航空学报 > 2022, Vol. 43 Issue (3): 125009-125009   doi: 10.7527/S1000-6893.2021.25009

应用维数分裂方法推广MUSCL和WENO格式的若干问题

刘君, 韩芳, 魏雁昕   

  1. 大连理工大学 航天航空学院, 大连 116024
  • 收稿日期:2020-11-26 修回日期:2021-01-14 出版日期:2022-03-15 发布日期:2021-04-21
  • 通讯作者: 刘君 E-mail:liujun65@dlut.edu.cn
  • 基金资助:
    国家数值风洞项目(NNW2018-ZT4B09);国家自然科学基金(11872144)

MUSCL and WENO schemes problems generated by dimension splitting approach

LIU Jun, HAN Fang, WEI Yanxin   

  1. School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China
  • Received:2020-11-26 Revised:2021-01-14 Online:2022-03-15 Published:2021-04-21
  • Supported by:
    National Numerical Wind Tunnel Project (NNW2018-ZT4B09);National Natural Science Foundation of China (11872144)

摘要: 首先对有限差分法和有限体积法的差异进行了讨论,在已有文献观点的基础上补充了二者在边界条件处理及网格需求等方面存在差异的新论据。介绍了逐维推导的MUSCL和WENO格式计算控制体界面通量的过程,认为此类格式计算界面通量的方法直接应用于高斯积分型有限体积法不够严谨,从而得到了应用维数分裂方法构造的MUSCL格式和WENO格式不属于高斯积分型有限体积法的观点,“积分格式”这一定义更能准确反映这类格式的特点。此外,讨论了MUSCL格式和WENO格式在曲线坐标系下不能保证守恒的原因,并简单介绍了消除方法。

关键词: 逐维方法, 有限体积法, MUSCL格式, WENO格式, 几何守恒律

Abstract: This paper first discuss the difference between finite difference method and finite volume method, subsequently supplementing new arguments for the existence of differences in the boundary condition treatment and grid requirements between these two methods based on the existing literature.The calculation process of the interface flux of the control volume by dimension-by-dimension derived MUSCL and WENO schemes is further introduced.Since the direct application of these schemes to the Gaussian integral finite volume method is considered not rigorous enough, it is concluded that the MUSCL scheme and WENO scheme constructed by the dimension splitting method do not belong to the Gaussian integral finite volume method, while the definition of "integral scheme" can more accurately reflect the characteristics of these schemes.In addition, the reasons for the inability of the MUSCL and WENO schemes to guarantee conservation in the curvilinear coordinate system are discussed, and the elimination methods briefly introduced.Finally, research results obtained according to the viewpoint of this paper are briefly presented.

Key words: dimension-by-dimension, finite volume method, MUSCL scheme, WENO scheme, geometric conservation law

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