The present paper deals with the development of a numerical scheme for the solution of two-dimensional Boltzmann transport equation (BTE) under electronic nonequilibrium conditions. A two-dimensional explicit modal discontinuous Galerkin (DG) method with uniform meshes is developed for solving the BTE in conjunction with the relaxation time approximation. The spatial discretization is carried out using a high-order DG method, where the polynomial solutions are represented using scaled Legendre basis functions. A third-order explicit SSP-RK scheme is applied for temporal discretization to the resulting semi-discrete ordinary differential equation. The analytic steady state solution of BTE at low electromagnetic field is considered as the validation study. The numerical scheme is applied to the description of electron transport in non-linear dynamic conductivity based on static electric field. The electrical and Hall conductivities with nonequilibrium conditions is estimated for the BTE solution in presence of the electromagnetic field. These transport coefficients are also examined with the dependence of temperature and chemical potential. It is observed that the electrical and Hall conductivity decreases in the presence of a magnetic field. Numerical results demonstrate the potential advantages of the high-order scheme in treating ultrafast nonequilibrium dynamics.

本文研究了在电子非平衡条件下求解二维玻尔兹曼输运方程（BTE）的数值方案的发展。提出了一种具有均匀网格的二维显式模态不连续伽勒金（DG）方法，用于结合松弛时间近似来求解BTE。使用高阶DG方法执行空间离散化，其中多项式解使用可缩放的Legendre基函数表示。将三阶显式SSP-RK方案用于时间离散化到所得的半离散常微分方程。在低电磁场下，BTE的解析稳态解被认为是验证性研究。数值方案被用于描述基于静态电场的非线性动态电导率中的电子传输。在存在电磁场的情况下，针对BTE解决方案估算了具有非平衡条件的电导率和霍尔电导率。还根据温度和化学势来检查这些传输系数。可以观察到，在存在磁场的情况下，电导率和霍尔电导率降低。数值结果证明了高阶方案在处理超快非平衡动力学方面的潜在优势。还根据温度和化学势来检查这些传输系数。可以观察到，在存在磁场的情况下，电导率和霍尔电导率降低。数值结果证明了高阶方案在处理超快非平衡动力学方面的潜在优势。还根据温度和化学势来检查这些传输系数。可以观察到，在存在磁场的情况下，电导率和霍尔电导率降低。数值结果证明了高阶方案在处理超快非平衡动力学方面的潜在优势。