This paper performs a stability analysis of a class of moment closure systems derived with an extended quadrature method of moments (EQMOM) for the one-dimensional BGK equation. The class is characterized with a kernel function. A sufficient condition on the kernel is identified for the EQMOM-derived moment systems to be strictly hyperbolic. We also investigate the realizability of the moment method. Moreover, sufficient and necessary conditions are established for the two-node systems to be well-defined and strictly hyperbolic, and to preserve the dissipation property of the kinetic equation.

翻译：本文针对一维BGK方程，基于扩展象限矩法（EQMOM）导出的矩封闭系统进行稳定性分析。该类系统以核函数为特征，本文识别出使EQMOM推导的矩系统保持严格双曲性的核函数充分条件。同时研究了矩方法的可实现性。此外，针对双节点系统，建立了其适定性、严格双曲性以及保持动力学方程耗散性质的充要条件。