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：本文研究具有恒定速度的动力学方程。我们提出了一种基于泊松核的矩方法，称为泊松-EQMOM。所推导的矩封闭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矩数量增加而收敛。该收敛性使本方法区别于大多数现有矩方法。此外，我们设计了一种精密的矩反演算法。作为应用案例，研究了过阻尼活性粒子的Vicsek模型。随后通过一系列数值实验（包括空间均匀、一维及二维问题）对泊松-EQMOM进行了验证。