In this paper, we apply projective integration methods to hyperbolic moment models of the Boltzmann equation and the BGK equation, and investigate the numerical properties of the resulting scheme. Projective integration is an explicit scheme that is tailored to problems with large spectral gaps between slow and (one or many) fast eigenvalue clusters of the model. The spectral analysis of a linearized moment model clearly shows spectral gaps and reveals the multi-scale nature of the model for which projective integration is a matching choice. The combination of the non-intrusive projective integration method with moment models allows for accurate, but efficient simulations with significant speedup, as demonstrated using several 1D and 2D test cases with different collision terms, collision frequencies and relaxation times.

中文翻译：

---

双曲矩方程的投影积分格式

在本文中，我们将射影积分方法应用于Boltzmann方程和BGK方程的双曲矩模型，并研究了所得方案的数值性质。投影积分是一种显式方案，适用于模型的慢特征值簇和（一个或多个）快速特征值簇之间具有较大光谱间隙的问题。线性矩模型的频谱分析清楚地显示了频谱缺口，并揭示了模型的多尺度性质，投射积分是该模型的匹配选择。非侵入式射影积分方法与弯矩模型的结合可实现准确而有效的仿真，并具有显着的加速效果，如使用几个具有不同碰撞条件，碰撞频率和弛豫时间的1D和2D测试案例所证明的那样。