The moment method is a successful way to approximate the solution of the Boltzmann equation in reasonable runtime with relatively few unknowns while allowing for non-equilibrium effects of the gas. However, the convergence of the moment method with respect to an increasing number of moments is typically slow. This paper aims to improve the convergence of the moment method by introducing filtered hyperbolic moment equations that result in virtually no additional computational overhead while significantly reducing the error. The filter approach is based on a careful study of averaging solutions of two adjacent moment systems and the reformulation of the averaging using an artificial collision method that naturally gives rise to the filter. We study the properties of the filter and show numerical test cases of one-dimensional problems that demonstrate the superior quality of the new filtered moment method.

矩量法是一种在合理的运行时间内近似Boltzmann方程解的成功方法，具有相对较少的未知数，同时考虑了气体的非平衡效应。然而，关于增加的力矩，力矩方法的收敛通常很慢。本文旨在通过引入滤波后的双曲矩方程来改善矩量法的收敛性，该方程几乎不导致额外的计算开销，同时显着减少了误差。过滤器方法基于对两个相邻矩系统的平均解的仔细研究，并使用自然产生过滤器的人工碰撞方法对平均进行了重新公式化。