一维Grad矩系统的整体双曲正则化
Globally Hyperbolic Regularization of Grad's Moment System in One Dimensional Space
摘要：
本文对一维Grad矩系统提出了一种正则化方法，以获得全局双曲性。正则化的基础是观察到的特征多项式的雅可比矩阵的通量在格拉德的时刻系统是独立的中间时刻。该方法完全不依赖于碰撞的形式，因此该正则化方法适用于无碰撞项的系统。此外，该方法被证明是唯一的，只要最后时刻方程被允许更换，以满足非平衡独立特征速度的条件。给出了理想地层中正则化系统的双曲结构，包括信号速度、Riemann不变量以及稀疏波、接触间断和激波等特征波的性质。
英文摘要：
In this paper, we present a regularization to 1D Grad's moment system to achieve global hyperbolicity. The regularization is based on the observation that the characteristic polynomial of the Jacobian of the flux in Grad's moment system is independent of the intermediate moments. The method is not relied on the form of the collision at all, thus this regularization is applicable to the system without collision terms. Moreover, the proposed approach is proved to be the unique one if only the last moment equation is allowed to be alternated to match the condition of non-equilibrium independent characteristic speeds. The hyperbolic structure of the regularized system, including the signal speeds, Riemann invariants and the properties of the characteristic waves including the rarefaction wave, contact discontinuity and shock are provided in the perfect formations.
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