In this paper, we present a gas-kinetic scheme using discrete velocity space to solve Maxwell equations. The kinetic model recovers Maxwell equations in the zero relaxation time limit. The scheme achieves second-order spatial and temporal accuracy in structured meshes comparable to the finite-difference time-domain (FDTD) method, without requiring staggered grids or leapfrog discretization. Our kinetic scheme is inherently multidimensional due to its use of kinetic beams in multiple directions, allowing larger time steps in multidimensional computations. It demonstrates better stability than FDTD when handling discontinuities and readily extends to unstructured meshes. We validate the method through various test cases including antenna simulation, sphere scattering, and flight vehicle scattering. The results align well with Riemann-solver-based solutions. Finally, we examine charge conservation for Maxwell equations through test cases.

翻译：本文提出了一种采用离散速度空间的气体动理学格式来求解麦克斯韦方程组。该动理学模型在零松弛时间极限下可恢复为麦克斯韦方程组。该格式在结构化网格上达到了与有限差分时域（FDTD）方法相当的二阶空间与时间精度，且无需使用交错网格或蛙跳离散。由于采用了多方向的动理学束，我们的动理学格式本质上是多维的，从而允许在多维计算中使用更大的时间步长。在处理不连续问题时，该格式表现出优于FDTD的稳定性，并能方便地推广至非结构网格。我们通过多种测试算例验证了该方法，包括天线仿真、球体散射和飞行器散射。计算结果与基于黎曼解算器的解吻合良好。最后，我们通过测试算例检验了该格式对麦克斯韦方程组电荷守恒性的保持。