双曲型矩方程的投影积分格式
Projective Integration Schemes for Hyperbolic Moment Equations
摘要：
本文将投影积分方法应用于Boltzmann方程和BGK方程的双曲矩模型，并研究了所得格式的数值性质。投影积分是一个显式的，渐近保持计划，是专为慢和（一个或多个）快速特征值集群的模型之间的大的频谱间隙的问题。线性化矩模型的谱分析清楚地显示了谱隙，并揭示了投影积分是匹配选择的模型的多尺度性质。非侵入式投影积分方法与矩模型的组合允许准确，但有效的模拟具有显着的加速，如使用具有不同碰撞项，碰撞频率和松弛时间的几个1D和2D测试用例所示。
英文摘要：
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, asymptotic-preserving 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.
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