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混合动理学通量WENO方法拓展研究-高超边界层专栏

何康1,2,李新亮2,刘洪伟2   

  1. 1. 中国科学院大学
    2. 中国科学院力学研究所
  • 收稿日期:2021-06-03 修回日期:2021-09-15 出版日期:2021-09-22 发布日期:2021-09-22
  • 通讯作者: 刘洪伟
  • 基金资助:
    国家重点研发计划;中国科学院战略先导专项;国家自然科学基金

An extension study of a hybrid kinetic WENO method

Kang HE1,2,Xinliang LiHong-Wei LIU   

  • Received:2021-06-03 Revised:2021-09-15 Online:2021-09-22 Published:2021-09-22
  • Contact: Hong-Wei LIU

摘要: 对基于气体动理论的高精度WENO方法进行了拓展研究,将 Int. J. Numer. Meth. Fluids 79, 290 (2015) 中提出的5阶混合动理学通量WENO方法进一步拓展到7阶和9阶;在5阶混合动理学WENO方法框架下,比较了采用不同激波探测技术的计算准确度和效率。在时间方向采用三阶Runge-Kutta方法进行推进,空间离散采用混合动理学通量WENO方法。通过一维和二维算例,验证了构造的7阶和9阶混合动理学方法比传统的矢通量分裂技术具有更高的分辨率和更小的数值耗散,并保持了较好的激波捕捉能力;对比发现Ohwada等提出的激波探测技术具备良好的激波探测能力和计算效率。

关键词: WENO重构, 气体动理论, 高阶方法, 数值耗散, 激波探测技术

Abstract: The extension study of high-order WENO methods based on the gas-kinetic theory is carried out. The hybrid kinetic WENO method proposed in Int.J.Numer.Meth.Fluids 79,290(2015) is further extended to 7th-order and 9th-order cases. Under the framework of the 5th-order hybrid kinetic WENO method, the computational accuracy and effi-ciency of different shock detection techniques are compared. The TVD Runge-Kutta method is used for the tem-poral integration and the hybrid kinetic WENO method is employed for the spatial discretization. Both one-dimensional and two-dimensional numerical examples are presented to show that the extended hybrid kinetic methods have higher resolution and less numerical dissipation than the traditional flux vector splitting technique , and can keep the good shock-capturing ability. Besides, it is found that the shock detection technology proposed by Ohwada et al. has good shock-detection ability and computational efficiency.

Key words: WENO reconstruction, gas kinetic theory, higher-order methods, numerical dissipation, shock detection methods

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