EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于人工神经网络的亚格子应力建模

吴磊 肖左利

吴磊, 肖左利. 基于人工神经网络的亚格子应力建模. 力学学报, 2021, 53(10): 2667-2681 doi: 10.6052/0459-1879-21-356
引用本文: 吴磊, 肖左利. 基于人工神经网络的亚格子应力建模. 力学学报, 2021, 53(10): 2667-2681 doi: 10.6052/0459-1879-21-356
Wu Lei, Xiao Zuoli. Subgrid-scale stress modeling based on artificial neural network. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2667-2681 doi: 10.6052/0459-1879-21-356
Citation: Wu Lei, Xiao Zuoli. Subgrid-scale stress modeling based on artificial neural network. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2667-2681 doi: 10.6052/0459-1879-21-356

基于人工神经网络的亚格子应力建模

doi: 10.6052/0459-1879-21-356
基金项目: 国家自然科学基金资助项目(91852112)
详细信息
    作者简介:

    肖左利, 研究员, 主要研究方向: 湍流理论与数值模拟. E-mail: z.xiao@pku.edu.cn

  • 中图分类号: O357

SUBGRID-SCALE STRESS MODELING BASED ON ARTIFICIAL NEURAL NETWORK

  • 摘要: 亚格子(SGS)应力建模在湍流大涡模拟(LES)中有着极为重要的作用. 传统亚格子应力模型存在相对误差较大、耗散过强等问题. 近年来, 计算机技术的发展使得人工神经网络(ANN)等机器学习方法逐渐成为亚格子应力建模型的新研究范式. 本文着重考虑滤波宽度及雷诺数影响, 在不可压缩槽道湍流中建立了亚格子应力的ANN模型. 该模型以滤波后的直接数值模拟(fDNS)流场物理量及滤波尺度为输入信息, 相应滤波尺度下的亚格子应力为输出量. 通过对不同滤波尺度及不同雷诺数数据的训练, ANN模型能够给出与直接数值模拟(DNS)高度吻合的亚格子应力. 此外, 模型在亚格子耗散等非ANN建模量上也有着优异的预测性能, 与基于DNS获得的对应物理量的相关系数大都在0.9以上, 较梯度模型及Smagorinsky模型有明显提升. 在后验测试中, ANN模型对流向平均速度剖面的预测同样优于梯度模型、Smagorinsky模型及隐式大涡模拟(ILES)等传统LES模型. 在脉动速度均方根预测方面, 除了某些法向位置外ANN模型的性能整体上相对其他3个模型有所提升. 然而, 随着网格尺度的增大ANN模型预测的结果与fDNS结果的偏差逐渐增大. 总之, ANN方法在发展高精度亚格子应力模型上具有很大的潜力.

     

  • 图  1  ANN模型框架

    Figure  1.  The framework of ANN model

    图  2  槽道流计算区域示意图

    Figure  2.  Schematic for computational domain of turbulent channel flow

    图  3  DNS计算结果

    Figure  3.  DNS results

    图  4  前馈人工神经网络示意图

    Figure  4.  Schematic of the feedforward ANN

    图  5  ${{R}}{{{e}}_\tau }$ = 180, ${\varDelta _f}/\varDelta$ = 4时$y$ = 0.9截面上亚格子应力分量${\tau _{11}}$${\tau _{12}}$的分布云图. (a,b) DNS; (c,d) ANN模型; (e,f)梯度模型; (g,h) Smagorinsky模型

    Figure  5.  Contours of the SGS stress components ${\tau _{11}}$ and ${\tau _{12}}$ at ${{R}}{{{e}}_\tau }$ = 180, ${\varDelta _f}/\varDelta $ = 4 and $y$ = 0.9. (a,b) DNS; (c,d) ANN model; (e,f) gradient model; (g,h) Smagorinsky model

    图  6  ${{R}}{{{e}}_\tau }$ = 180, ${\varDelta _{\rm{f}}}/\varDelta$ = 2时DNS与ANN模型的亚格子应力平均值及其脉动的均方根剖面

    Figure  6.  Profiles of mean SGS stress and RMS fluctuating SGS stress obtained from DNS and ANN model at ${{R}}{{{e}}_\tau }$ = 180, ${\varDelta _{\rm{f}}}/\varDelta$ = 2

    图  7  ${{R}}{{{e}}_\tau }$ = 180, ${\varDelta _{\rm{f}}}/\varDelta $ = 3时各模型与DNS亚格子应力的相关系数剖面(横坐标: $y$)

    Figure  7.  Profiles of correlation coefficient between modeled SGS stress and DNS data at ${{R}}{{{e}}_\tau }$ = 180,${\varDelta _{\rm{f}}}/\varDelta $ = 3 (x-coordinate: $y$)

    图  8  ${{R}}{{{e}}_\tau }$ = 180, ${\varDelta _{\rm{f}}}/\varDelta $ = 3时各模型与DNS亚格子应力的相关系数随${y^ + }$的变化剖面(横坐标:${y^ + }$)

    Figure  8.  Profiles of correlation coefficient between modeled SGS stress and DNS data at ${{R}}{{{e}}_\tau }$ = 180,${\varDelta _{\rm{f}}}/\varDelta $ = 3 (x-coordinate: ${y^ + }$)

    图  9  亚格子应力空间平均相关系数

    Figure  9.  Spatially-averaged correlation coefficients between the modeled and DNS SGS stresses

    图  10  ${{R}}{{{e}}_\tau }$ = 300时3个测试算例的平均亚格子耗散剖面

    Figure  10.  Profiles of mean SGS dissipation for the three test cases at ${{R}}{{{e}}_\tau }$ = 300

    图  11  ${{R}}{{{e}}_\tau }$ = 300下3个测试算例的平均亚格子反传剖面

    Figure  11.  Profiles of mean SGS backscatter for the three test cases at ${{R}}{{{e}}_\tau }$ = 300

    图  12  ${{R}}{{{e}}_\tau }$ = 300下3个测试算例的平均亚格子力$ \partial {\tau _{1j}}/\partial {x_j} $剖面

    Figure  12.  Profiles of mean SGS force $ \partial {\tau _{1j}}/\partial {x_j} $ for three test cases at ${{R}}{{{e}}_\tau }$ = 300

    图  13  ${{R}}{{{e}}_\tau }$ = 300下3个测试算例的平均亚格子输运剖面

    Figure  13.  Profiles of mean SGS transport for three test cases at ${{R}}{{{e}}_\tau }$ = 300

    图  14  亚格子物理量空间平均相关系数

    Figure  14.  Spatially-averaged correlation coefficient of the SGS quantities

    图  15  DNS与ANN模型的亚格子应力平均值剖面

    Figure  15.  Profiles of mean SGS stress obtained from DNS and ANN model

    图  16  亚格子应力空间平均相关系数

    Figure  16.  Spatially-averaged correlation coefficient of SGS stress

    图  17  各个后验算例计算稳定后${{R}}{{{e}}_\tau }$值的相对误差率

    Figure  17.  The relative errors of ${{R}}{{{e}}_\tau }$ for a posteriori test cases at statistically steady state

    图  18  不同模型在3个网格尺度下的流向平均速度剖面

    Figure  18.  Profiles of mean streamwise velocity obtained using different models at three grid scales

    图  19  不同模型在3个网格尺度下脉动速度均方根剖面

    Figure  19.  Profiles of RMS fluctuating velocity obtained using different models at three grid scales

    表  1  DNS计算参数

    Table  1.   Computational parameters of DNS

    $ Re $$ R{e}_{\tau } $$ {L}_{x} $$ {L}_{y} $$ {L}_{z} $$ \mathrm{\Delta }{x}^{+} $$\mathrm{\Delta }{y}_{{\rm{min}}}^{+}$$\mathrm{\Delta }{y}_{{\rm{max}}}^{+}$$ \mathrm{\Delta }{\mathrm{z}}^{+} $$ ({N}_{x},{N}_{y},{N}_{z}) $
    2800180$ 4{\text{π}} $2$ 2{\text{π}} $8.8850.1987.1124.442(256, 129, 256)
    5000300$ 2{\text{π}} $2$ {\text{π}} $9.7520.2167.9054.876(192, 193, 192)
    7000395$ 2{\text{π}} $2$ {\text{π}} $9.8420.1288.8624.921(256, 257, 256)
    下载: 导出CSV

    表  2  相同雷诺数下不同滤波尺度ANN模型训练及测试集

    Table  2.   Training and test sets of ANN model at the same Reynolds number and different filter widths

    $ R{e}_{\tau } $ =
    180, 300, 395
    ${\mathrm{\varDelta } }_{\mathrm{f} }/\mathrm{\varDelta }$Size of dataset
    test set 2 whole field
    training set $ \sqrt{6} $ six planes of streamwise
    test set 3 whole field
    training set $2\sqrt{3}$ six planes of streamwise
    test set 4 whole field
    下载: 导出CSV

    表  3  亚格子应力空间平均相关系数

    Table  3.   The spatial averaged correlation coefficient of SGS stress

    ${ { {\varDelta } }_{\mathrm{f} } }/{ {\varDelta } }$DNS & ANNDNS & GRADNS & SMA
    $ {\tau }_{11} $$ {\tau }_{12} $$ {\tau }_{22} $$ {\tau }_{33} $$ {\tau }_{11} $$ {\tau }_{12} $$ {\tau }_{22} $$ {\tau }_{33} $$ {\tau }_{11} $$ {\tau }_{12} $$ {\tau }_{22} $$ {\tau }_{33} $
    20.990.980.980.990.650.740.840.630.280.210.300.14
    30.990.980.980.990.630.720.820.590.270.210.290.12
    40.980.960.970.970.600.700.800.550.250.220.270.12
    下载: 导出CSV

    表  4  不同雷诺数和不同滤波尺度下ANN模型训练及测试集

    Table  4.   Training and test sets of ANN model at different Reynolds numbers and filter widths

    Training or test set$ {Re}_{\tau } $$ {{\varDelta }}_{\mathrm{f}} /\varDelta $$ \mathrm{} $Size of dataset
    training set1802, $\sqrt{6},\; 3,\; 2\sqrt{3},\; 4$two planes of streamwise
    test set3002, $\sqrt{6}, \;3,\; 2\sqrt{3}, \;4$whole field
    training set3952, $\sqrt{6}, \;3,\; 2\sqrt{3}, \;4$one plane of streamwise
    下载: 导出CSV

    表  5  亚格子应力空间平均相关系数

    Table  5.   Spatially-averaged correlation coefficient of SGS stress

    ${\varDelta } _{\mathrm{f}} / {\varDelta }$DNS & ANNDNS & GRADNS & SMA
    $ {\tau }_{11} $$ {\tau }_{12} $$ {\tau }_{22} $$ {\tau }_{33} $$ {\tau }_{11} $$ {\tau }_{12} $$ {\tau }_{22} $$ {\tau }_{33} $$ {\tau }_{11} $$ {\tau }_{12} $$ {\tau }_{22} $$ {\tau }_{33} $
    2 0.91 0.85 0.95 0.95 0.66 0.76 0.83 0.63 0.21 0.21 0.28 0.13
    $ \sqrt{6} $ 0.92 0.92 0.92 0.94 0.65 0.75 0.83 0.61 0.20 0.21 0.27 0.13
    3 0.87 0.89 0.92 0.90 0.64 0.74 0.82 0.59 0.20 0.21 0.27 0.12
    $2\sqrt{3}$ 0.91 0.89 0.95 0.93 0.63 0.73 0.81 0.57 0.19 0.21 0.26 0.12
    4 0.92 0.89 0.93 0.92 0.61 0.72 0.80 0.55 0.19 0.21 0.25 0.11
    下载: 导出CSV

    表  6  各个后验算例计算稳定后的${{R}}{{{e}}_\tau }$

    Table  6.   Values of ${{R}}{{{e}}_\tau }$ for a posteriori test cases at statistically steady state

    ${ {{\varDelta } }_{\mathrm{f} } }/{{\varDelta } }$$ {Re}_{\tau }=180 $$ {Re}_{\tau }=300 $$ {Re}_{\tau }=395 $
    ANNSMAGRAILESANNSMAGRAILESANNSMAGRAILES
    2 179.4 175.5 177.1 177.4 296.6 289.7 293.0 294.4 392.3 388.4 388.0 386.7
    3 171.8 169.6 168.1 168.2 283.1 279.3 278.9 281.7 377.2 374.7 375.1 376.0
    4 168.2 166.4 160.8 161.8 273.8 271.3 264.0 268.1 365.5 361.3 358.3 360.4
    下载: 导出CSV
  • [1] Pope S. Turbulent Flows Cambridge: Cambridge University Press, 2000
    [2] Yang ZY. Large-eddy simulation: past, present and the future. Chinese Journal of Aeronautics, 2015, 28(1): 11-24 doi: 10.1016/j.cja.2014.12.007
    [3] 时北极, 何国威, 王士召. 基于滑移速度壁模型的复杂边界湍流大涡模拟. 力学学报, 2019, 51(3): 754-766 (Shi Beiji, He Guowei, Wang Shizhao. Large-eddy simulation of flows with complex geometries by using the slip-wall model. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 754-766 (in Chinese) doi: 10.6052/0459-1879-19-033
    [4] 陈林烽. 基于 Navier-Stokes 方程残差的隐式大涡模拟有限元模型. 力学学报, 2020, 52(5): 1314-1322 (Chen Linfeng. A residual based unresolved-scale finite element modelling for implict large eddy simulation. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1314-1322 (in Chinese) doi: 10.6052/0459-1879-20-055
    [5] 吴霆, 时北极, 王士召等. 大涡模拟的壁模型及其应用. 力学学报, 2018, 50(3): 453-466 (Wu Ting, Shi Beiji, Wang Shizhao, et al. Wall-model for large-eddy simulation and its applications. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 453-466 (in Chinese) doi: 10.6052/0459-1879-18-071
    [6] Smagorinsky J. General circulation experiments with the primitive equations: I. The basic experiment. Monthly Weather Review, 1963, 91(3): 99-164 doi: 10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
    [7] Moin P, Squires K, Cabot W, et al. A dynamic subgrid-scale model for compressible turbulence and scalar transport. Physics of Fluids A:Fluid Dynamics, 1991, 3(11): 2746-2757 doi: 10.1063/1.858164
    [8] Germano M, Piomelli U, Moin P, et al. A dynamic subgrid-scale eddy viscosity model. Physics of Fluids A:Fluid Dynamics, 1991, 3(7): 1760-1765 doi: 10.1063/1.857955
    [9] Lilly DK. A proposed modification of the Germano subgrid-cale closure method. Physics of Fluids A: Fluid Dynamics, 1992, 4(3): 633-635 doi: 10.1063/1.858280
    [10] Bardina J, Ferziger J, Reynolds WC. Improved subgrid-scale models for large-eddy simulation//13th Fluid and Plasmadynamics Conference, 1980: 1357
    [11] Liu S, Meneveau C, Katz J. On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet. Journal of Fluid Mechanics, 1994, 275: 83-119 doi: 10.1017/S0022112094002296
    [12] Domaradzki JA, Saiki EM. A subgrid-scale model based on the estimation of unresolved scales of turbulence. Physics of Fluids, 1997, 9(7): 2148-2164 doi: 10.1063/1.869334
    [13] Clark RA, Ferziger JH, Reynolds WC. Evaluation of subgrid-scale models using an accurately simulated turbulent flow. Journal of Fluid Mechanics, 1979, 91(1): 1-16 doi: 10.1017/S002211207900001X
    [14] Zang Y, Street RL, Koseff JR. A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows. Physics of Fluids A: Fluid Dynamics, 1993, 5(12): 3186-3196 doi: 10.1063/1.858675
    [15] Langford JA, Moser RD. Optimal LES formulations for isotropic turbulence. Journal of Fluid Mechanics, 1999, 398: 321-346 doi: 10.1017/S0022112099006369
    [16] Langford JA, Moser DR. Optimal large-eddy simulation results for isotropic turbulence. Journal of Fluid Mechanics, 2004, 521: 273 doi: 10.1017/S0022112004001776
    [17] Moser RD, Malaya NP, Chang H, et al. Theoretically based optimal large-eddy simulation. Physics of Fluids, 2009, 21(10): 105104 doi: 10.1063/1.3249754
    [18] Hughes TJR, Mazzei L, Jansen KE. Large eddy simulation and the variational multiscale method. Computing and Visualization in Science, 2000, 3(1): 47-59
    [19] Chai X, Mahesh K. Dynamic-equation model for large-eddy simulation of compressible flows. Journal of Fluid Mechanics, 2012, 699: 385-413 doi: 10.1017/jfm.2012.115
    [20] Xie CY, Wang JC, Li H, et al. An approximate second-order closure model for large-eddy simulation of compressible isotropic turbulence. CiCP, 2020, 27(775): 31
    [21] Slotnick J, Khodadoust A, Alonso J, et al. CFD vision 2030 study: a path to revolutionary computational aerosciences. Contractor Report, 20140003093, 2014
    [22] Krizhevsky A, Sutskever I, Hinton GE. Imagenet classification with deep convolutional neural networks. Advances in Neural Information Processing Systems, 2012, 25: 1097-1105
    [23] Sallab AEL, Abdou M, Perot E, et al. Deep reinforcement learning framework for autonomous driving. Electronic Imaging, 2017, 19: 70-76 doi: 10.2352/ISSN.2470-1173.2017.19.AVM-023
    [24] Alipanahi B, Delong A, Weirauch MT, et al. Predicting the sequence specificities of DNA-and RNA-binding proteins by deep learning. Nature Biotechnology, 2015, 33(8): 831-838 doi: 10.1038/nbt.3300
    [25] Duraisamy K, Iaccarino G, Xiao H. Turbulence modeling in the age of data. Annual Review of Fluid Mechanics, 2019, 51: 357-377 doi: 10.1146/annurev-fluid-010518-040547
    [26] 张伟伟, 朱林阳, 刘溢浪等. 机器学习在湍流模型构建中的应用进展. 空气动力学学报, 2019, 37(3): 444-454 (Zhang Weiwei, Zhu Linyang, Liu Yilang, et al. Progresses in the application of machine learning in turbulence modeling. Acta Aerodynamica Sinica, 2019, 37(3): 444-454 (in Chinese) doi: 10.7638/kqdlxxb-2019.0036
    [27] 谢晨月, 袁泽龙, 王建春等. 基于人工神经网络的湍流大涡模拟方法. 力学学报, 2021, 53(1): 1-16 (Xie Chenyue, Yuan Zelong, Wang Jianchun, et al. Artificial neural network-based subgrid-scale models for large-eddy simulation of turbulence. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(1): 1-16 (in Chinese)
    [28] Ren F, Hu H, Tang H. Active flow control using machine learning: A brief review. Journal of Hydrodynamics, 2020, 32: 247-253 doi: 10.1007/s42241-020-0026-0
    [29] 陈海昕, 邓凯文, 李润泽. 机器学习技术在气动优化中的应用. 航空学报, 2019, 40(1): 522480 (Chen Haixin, Deng Kaiwen. Utilization of machine learning technology in aerodynamic optimization. Acta Aeronautica et Astronautica Sinica, 2019, 40(1): 522480 (in Chinese)
    [30] Brunton SL, Noack BR, Koumoutsakos P. Machine learning for fluid mechanics. Annual Review of Fluid Mechanics, 2020, 52: 477-508 doi: 10.1146/annurev-fluid-010719-060214
    [31] 张伟伟, 寇家庆, 刘溢浪. 智能赋能流体力学展望. 航空学报, 2021, 42(4): 524689 (Zhang Weiwei, Kou Jiaqing, Liu Yilang. Prospect of artificial intelligence empowered fluid mechanics. Acta Aeronautica et Astronautica Sinica, 2021, 42(4): 524689 (in Chinese)
    [32] Maulik R, San O, Rasheed A, et al. Data-driven deconvolution for large eddy simulations of Kraichnan turbulence. Physics of Fluids, 2018, 30(12): 125109 doi: 10.1063/1.5079582
    [33] Maulik R, San O, Rasheed A, et al. Subgrid modelling for two-dimensional turbulence using neural networks. Journal of Fluid Mechanics, 2019, 858: 122-144 doi: 10.1017/jfm.2018.770
    [34] Vollant A, Balarac G, Corre C. Subgrid-scale scalar flux modelling based on optimal estimation theory and machine-learning procedures. Journal of Turbulence, 2017, 18(9): 854-878 doi: 10.1080/14685248.2017.1334907
    [35] Zhou Z, He G, Wang S, et al. Subgrid-scale model for large-eddy simulation of isotropic turbulent flows using an artificial neural network. Computers & Fluids, 2019, 195: 104319
    [36] Xie C, Wang J, Weinan E. Modeling subgrid-scale forces by spatial artificial neural networks in large eddy simulation of turbulence. Physical Review Fluids, 2020, 5(5): 054606 doi: 10.1103/PhysRevFluids.5.054606
    [37] Yuan Z, Xie C, Wang J. Deconvolutional artificial neural network models for large eddy simulation of turbulence. Physics of Fluids, 2020, 32(11): 115106 doi: 10.1063/5.0027146
    [38] Wang Z, Luo K, Li D, et al. Investigations of data-driven closure for subgrid-scale stress in large-eddy simulation. Physics of Fluids, 2018, 30(12): 125101 doi: 10.1063/1.5054835
    [39] Xie C, Li K, Ma C, et al. Modeling subgrid-scale force and divergence of heat flux of compressible isotropic turbulence by artificial neural network. Physical Review Fluids, 2019, 4(10): 104605 doi: 10.1103/PhysRevFluids.4.104605
    [40] Xie C, Wang J, Li H, et al. Artificial neural network mixed model for large eddy simulation of compressible isotropic turbulence. Physics of Fluids, 2019, 31(8): 085112 doi: 10.1063/1.5110788
    [41] Xie C, Wang J, Li K, et al. Artificial neural network approach to large-eddy simulation of compressible isotropic turbulence. Physical Review E, 2019, 99(5): 053113 doi: 10.1103/PhysRevE.99.053113
    [42] Sarghini F, De Felice G, Santini S. Neural networks based subgrid scale modeling in large eddy simulations. Computers & Fluids, 2003, 32(1): 97-108
    [43] Gamahara M, Hattori Y. Searching for turbulence models by artificial neural network. Physical Review Fluids, 2017, 2(5): 054604 doi: 10.1103/PhysRevFluids.2.054604
    [44] Park J, Choi H. Toward neural-network-based large eddy simulation: application to turbulent channel flow. Journal of Fluid Mechanics, 2021, 914: A16
    [45] Vreman AW, Kuerten JGM. Comparison of direct numerical simulation databases of turbulent channel flow at Reτ = 180. Physics of Fluids, 2014, 26(1): 015102 doi: 10.1063/1.4861064
    [46] Moser RD, Kim J, Mansour NN. Direct numerical simulation of turbulent channel flow up to Reτ = 590. Physics of Fluids, 1999, 11(4): 943-945 doi: 10.1063/1.869966
    [47] Sagaut P, Grohens R. Discrete filters for large eddy simulation. International Journal for Numerical Methods in Fluids, 1999, 31(8): 1195-1220 doi: 10.1002/(SICI)1097-0363(19991230)31:8<1195::AID-FLD914>3.0.CO;2-H
    [48] 周志华. 机器学习. 北京: 清华大学出版社, 2016

    Zhou Zhihua. Machine Learning. Beijing: Tsinghua University Press, 2016 (in Chinese)
    [49] LeCun Y, Bengio Y, Hinton G. Deep learning. Nature, 2015, 521(7553): 436-444 doi: 10.1038/nature14539
    [50] Rumelhart DE, Hinton GE, Williams RJ. Learning representations by back-propagating errors. Nature, 1986, 323(6088): 533-536 doi: 10.1038/323533a0
    [51] Goodfellow I, Bengio Y, Courville A, et al. Deep Learning. Cambridge: MIT Press, 2016
    [52] Loshchilov I, Hutter F. Decoupled weight decay regularization. arXiv preprint arXiv: 1711.05101, 2017.
    [53] Georgiadis NJ, Rizzetta DP, Fureby C. Large-eddy simulation: current capabilities, recommended practices, and future research. AIAA Journal, 2010, 48(8): 1772-1784
    [54] Scotti A, Meneveau C. A fractal model for large eddy simulation of turbulent flow. Physica D: Nonlinear Phenomena, 1999, 127(3-4): 198-232
    [55] Park N, Lee S, Lee J, et al. A dynamic subgrid-scale eddy viscosity model with a global model coefficient. Physics of Fluids, 2006, 18(12): 125109 doi: 10.1063/1.2401626
    [56] Chumakov SG. Scaling properties of subgrid-scale energy dissipation. Physics of Fluids, 2007, 19(5): 058104 doi: 10.1063/1.2735001
    [57] Härtel C, Kleiser L, Unger F, et al. Subgrid-scale energy transfer in the near-wall region of turbulent flows. Physics of Fluids, 1994, 6(9): 3130-3143 doi: 10.1063/1.868137
    [58] Piomelli U, Yu Y, Adrian RJ. Subgrid-scale energy transfer and near-wall turbulence structure. Physics of Fluids, 1996, 8(1): 215-224 doi: 10.1063/1.868829
    [59] Balarac G, Le Sommer J, Meunier X, et al. A dynamic regularized gradient model of the subgrid-scale scalar flux for large eddy simulations. Physics of Fluids, 2013, 25(7): 075107 doi: 10.1063/1.4813812
    [60] Leonard A. Energy cascade in large-eddy simulations of turbulent fluid flows. Advances in Geophysics, 1975, 18: 237-248
    [61] Völker S, Moser RD, Venugopal P. Optimal large eddy simulation of turbulent channel flow based on direct numerical simulation statistical data. Physics of Fluids, 2002, 14(10): 3675-3691 doi: 10.1063/1.1503803
    [62] Van Driest ER. On turbulent flow near a wall. Journal of the Aeronautical Sciences, 1956, 23(11): 1007-1011 doi: 10.2514/8.3713
    [63] Boris JP, Grinstein FF, Oran ES, et al. New insights into large eddy simulation. Fluid Dynamics Research, 1992, 10(4-6): 199 doi: 10.1016/0169-5983(92)90023-P
    [64] Visbal M, Morgan P, Rizzetta D. An implicit LES approach based on high-order compact differencing and filtering schemes//16th AIAA Computational Fluid Dynamics Conference, 2003: 4098
    [65] Park N, Yoo JY, Choi H. Toward improved consistency of a priori tests with a posteriori tests in large eddy simulation. Physics of Fluids, 2005, 17(1): 015103 doi: 10.1063/1.1823511
    [66] Komen EMJ, Camilo LH, Shams A, et al. A quantification method for numerical dissipation in quasi-DNS and under-resolved DNS, and effects of numerical dissipation in quasi-DNS and under-resolved DNS of turbulent channel flows. Journal of Computational Physics, 2017, 345: 565-595 doi: 10.1016/j.jcp.2017.05.030
    [67] Haering SW, Lee M, Moser RD. Resolution-induced anisotropy in large-eddy simulations. Physical Review Fluids, 2019, 4(11): 114605 doi: 10.1103/PhysRevFluids.4.114605
  • 加载中
图(21) / 表(6)
计量
  • 文章访问数:  1309
  • HTML全文浏览量:  501
  • PDF下载量:  196
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-07-26
  • 录用日期:  2021-09-17
  • 网络出版日期:  2021-09-18
  • 刊出日期:  2021-10-26

目录

    /

    返回文章
    返回