium (transient simulation). Our numerical experiments demonstrate $N\log N$ scaling. Unlike many BTE-specific numerical techniques, the numerical tensor-decomposition method we propose is a general technique that can be applied to other high-dimensional systems.

我们提出了张量分解方法来解决Bhatnagar-Gross-Krook逼近中的Boltzmann输运方程。该方法将六维BTE表示为六个一维问题的集合，这些问题通过交替最小二乘算法和N个搭配点处的离散傅立叶变换解决。我们使用这种方法来预测平衡分布（稳态模拟）和返回平衡的非平衡分布（瞬态模拟）。我们的数值实验表明$ñ\mathrm{日志}ñ$缩放。与许多特定于BTE的数值技术不同，我们提出的数值张量分解方法是可以应用于其他高维系统的通用技术。