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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2021, Vol. 38 ›› Issue (5): 610-626.doi: 10.3969/j.issn.1005-3085.2021.05.002

• • 上一篇    下一篇

尺度自适应的离散统一气体动理学格式

许  丁1,2,   刘  欣1,    孙  祥1   

  1. 1. 西安交通大学航天航空学院 机械结构强度与振动国家重点实验室，西安 710049
    2. 陕西省先进飞行器服役环境与控制重点实验室，西安 710049
  • 出版日期:2021-10-15 发布日期:2021-12-15
  • 基金资助:
    中央高校基本科研业务费专项资金；国家重点基础研究发展计划 (973计划)(2013CB305702).

A Scale Adaptive Discrete Unified Gas Kinetic Scheme

XU Ding1,2,   LIU Xin1,   SUN Xiang1   

  1. 1. State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an 710049 
    2. Shaanxi Key Laboratory of Environment and Control for Flight Vehicle, Xi'an 710049
  • Online:2021-10-15 Published:2021-12-15
  • Supported by:
    The Fundamental Research Funds for the Central Universities; the National Basic Research Program of China (973 Program) (2013CB035702).

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摘要：

本文基于 Boltzmann-BGK 模型方程，建立其沿特征线离散的一般形式，离散过程中对于碰撞项的处理采用显式和隐式加权平均的方法，其中权系数依赖于当地努森数，可根据当地流动尺度不同进行自适应调节．通过权系数的引入，在文献现有离散统一气体动理学格式基础上发展出具有尺度自适应特性的离散统一气体动理学格式．数学上讨论了权系数的取值范围，并从物理上分析了权系数的不同取值所对应的流动特征，理论上指出权系数的引入使得该方法可以根据当地流动尺度的不同进行自适应调节．最后通过四个流动问题对该格式进行了考察和检验，结果表明该格式在精度、稳定性、尺度自适应性、流动边界层分辨能力以及旋涡分离和再附的捕捉能力等方面均具有较好的表现．

关键词: 气体动理学, 统一格式, 尺度自适应, Boltzmann 方程

Abstract:

In this paper, a general discretization of Boltzmann-BGK model equation along the characteristic line is obtained, where the time integration of collision term is handled as a weighted average between the implicit and explicit part. Moreover, the value of weight factor depends on the local Knudsen number, which represents the local flow regime and scale. With the aid of this weight factor, a scale adaptive discrete unified gas kinetic scheme (SADUGKS) has been developed based on the existing discrete unified gas kinetic scheme (DUGKS). The range of the value of weight factor is analyzed mathematically, and discussed physically. It is found that the value of weight factor could adjust dynamically according to the local flow regime and scale. Finally, four numerical simulations, including Taylor vortex flow, lid-driven cavity flow, backward-facing step flows and micro-Couette flow, are performed to investigate the accuracy and validity of SADUGKS in both continuum and rarefied flow regimes. It is concluded that the present SADUGKS is a reliable and practical multiscale method for all Knudsen number gas flows.

Key words: gas kinetic theory, unified scheme, scale adaptive, Boltzmann equation

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