[1] ELSINGA G E, SCARANO F, WIENEKE B, et al. Tomographic particle image velocimetry[J]. Experiments in Fluids, 2006, 41(6):933-947.
[2] RAFFEL M, WILLERT C E, WERELEY S T, et al. Particle image velocimetry:A practical guide[M]. 2nd ed. Berlin:Springer-Verlag, 2007.
[3] FREYMUTH P. Frequency response and electronic testing for constant-temperature hot-wire anemometers[J]. Journal of Physics E:Scientific Instruments, 1977, 10(7):705.
[4] PIOMELLI U. Large-eddy simulation:Achievements and challenges[J]. Progress in Aerospace Sciences, 1999, 35(4):335-362.
[5] SPALART P R. Detached-eddy simulation[J]. Annual Review of Fluid Mechanics, 2009, 41:181-202.
[6] HE C, LIU Y, YAVUZKURT S. A dynamic delayed detached-eddy simulation model for turbulent flows[J]. Computers & Fluids, 2017, 146:174-189.
[7] EVENSEN G. Data assimilation[M]. Berlin:Springer-Verlag, 2009.
[8] NAVON I M. Data assimilation for numerical weather prediction:A review[M]//Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications. Berlin:Springer-Verlag, 2009:21-65.
[9] EDWARDS C A, MOORE A M, HOTEIT I, et al. Regional ocean data assimilation[J]. Annual Review of Marine Science, 2015, 7(1):21-42.
[10] 王文, 寇小华. 水文数据同化方法及遥感数据在水文数据同化中的应用进展[J]. 河海大学学报(自然科学版),2009,37(5):556-562. WANG W, KOU X H. Methods for hydrological data assimilation and advances of assimilating remotely sensed data into rainfall-runoff models[J]. Journal of Hohai University(Natural Sciences), 2009,37(5):556-562(in Chinese).
[11] 秦耀军, 周晓勇, 杨亚宾, 等. 基于数据同化技术的地质参数反演分析研究[J]. 水科学与工程技术,2017(6):78-82. QIN Y J, ZHOU X Y, YANG Y B, et al. Back analysis of geological parameters based on data assimilation[J]. Water Sciences and Engineering Technology,2017(6):78-82(in Chinese).
[12] YAMAGUCHI J, YOSHIDA K, KANEDA Y. Suppression of error growth in turbulence by data assimilation in isotropic turbulence[C]//American Physical Society, Division of Fluid Dynamics 56th Annual Meeting, 2003.
[13] KATO H, OBAYASHI S. Statistical approach for determining parameters of a turbulence model[C]//15th International Conference on Information Fusion, 2012.
[14] TR'EMOLET Y. Accounting for an imperfect model in 4D-Var[J]. Quarterly Journal of the Royal Meteorological Society, 2006, 132:2483-2504.
[15] LAKSHMIVARAHAN S, STENSRUD D. Ensemble Kalman filter[J]. IEEE Control Systems, 2009, 29(3):34-46.
[16] HE C, LIU Y, GAN L. A data assimilation model for turbulent flows using continuous adjoint formulation[J]. Physics of Fluids, 2018, 30(10):105108.
[17] WANG J X, WU J L, XIAO H. Physics-informed machine learning for predictive turbulence modeling:Using data to improve RANS modeled Reynolds stresses[J]. Physical Review Fluids, 2016, 2(3):1-22.
[18] SINGH A P, MEDIDA S, DURAISAMY K. Machine-learning-augmented predictive modeling of turbulent separated flows over airfoils[J]. AIAA Journal, 2017, 55(7):2215-2227.
[19] PARISH E J, DURAISAMY K. A paradigm for data-driven predictive modeling using field inversion and machine learning[J]. Journal of Computational Physics, 2016, 305:758-774.
[20] 马艺敏, 陈铭, 王强, 等. 应用PIV测量缩比共轴双旋翼流场特性的研究[J]. 南京航空航天大学学报, 2015, 47(2):220-227. MA Y M, CHEN M, WANG Q, et al. PIV measurements of model-scale coaxial rotors flow features[J]. Journal of Nanjing University of Aeronautics & Astronautics, 2015, 47(2):220-227(in Chinese).
[21] 张俊, 陈柳君, 胥頔, 等. 航空涡轮发动机燃烧室内流场的PIV测量[J]. 航空动力学报,2017, 32(6):1289-1295. ZHANG J, CHEN L J, XU D, et al. PIV measurement for inner flowfield in aero turbine engine combustor[J]. Journal of Aerospace Power, 2017, 32(6):1289-1295(in Chinese).
[22] GULYÁS A, BODOR Á, REGERT T, et al. PIV measurement of the flow past a generic car body with wheels at LES applicable Reynolds number[J]. International Journal of Heat & Fluid Flow, 2013, 43:220-232.
[23] WIENEKE B. Stereo-PIV using self-calibration on particle images[J]. Experiments in Fluids, 2005, 39(2):267-280.
[24] WORTH N A, NICKELS T B. Acceleration of Tomo-PIV by estimating the initial volume intensity distribution[J]. Experiments in Fluids, 2008, 45(5):847-856.
[25] DE SILVA C M, BAIDYA R, MARUSIC I. Enhancing Tomo-PIV reconstruction quality by reducing ghost particles[J]. Measurement Science & Technology, 2013, 24(2):024010.
[26] HE C, LIU Y, PENG D, et al. Measurement of flow structures and heat transfer behind a wall-proximity square rib using TSP, PIV and split-fiber film[J]. Experiments in Fluids, 2016, 57(11):165.
[27] 韩振兴. 热敏液晶测温技术及其在平板气膜冷却实验中的应用[D]. 北京:中国科学院工程热物理研究所, 2005. HAN Z X. Liquid crystal thermography and its application in film cooling on flat plate[D]. Beijing:Institute of Engineering Thermophysics, Chinese Academy of Sciences, 2005(in Chinese).
[28] HE C, LIU Y. Proper orthogonal decomposition of time-resolved LIF visualization:Scalar mixing in a round jet[J]. Journal of Visualization, 2017, 20:789-815.
[29] HSU P S, HALLS B R, ROY S, et al. Three-dimensional temperature measurements in turbulent reacting flows[C]//Laser Applications to Chemical, Security & Environmental Analysis, 2018.
[30] PENG D, JENSEN C D, JULIANO T J, et al. Temperature-compensated fast pressure-sensitive paint[J]. AIAA Journal, 2013, 51(10):2420-2431.
[31] VAN OUDHEUSDEN B. PIV-based pressure measurement[J]. Measurement Science and Technology, 2013, 24(3):032001.
[32] HE C, LIU Y, GAN L. Instantaneous pressure determination from unsteady velocity fields using adjoint-based sequential data assimilation[J]. Physics of Fluids, 2020, 32(3):035101.
[33] 付在国, 赵飞宇, 张莉, 等. PIV与PLIF同步测量方法在湍流扩散研究中的应用[J]. 上海电力大学学报, 2019, 35(1):90-95. FU Z G, ZHAO F Y, ZHANG L, et al. Application of simultaneous PIV and PLIF measurements in turbulent diffusion study[J]. Journal of Shanghai University of Electric Power, 2019, 35(1):90-95(in Chinese).
[34] SARATHI P, GURKA R, KOPP G A, et al. A calibration scheme for quantitative concentration measurements using simultaneous PIV and PLIF[J]. Experiments in Fluids, 2012, 52(1):247-259.
[35] PENG D, LIU Y. A grid-pattern PSP/TSP system for simultaneous pressure and temperature measurements[J]. Sensors & Actuators B Chemical, 2016, 222:141-150.
[36] DURAISAMY K, IACCARINO G, XIAO H. Turbulence modeling in the age of data[J]. Annual Review of Fluid Mechanics, 2018, 51:357-377.
[37] XIAO H, CINNELLA P. Quantification of model unertainty in RANS simulations:A review[J]. Progress in Aerospace Sciences, 2019, 108:1-31.
[38] 张兆顺, 崔桂香, 许春晓. 湍流大涡数值模拟的理论和应用[M]. 北京:清华大学出版社, 2008. ZHANG Z S, CUI G X, XU C X. Theory and application of turbulence large eddy simulation[M]. Beijing:Tsinghua University Press, 2008(in Chinese).
[39] ASHTON N, REVELL Z, PROSSER R, et al. Development of an alternative delayed detached-eddy simulation formulation based on elliptic relaxation[J]. AIAA Journal, 2013, 51(2):513-519.
[40] XIAO Z, LIU J, ZUO K, et al. Numerical investigations of massively separated flows past rudimentary landing gear using SST-DDES:AIAA-2012-0385[R]. Reston:AIAA, 2012.
[41] ISHIHARA T, QI Y. Numerical study of turbulent flow fields over steep terrain by using modified delayed detached-eddy simulations[J]. Boundary-Layer Meteorology, 2019, 170(1):45-68.
[42] SILVA C M D, PHILIP J, MARUSIC I. Minimization of divergence error in volumetric velocity measurements and implications for turbulence statistics[J]. Experiments in Fluids, 2013, 54(7):1-17.
[43] LI Z, ZHANG H, BAILEY S C C, et al. A data-driven adaptive Reynolds-averaged Navier-Stokes k-ω model for turbulent flow[J]. Journal of Computational Physics, 2017, 345:111-131.
[44] WU J L, WANG J X, XIAO H. A Bayesian calibration-prediction method for reducing model-form uncertainties with application in RANS simulations[J]. Flow, Turbulence and Combustion, 2016, 97(3):761-786.
[45] 邓志文, 何创新, 付豪, 等. 基于卡尔曼滤波数据同化和PIV测量的射流场重构[C]//第十届全国流体力学学术会议论文摘要集, 2018. DENG Z W, HE C X, FU H, et al. Reconstruction of jet flow based on EnKF data assimilation and PIV measurements[C]//Abstracts of the 10th National Conference on Fluid Mechanics, 2018(in Chinese).
[46] ZHANG X, GOMEZ T, COUTIER-DELGOSHA O. Bayesian optimisation of RANS simulation with ensemble-based variational method in convergent-divergent channel[J]. Journal of Turbulence, 2019, 20(5):1-26.
[47] DENG Z, HE C, WEN X, et al. Recovering turbulent flow field from local quantity measurement:Turbulence modeling using ensemble-Kalman-filter-based data assimilation[J]. Journal of Visualization 2018, 21(6):1043-1063.
[48] MARGHERI L. Quantification of epistemic uncertainties and parameter calibration in RANS turbulence models[D]. Pisa:University of Pisa, 2012.
[49] EMORY M, LARSSON J, IACCARINO G. Modeling of structural uncertainties in Reynolds-averaged Navier-Stokes closures[J]. Physics of Fluids, 2013, 25(11):110822.
[50] CHEUNG S H, OLIVER T, PRUDENCIO E E, et al. Bayesian uncertainty analysis with applications to turbulence modeling[J]. Reliability Engineering & System Safety, 2011, 96(9):1137-1149.
[51] OLIVER T A, MOSER R D. Bayesian uncertainty quantification applied to RANS turbulence models[J]. Journal of Physics Conference, 2011, 318(4):042032.
[52] SINGH A P, DURAISAMY K. Using field inversion to quantify functional errors in turbulence closures[J]. Physics of Fluids, 2016, 28(4):045110.
[53] SPALART P R, ALLMARAS S R. A one-equation turbulence model for aerodynamic flows:AIAA-1992-0439[R]. Reston:AIAA, 1992.
[54] SINGH A P, SHIVAJI M, DURAISAMY K. Machine-learning-augmented predictive modeling of turbulent separated flows over airfoils[J]. AIAA Journal, 2017, 55(7):2215-2227.
[55] PAPOUTSIS-KIACHAGIAS E M, GIANNAKOGLOU K C. Continuous adjoint methods for turbulent flows, applied to shape and topology optimization:Industrial applications[J]. Archives of Computational Methods in Engineering, 2016, 23(2):255-299.
[56] FOURES D P G, DOVETTA N, SIPP D, et al. A data-assimilation method for Reynolds-averaged Navier-Stokes-driven mean flow reconstruction[J]. Journal of Fluid Mechanics, 2014, 759:404-431.
[57] SYMON S, SIPP D, SCHMID P J, et al. Mean and unsteady flow reconstruction using data-assimilation and resolvent analysis[J]. AIAA Journal, 2020, 58(2):575-588.
[58] SYMON S, DOVETTA N, MCKEON B J, et al. Data assimilation of mean velocity from 2D PIV measurements of flow over an idealized airfoil[J]. Experiments in Fluids, 2017, 58(5):61.
[59] CHANDRAMOULI P, MEMIN E, HEITZ D. 4D large scale variational data assimilation of a turbulent flow with a dynamics error model[J]. Journal of Computational Physics, 2020, 412:109446.
[60] 刘蕴. 基于变分数据同化的核事故源项反演模型研究[D]. 北京:清华大学, 2017. LIU Y. Research on source inversion for nuclear accidents based on variational data assimilation[D]. Beijing:Tsinghua University, 2017.
[61] 谢衍新. 基于卫星观测的临近空间大气变分数据同化研究[D]. 北京:中国科学院国家空间科学中心, 2017. XIE Y X. Researches on near space atmosphere variational data assimilation technology based on satellite data[D]. Beijing:National Space Science Center, Chinese Academy of Sciences, 2017.
[62] 赵海贝,王斌,戴永久. 基于历史样本投影的四维变分陆面数据同化方法及其初步应用[J]. 气候与环境研究, 2009, 14(4):383-389. ZHAO H B, WANG B, DAI Y J. Historical-sample-projection four-dimensional variational land surface data assimilation and its preliminary application[J].Climatic and Environmental Research, 2009, 14(4):383-389(in Chinese).
[63] 杨向阳, 舒红, 吴凯, 等. 遥感数据同化中亮温数据质量控制分析[J]. 城市勘测, 2018(5):54-58,66. YANG X Y, SHU H, WU K, et al. Data quality control of brightness temperature in remote sensing data assimilation[J]. Urban Geotechnical Investigation & Surveying, 2018(5):54-58,66(in Chinese).
[64] MONS V, CHASSAING J C, GOMEZ T, et al. Reconstruction of unsteady viscous flows using data assimilation schemes[J]. Journal of Computational Physics, 2016, 316:255-280.
[65] GRONSKIS A, HEITZ D, MÉMIN E. Inflow and initial conditions for direct numerical simulation based on adjoint data assimilation[J]. Journal of Computational Physics, 2013, 242:480-497.
[66] LEMKE M, SESTERHENN J R. Adjoint-based pressure determination from PIV data in compressible flows-Validation and assessment based on synthetic data[J]. European Journal of Mechanics-B/Fluids, 2016, 58:29-38.
[67] BAUWERAERTS P, MEYERS J. Towards an adjoint based 4D-Var state estimation for turbulent flow[J]. Journal of Physics Conference Series, 2018, 1037(7):072055.
[68] MELDI M, POUX A. A reduced order model based on Kalman filtering for sequential data assimilation of turbulent flows[J]. Journal of Computational Physics, 2017, 347:207-234.
[69] KATO H, YOSHIZAWA A, UENO G, et al. A data assimilation methodology for reconstructing turbulent flows around aircraft[J]. Journal of Computational Physics, 2015, 283:559-581.
[70] KATO H, OBAYASHI S. Approach for uncertainty of turbulence modeling based on data assimilation technique[J]. Computers & Fluids, 2013, 85:2-7.
[71] HACK M J P, ZAKI T A. Data-enabled prediction of streak breakdown in pressure-gradient boundary layers[J]. Journal of Fluid Mechanics, 2016, 801:43-64.
[72] MOGHADDAM A A, SADAGHIYANI A. A deep learning framework for turbulence modeling using data assimilation and feature extraction[DB/OL]. arXiv preprint:1802.06106, 2018.
[73] SEKAR V, JIANG Q, SHU C, et al. Fast flow field prediction over airfoils using deep learning approach[J]. Physics of Fluids, 2019, 31(5):057103.
[74] LEE S, YOU D. Prediction of laminar vortex shedding over a cylinder using deep learning[DB/OL]. arXiv preprint:1712.07854, 2017.
[75] DENG Z, CHEN Y, LIU Y, et al. Time-resolved turbulent velocity field reconstruction using a long short-term memory (LSTM)-based artificial intelligence framework[J]. Physics of Fluids, 2019, 31(7):075108.
[76] SRINIVASAN P A, GUASTONI L, AZIZPOUR H, et al. Predictions of turbulent shear flows using deep neural networks[J]. Physical Review Fluids, 2019, 4(5):054603.
[77] WU Z, LEE J, MENEVEAU C, et al. Application of a self-organizing map to identify the turbulent-boundary-layer interface in a transitional flow[J]. Physical Review Fluids, 2019, 4(2):023902.
[78] ZHANG W, ZHU L, LIU Y, et al. Machine learning methods for turbulence modeling in subsonic flows over airfoils[DB/OL].arXiv preprint:1806.05904,2018.
[79] MURATA T, FUKAMI K, FUKAGATA K. Nonlinear mode decomposition with convolutional neural networks for fluid dynamics[J]. Journal of Fluid Mechanics, 2020, 882:A13.
[80] FUKAMI K, FUKAGATA K, TAIRA K. Super-resolution reconstruction of turbulent flows with machine learning[J]. Journal of Fluid Mechanics, 2019, 870:106-120.
[81] DENG Z, HE C, LIU Y, et al. Super-resolution reconstruction of turbulent velocity fields using a generative adversarial network-based artificial intelligence framework[J]. Physics of Fluids, 2019, 31(12):125111.
[82] XIE Y, FRANZ E, CHU M, et al. TempoGAN:A temporally coherent, volumetric GAN for super-resolution fluid flow[J]. ACM Transactions on Graphics, 2018, 37(4):95.
[83] RAISSI M, YAZDANI A, KARNIADAKIS G E. Hidden fluid mechanics:A Navier-Stokes informed deep learning framework for assimilating flow visualization data[EB/OL]. arXiv preprint:1808.04327,2018.
[84] RAISSI M, WANG Z, TRIANTAFYLLOU M S, et al. Deep learning of vortex-induced vibrations[J]. Journal of Fluid Mechanics, 2019, 861:119-137.
[85] DOVETTA N, FOURES D P G, SIPP D, et al. Mean-flow reconstruction by data-assimilation techniques from PIV-measurements of flow over an idealized airfoil[C]//65th Annual Meeting of the APS Division of Fluid Dynamics, 2012.
[86] DOVETTA N, MCKEON B J, FOURES D P G, et al. Data-assimilation for mean flow and shear stressreconstruction in turbulent pipe flow[C]//21ème Congrès Français de Mécanique, 2013.
[87] HE C, LIU Y, GAN L, et al. Data assimilation and resolvent analysis of turbulent flow behind a wall-proximity rib[J]. Physics of Fluids, 2019, 31(2):025118.
[88] CHARONKO J J, KING C V, SMITH B L, et al. Assessment of pressure field calculations from particle image velocimetry measurements[J]. Measurement Science and Technology, 2010, 21(10):105401.
[89] HE C, LIU Y. Time-resolved reconstruction of turbulent flows using linear stochastic estimation and sequential data assimilation[J]. Physics of Fluids, 2020, 32(10):075106.
[90] GLAESSGEN E, STARGEL D. The digital twin paradigm for future NASA and U.S. air force vehicles[C]//53rd Structures, Structural Dynamics, and Materials Conference:Special Session on the Digital Twin, 2012.
[91] RENGANATHAN S A, HARADA K, MAVRIS D N. Aerodynamic data fusion towards the digital twin paradigm[DB/OL]. arXiv preprint:1911.02924,2019.
[92] AFSHAR Y, BHATNAGAR S, PAN S, et al. Prediction of aerodynamic flow fields using convolutional neural networks[J]. Computational Mechanics, 2019, 64(2):525-545.
[93] LEE S, YOU D. Data-driven prediction of unsteady flow over a circular cylinder using deep learning[J]. Journal of Fluid Mechanics, 2019, 879:217-254.
[94] MIYANAWALA T P, JAIMAN R K. An efficient deep learning technique for the Navier-Stokes equations:Application to unsteady wake flow dynamics[DB/OL].arXiv preprint:1710.09099, 2017.
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