4.6 Article

Boundary conditions for kinetic theory-based models II: A linearized moment system

期刊

MATHEMATICAL METHODS IN THE APPLIED SCIENCES
卷 44, 期 18, 页码 14148-14172

出版社

WILEY
DOI: 10.1002/mma.7682

关键词

boundary conditions; generalized Kreiss condition; hyperbolic relaxation systems; moment closure systems; reduced boundary conditions

资金

  1. National Natural Science Foundation of China [11801030, 12071246]

向作者/读者索取更多资源

This work focuses on boundary conditions for a linearized hyperbolic moment system of the Boltzmann equation in one dimension. By introducing the Generalized Kreiss Conditions (GKC), the stability of the moment system is proven and reduced boundary conditions are derived for the corresponding equilibrium system. Numerical results confirm the convergence of the solution of the moment system to that of the equilibrium system under the GKC in the relaxation limit.
This work is concerned with boundary conditions (BCs) for a linearized hyperbolic moment system of the Boltzmann equation in one dimension. We show that even if the usual relaxation stability conditions and the Kreiss condition hold, there exists an exponentially increasing solution to the initial-boundary-value problem (IBVP) of the moment system. To clarify this problem, we check the generalized Kreiss condition (GKC) for hyperbolic relaxation systems. With the GKC, the stability of the moment system is proved by using an energy estimate together with the Laplace transformation. Moreover, under the GKC, we derive the reduced boundary conditions for the corresponding equilibrium system. Numerical results verify the convergence of the solution of the moment system to that of the equilibrium system with the derived BCs in the relaxation limit. Our analysis indicates that special attention should be paid when imposing boundary conditions for moment systems and the GKC should be respected to ensure the zero relaxation limit of the IBVP.

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