This work is concerned with kinetic equations with velocity of constant magnitude. We propose a quadrature method of moments based on the Poisson kernel, called Poisson-EQMOM. The derived moment closure systems are well defined for all physically relevant moments and the resultant approximations of the distribution function converge as the number of moments goes to infinity. The convergence makes our method stand out from most existing moment methods. Moreover, we devise a delicate moment inversion algorithm. As an application, the Vicsek model is studied for overdamped active particles. Then the Poisson-EQMOM is validated with a series of numerical tests including spatially homogeneous, one-dimensional and two-dimensional problems.

翻译：本文研究速度恒幅的动力学方程。我们提出了一种基于泊松核的求积累积量方法，称为Poisson-EQMOM。所推导的矩闭合系统对所有物理相关矩均有良好定义，且分布函数的近似解随着矩数量趋于无穷而收敛。这种收敛性使得我们的方法优于现有的大多数矩方法。此外，我们设计了一种精细的矩反演算法。作为应用，我们针对过阻尼活性粒子研究了Vicsek模型。随后，通过一系列数值测试（包括空间均匀问题、一维和二维问题）验证了Poisson-EQMOM的有效性。