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LMS Method: a Spatiotemporal Optimal Low-Dimensional Dynamical Systems of Multi-Scale Numerical Simulation Method for Compressible Turbulence

QI Jin WU Chuijie

齐进,吴锤结. 基于时空最优低维动力系统的多尺度可压缩湍流数值模拟方法 [J]. 应用数学和力学,2024,45(3):318-336 doi: 10.21656/1000-0887.440294
引用本文: 齐进,吴锤结. 基于时空最优低维动力系统的多尺度可压缩湍流数值模拟方法 [J]. 应用数学和力学,2024,45(3):318-336 doi: 10.21656/1000-0887.440294
QI Jin, WU Chuijie. LMS Method: a Spatiotemporal Optimal Low-Dimensional Dynamical Systems of Multi-Scale Numerical Simulation Method for Compressible Turbulence[J]. Applied Mathematics and Mechanics, 2024, 45(3): 318-336. doi: 10.21656/1000-0887.440294
Citation: QI Jin, WU Chuijie. LMS Method: a Spatiotemporal Optimal Low-Dimensional Dynamical Systems of Multi-Scale Numerical Simulation Method for Compressible Turbulence[J]. Applied Mathematics and Mechanics, 2024, 45(3): 318-336. doi: 10.21656/1000-0887.440294

基于时空最优低维动力系统的多尺度可压缩湍流数值模拟方法

doi: 10.21656/1000-0887.440294
详细信息
  • 中图分类号: O35

LMS Method: a Spatiotemporal Optimal Low-Dimensional Dynamical Systems of Multi-Scale Numerical Simulation Method for Compressible Turbulence

More Information
    Author Bio:

    齐进(1977—),女,副研究员(E-mail: qi_jin@iapcm.ac.cn)

    Corresponding author: 吴锤结(1955—),男,教授(通讯作者. E-mail: cjwudut@dlut.edu.cn).
  • (我刊编委吴锤结来稿)
  • (Contributed by WU Chuijie, M. AMM Editorial Board)
  • 摘要: 按照周培源教授关于研究湍流数值模拟建模时必须分析和求解脉动速度场的思想,该研究基于第一性原理,系统地建立了基于时空低维最优动力系统的多尺度可压缩湍流数值模拟方法(LMS方法),并将其应用于多次冲击Richtmyer-Meshkov问题的数值模拟中,首次得到了可压缩湍流的中尺度流场和不同于DNS近似解的湍流近似解。数值结果表明,LMS方法可以用较少的网格获得更精确的湍流近似解。首先解决了研究中遇到的几个问题,为LMS方法的构建铺平了道路。这些问题是:基于湍流的物理特性,提出了湍流大、中、小尺度分解的新概念;找到了box滤波空间相关性的计算方法;指出了湍流建模理论中长期存在的逻辑错误,提出了多尺度湍流模型的概念;讨论了湍流封闭问题的本质和关键,给出了克服湍流封闭问题的数值方法。采用box滤波方法/空间网格平均方法且在大尺度网格的意义下,LMS方法的本质是一种将RANS、LES、DES和DNS等湍流数值模拟方法统一的全新湍流数值模拟方法。需要指出的是,LMS方法也可以作为湍流模型研究的辅助工具,以检验SGS尺度方程/脉动方程中各项所对应的湍流模型是否正确。
    (我刊编委吴锤结来稿)
    (Contributed by WU Chuijie, M. AMM Editorial Board)
  • Figure  1.  Basic characteristics of turbulence

    Figure  2.  Box filter: flat top hat filter

    Figure  3.  Predictability of low-dimensional dynamical systems (N=30, Re=2 000)

    Note To get the meanings of different colors in the figure, the readers could refer to the electronic webpage of this article.

    Figure  4.  Schematic diagram of the re-shock RMI initial state in a rectangular cavity

    Figure  5.  Time evolution of iso-surface of $\rho$ of the re-shock RM

    Figure  6.  Time evolution of iso-surface of $T$ of the re-shock RM

    Figure  7.  Time evolution of iso-surface of $u$ of the re-shock RM

    Figure  8.  Time evolution of iso-surface of v of the re-shock RM

    Figure  9.  Time evolution of iso-surface of $w$ of the re-shock RM

  • [1] CHOU P Y, CHOU R L. 50 years of turbulence research in China[J]. Annual Review of Fluid Mechanics, 1995, 27: 1-15. doi: 10.1146/annurev.fl.27.010195.000245
    [2] CHOU P Y. On an extension of Reynolds’ method of finding apparent stress and the nature of turbulence[J]. Acta Physica Sinica, 1940, 4(1): 1-34.
    [3] FU S, WANG L. Theory of Turbulence Modelling[M]. Beijing: Science Press, 2023.
    [4] GARNIER E, ADAMS N, SAGAUT P. Large Eddy Simulation for Compressible Flows[M]. New York: Springer, 2009.
    [5] SPALART P R. Strategies for turbulence modelling and simulations[J]. International Journal of Heat and Fluid Flow, 2000, 21: 252-263. doi: 10.1016/S0142-727X(00)00007-2
    [6] FU D X, MA Y W, LI X L, et al. Direct Numerical Simulation of Compressible Turbulence[M]. Beijing: Science Press, 2010.
    [7] WU C J, GUAN H, ZHAO H L. Large eddy simulation method based on small-scale SGS model, new development and applications of turbulence theory[C]//New Developments of Turbulence Theory and Applications. Shanghai: Shanghai University Press, 2000: 76-82.
    [8] GUAN H, WU C J. Large-eddy simulations of turbulent flows with lattice Boltzmann dynamics and dynamical system sub-grid models[J]. Science in China Series E:Technological Sciences, 2009, 52(3): 670-679. doi: 10.1007/s11431-009-0069-5
    [9] QI J, WU C J. Construction of spatiotemporal-coupling optimal low-dimensional dynamical systems for compressible Navier-Stokes equations[J]. Applied Mathematics and Mechanics, 2022, 43(10): 1053-1085.
    [10] BASSE N T. Turbulence intensity scaling: a fugue[J]. Fluids, 2019, 4(4): 180. doi: 10.3390/fluids4040180
    [11] BASSE N T. Scaling of global properties of fluctuating and mean streamwise velocities in pipe flow: characterization of a high Reynolds number transition region[J]. Physics of Fluids, 2021, 33: 065127. doi: 10.1063/5.0054769
    [12] TRITSCHLER V K, HICKEL S, HU X Y, et al. On the Kolmogorov inertial subrange developing from Richtmyer-Meshkov instability[J]. Physics of Fluids, 2013, 25: 071701. doi: 10.1063/1.4813608
    [13] COURANT R, FRIEDRICHS K O. Supersonic Flow and Shock Waves[M]. New York: Interscience, 1948.
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出版历程
  • 收稿日期:  2023-09-28
  • 修回日期:  2023-11-03
  • 刊出日期:  2024-03-01

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