论文标题
双曲线方程的投射集成方案
Projective Integration Schemes for Hyperbolic Moment Equations
论文作者
论文摘要
在本文中，我们将投影整合方法应用于玻尔兹曼方程和BGK方程的双曲矩模型，并研究结果方案的数值特性。投射整合是一种明确的，渐近保护的方案，它是根据模型的慢速和（一个或多个）快速特征值集群之间具有较大光谱差异的问题量身定制的。线性力矩模型的光谱分析清楚地显示了光谱差距，并揭示了该模型的多尺度性质，该模型的多尺度性质是该模型是匹配的选择。非侵入式投影集成方法与矩模型的组合允许使用具有不同碰撞项，碰撞频率和放松时间的几个1D和2D测试用例进行准确但有效的仿真。
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.
