对硬双曲双曲放松系统和动动BGK模型的半拉格朗吉亚方法的准确性和稳定性分析 (Accuracy and stability analysis of the Semi-Lagrangian method for stiff hyperbolic relaxation systems and kinetic BGK model)

In this paper, we develop a family of third order asymptotic-preserving (AP) and asymptotically accurate (AA) diagonally implicit Runge-Kutta (DIRK) time discretization methods for the stiff hyperbolic relaxation systems and kinetic Bhatnagar-Gross-Krook (BGK) model in the semi-Lagrangian (SL) setting. The methods are constructed based on an accuracy analysis of the SL scheme for stiff hyperbolic relaxation systems and kinetic BGK model in the limiting fluid regime when the Knudsen number approaches $0$. An extra order condition for the asymptotic third order accuracy in the limiting regime is derived. Linear Von Neumann stability analysis of the proposed third order DIRK methods are performed to a simplified two-velocity linear kinetic model. Extensive numerical tests are presented to demonstrate the AA, AP and stability properties of our proposed schemes.

翻译：在本文中,我们为硬双曲放松系统和半Lagrangian(SL)设置的动性Bhatnagar-Gross-Krook(BGK)模型开发了三等无症状保存(AP)和无症状保存(AA)直隐的龙格-Kutta(DIRK)时间分解方法,对硬双曲放松系统SL方案的精确分析以及Knudsen数字接近0美元时限制流体系统的动性BGK模型。对限制制度中的无症状第三顺序精确性附加了条件。对提议的DIRK第三顺序的线性Von Neumann稳定性分析进行了简化的双速线动能模型。进行了广泛的数字测试,以证明我们拟议办法的AA、AP和稳定性。