【作者】 胡文强； 李志辉；

【Author】 Hu Wenqiang;Li Zhihui;National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics;Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center;

【机构】 北京航空航天大学国家计算流体力学实验室； 中国空气动力研究与发展中心超高速所；

【摘要】 在可计算建模Boltzmann方程气体动理论统一算法(GKUA)研究应用过程中,需要通过一套与积分规则相一致的离散速度坐标点分布,代替原分布函数对积分变量的连续依赖性。一旦各个离散速度坐标点处的气体分子离散速度分布函数被数值求解,需要通过离散速度数值积分,任一时刻物理空间各点的宏观流动量才能获得适时演化更新。为此,发展合适有效的离散速度数值积分方法在气体动理论统一算法框架中,是一个很重要的过程,必须同时保证拥有足够的计算精度和采用尽量少的离散速度坐标点,以减少对于计算机存储需求和达到加速计算的目的。本文首先讨论了各种类型离散速度数值积分方法,即:无限区间、非等距型,包括原始和改进型Gauss-Hermite积分方法;有限区间、等距型,包括复合Simpson和高阶复合Newton-Cotes积分方法;有限区间、非等距型,包括多子区间Gauss-Legendre和Gauss-Chebyshev积分方法。接着在此基础上,本文探讨了各种积分方法对不同马赫数流动状态的适应性和所需离散速度积分节点数等问题。研究结果发现对于低马赫数流动,推荐使用改进型Gauss-Hermite积分方法,而对于高马赫数复杂流动推荐使用Gauss-Chebyshev积分方法。结果在求解跨流域高超声速绕流问题气体动理论统一算法框架下得到成功应用与检验。更多还原

【Abstract】 In the process of the applications for the gas kinetic unified algorithm(GKUA), based on the computing Boltzmann model equations, the discrete velocity ordinate method is introduced to get rid of the continuous dependency of the molecular velocity distribution function on the velocity space. Once the discrete distribution functions are solved, the macroscopic flow moments at any time in each point of the physical space can be obtained and updated by the appropriate discrete velocity quadrature method. Hence, developing the suitable and high-efficiency quadrature rules is an important procedure in GKUA, which should apply the discrete velocity nodes as little as possible and guarantee the sufficient computational accuracy in the meantime. In this paper, we discuss various discrete velocity quadrature methods, including the original and modified Gauss-Hermite, composite Newton–Cotes, multi-subinterval Gauss–Legendre and the Gauss–Chebyshev quadrature rules. Based on the previous works, we discuss the applicability of these rules when simulate some flows with different Mach numbers. From the results, it can be found that the original and modified Gauss–Hermite quadrature rules are the best options for the GKUA simulating low Mach number flows, while the Gauss–Chebyshev quadrature rule is the most appropriate integration method solving some complex and high Mach number flows. All research results have been utilized in the framework of the GKUA solving the hypersonic flows covering various flow regimes successfully.更多还原