Recent progress in augmenting turbulence models with physics-informed machine learning
In view of the long stagnation in traditional turbulence modeling, researchers have attempted using machine learning to augment turbulence models. This paper presents some of the recent progresses in our group on augmenting turbulence models with physics-informed machine learning. We also discuss ou...
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| Published in: | Journal of hydrodynamics. Series B Vol. 31; no. 6; pp. 1153 - 1158 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Singapore
Springer Singapore
01.12.2019
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| ISSN: | 1001-6058, 1878-0342 |
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| Abstract | In view of the long stagnation in traditional turbulence modeling, researchers have attempted using machine learning to augment turbulence models. This paper presents some of the recent progresses in our group on augmenting turbulence models with physics-informed machine learning. We also discuss our works on ensemble-based field inversion to provide training data for constructing machine learning models. Future and on-going research efforts are introduced. |
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| AbstractList | In view of the long stagnation in traditional turbulence modeling, researchers have attempted using machine learning to augment turbulence models. This paper presents some of the recent progresses in our group on augmenting turbulence models with physics-informed machine learning. We also discuss our works on ensemble-based field inversion to provide training data for constructing machine learning models. Future and on-going research efforts are introduced. |
| Author | Zhang, Xinlei Xiao, Heng Wu, Jinlong Coutier-Delgosha, Olivier |
| Author_xml | – sequence: 1 givenname: Xinlei surname: Zhang fullname: Zhang, Xinlei organization: Kevin T. Crofton Department of Aerospace and Ocean Engineering, Virginia Tech, Laboratoire de Mécanique des Fluides de Lille — Kampé de Fériet, Arts et Metiers ParisTech – sequence: 2 givenname: Jinlong surname: Wu fullname: Wu, Jinlong organization: Kevin T. Crofton Department of Aerospace and Ocean Engineering, Virginia Tech – sequence: 3 givenname: Olivier surname: Coutier-Delgosha fullname: Coutier-Delgosha, Olivier organization: Kevin T. Crofton Department of Aerospace and Ocean Engineering, Virginia Tech, Laboratoire de Mécanique des Fluides de Lille — Kampé de Fériet, Arts et Metiers ParisTech – sequence: 4 givenname: Heng surname: Xiao fullname: Xiao, Heng email: hengxiao@vt.edu organization: Kevin T. Crofton Department of Aerospace and Ocean Engineering, Virginia Tech |
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| Cites_doi | 10.1016/j.ijheatfluidflow.2017.09.017 10.1016/j.jcp.2016.07.038 10.1016/j.cma.2018.09.010 10.1007/s00162-018-0480-2 10.1038/scientificamerican0197-62 10.1007/s42241-018-0156-9 10.1063/1.5061693 10.1146/annurev-fluid-010518-040547 10.1016/j.compfluid.2008.05.002 10.1063/1.4927765 10.1016/j.cma.2020.113097 10.1016/0094-4548(74)90150-7 10.1103/PhysRevFluids.2.034603 10.1016/j.paerosci.2018.10.001 10.1016/S1270-9638(97)90051-1 10.1103/PhysRevFluids.3.074602 10.1063/1.4824659 10.1017/jfm.2016.615 10.1016/j.compfluid.2020.104431 10.2514/6.2015-1287 10.1016/j.compfluid.2019.104292 10.2514/3.12149 10.1017/jfm.2019.205 10.1016/j.jcp.2020.109517 10.1016/j.compfluid.2004.06.005 10.1007/s10494-017-9807-0 10.1016/j.jcp.2015.11.012 10.2514/1.J055595 10.1016/j.jcp.2016.08.015 10.1016/j.paerosci.2014.12.004 10.2514/6.2011-479 |
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| Keywords | turbulence modeling model uncertainty data-driven modeling Machine learning |
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| References | WuJXiaoHSunRReynolds-averaged Navier-Stokes equations with explicit data-driven Reynolds stress closure can be ill-conditioned [J]Journal of Fluid Mechanics2019869553586394409310.1017/jfm.2019.205 WuJXiaoHPatersonE GPhysics-informed machine learning approach for augmenting turbulence models: A comprehensive framework [J]Physical Review Fluids2018307460210.1103/PhysRevFluids.3.074602 ZhangWZhuLLiuYProgresses in the application of machine learning in turbulence modeling [J]Acta Aerodynamica Sinica2019373444454(in Chinese) Rumsey C. L. NASA Langley turbulence modeling portal [EB/OL]. https://turbmodels.larc.nasa.gov, 2018. Michelén-Ströfer C., Zhang X., Xiao H. et al. Enforcing boundary conditions on physical fields in Bayesian inversion [J]. 2019 (Submitted). MoinPKimJTackling turbulence with supercomputers [J]Scientific American19972761465210.1038/scientificamerican0197-62 LingJKurzawskiATempletonJReynolds averaged turbulence modelling using deep neural networks with embedded invariance [J]Journal of Fluid Mechanics2016807155166356930810.1017/jfm.2016.615 Xiao H., Wu J., Laizet S. et al. Flow over periodic hills of parameterized geometries: Example code and dataset for data-driven turbulence modeling [EB/OL]. https://github.com/xiaoh/para-database-for-PIML, 2019. WangJHuangJDuanLPrediction of Reynolds stresses in high-Mach-number turbulent boundary layers using physics-informed machine learning [J]Theoretical and Computational Fluid Dynamics2019331119392873610.1007/s00162-018-0480-2 XiaoHWuJWangJQuantifying and reducing model-form uncertainties in Reynolds-averaged Navier-Stokes equations: A data-driven, physics-based, Bayesian approach [J]Journal of Computational Physics2016324115136354033810.1016/j.jcp.2016.07.038 Oliver T., Moser R. Uncertainty quantification for RANS turbulence model predictions [C]. APS Division of Fluid Dynamics Meeting, Minneapolis, MN, USA, 2009. Mahaffy J., Chung B., Song C. et al. Best practice guidelines for the use of CFD in nuclear reactor safety applications [R]. Technical Report, Organisation for Economic Cooperation and Development, 2007. OliverT AMoserR DBayesian uncertainty quantification applied to RANS turbulence models [J]Journal of Physics: Conference Series2011318042032 WeatherittJSandbergR DThe development of algebraic stress models using a novel evolutionary algorithm [J]International Journal of Heat and Fluid Flow20176829831810.1016/j.ijheatfluidflow.2017.09.017 Xiao H., Wu J., Laizet S. et al. Flows over periodic hills of parameterized geometries: A dataset for data-driven turbulence modeling from direct simulations [J]. Fluid Dynamics, 2019 (Submitted). LingJTempletonJEvaluation of machine learning algorithms for prediction of regions of high Reynolds-averaged Navier-Stokes uncertainty [J]Physics of Fluids201527808510310.1063/1.4927765 XiaoHCinnellaPQuantification of model uncertainty in RANS simulations: A review [J]Progress in Aerospace Sciences201910813110.1016/j.paerosci.2018.10.001 Xiao H., Wu J. L., Laizet S. et al. Flows over periodic hills of parameterized geometries: A dataset for data-driven turbulence modeling from direct simulations [J]. Computers and Fluids, 2019, Preprint arxiv: 1910.01264. Emory M., Pecnik R., Iaccarino G. Modeling structural uncertainties in Reynolds-averaged computations of shock/boundary layer interactions [C]. 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Orlando, FL, USA, 2011, AIAA paper 2011-479. Kroll N., Rossow C., Schwamborn D. et al. MEGAFLOW: A numerical flow simulation tool for transport aircraft design [C]. ICAS Congress, Braunschweig, Germany, 2002, 1–105. WangJWuJ LXiaoHPhysics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data [J]Physical Review Fluids20172303460310.1103/PhysRevFluids.2.034603 BreuerMPellerNRappCFlow over periodic hills: Numerical and experimental study in a wide range of Reynolds numbers [J]Computers and Fluids200938243345710.1016/j.compfluid.2008.05.002 Tracey B., Duraisamy K., Alonso J. J. A machine learning strategy to assist turbulence model development [C]. 53rd AIAA Aerospace Sciences Meeting, Kissimmee, USA, 2015, AIAA paper 2015-1287. ParishE JDuraisamyKA paradigm for data-driven predictive modeling using field inversion and machine learning [J]Journal of Computational Physics2016305758774342960510.1016/j.jcp.2015.11.012 LaunderBSharmaBApplication of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc [J]Letters in Heat and Mass Transfer19741213113710.1016/0094-4548(74)90150-7 Zhang X., Michelen-Ströfer C., Xiao H. Regularization of ensemble kalman methods for inverse problems [J]. 2019 (Submitted). DuraisamyKIaccarinoGXiaoHTurbulence modeling in the age of data [J]Annual Review of Fluid Mechanics201951357377396562310.1146/annurev-fluid-010518-040547 ZhuLZhangWKouJMachine learning methods for turbulence modeling in subsonic flows around airfoils [J]Physics of Fluids201931101510510.1063/1.5061693 MenterF RTwo-equation eddy-viscosity turbulence models for engineering applications [J]AIAA Journal19943281598160510.2514/3.12149 WuJSunRLaizetSRepresentation of stress tensor perturbations with application in machine-learning-assisted turbulence modeling [J]Computer Methods in Applied Mechanics and Engineering2019346707726391299110.1016/j.cma.2018.09.010 JohnsonF TTinocoE NYuN JThirty years of development and application of CFD at Boeing Commercial Airplanes, Seattle [J]Computers and Fluids200534101115115110.1016/j.compfluid.2004.06.005 ZhangZSongX DYeS RApplication of deep learning method to Reynolds stress models of channel flow based on reduced-order modeling of DNS data [J]Journal of Hydrodynamics2019311586510.1007/s42241-018-0156-9 EmoryMLarssonJIaccarinoGModeling of structural uncertainties in Reynolds-averaged Navier-Stokes closures [J]Physics of Fluids2013251111082210.1063/1.4824659 SinghA PMedidaSDuraisamyKMachine learning-augmented predictive modeling of turbulent separated flows over airfoils [J]AIAA Journal20175572215222710.2514/1.J055595 SpalartP RPhilosophies and fallacies in turbulence modeling [J]Progress in Aerospace Sciences20157411510.1016/j.paerosci.2014.12.004 SpalartPShurMOn the sensitization of turbulence models to rotation and curvature [J]Aerospace Science and Technology19971529730210.1016/S1270-9638(97)90051-1 WuJWangJXiaoHA priori assessment of prediction confidence for data-driven turbulence modeling [J]Flow, Turbulence and Combustion2017991254610.1007/s10494-017-9807-0 IAEA. Use of computational fluid dynamics codes for safety analysis of nuclear reac- tor systems [R]. Technical Report IAEA-TECDOC-1379, Pisa, Italy: International Atomic Energy Agency, 2002. WeatherittJSandbergRA novel evolutionary algorithm applied to algebraic modifications of the RANS stressstrain relationship [J]Journal of Computational Physics20163252237354683410.1016/j.jcp.2016.08.015 WuJMichelen-StröferCXiaoHPhysics-informed covariance kernel for model-form uncertainty quantification with application to turbulent flows [J]Computers and Fluids2019193104292401107010.1016/j.compfluid.2019.104292 SpalartP RAllmarasS RA one equation turbulence model for aerodynamic flows [J]Recherche Aerospatiale199411521 M Breuer (89_CR33) 2009; 38 P R Spalart (89_CR15) 2015; 74 J Wu (89_CR29) 2017; 99 L Zhu (89_CR19) 2019; 31 J Wu (89_CR37) 2019; 193 F T Johnson (89_CR5) 2005; 34 M Emory (89_CR8) 2013; 25 89_CR41 J Wu (89_CR24) 2018; 3 W Zhang (89_CR30) 2019; 37 A P Singh (89_CR16) 2017; 55 T A Oliver (89_CR9) 2011; 318 J Ling (89_CR20) 2016; 807 F R Menter (89_CR13) 1994; 32 Z Zhang (89_CR21) 2019; 31 P Moin (89_CR4) 1997; 276 P Spalart (89_CR39) 1997; 1 J Weatheritt (89_CR22) 2016; 325 89_CR17 89_CR38 J Wang (89_CR27) 2019; 33 89_CR36 P R Spalart (89_CR14) 1994; 1 E J Parish (89_CR18) 2016; 305 J Wu (89_CR28) 2019; 869 89_CR7 89_CR35 89_CR34 J Ling (89_CR40) 2015; 27 89_CR6 J Wu (89_CR31) 2019; 346 89_CR32 89_CR3 89_CR1 H Xiao (89_CR25) 2016; 324 89_CR2 K Duraisamy (89_CR10) 2019; 51 H Xiao (89_CR11) 2019; 108 J Wang (89_CR26) 2017; 2 B Launder (89_CR12) 1974; 1 J Weatheritt (89_CR23) 2017; 68 |
| References_xml | – reference: SpalartPShurMOn the sensitization of turbulence models to rotation and curvature [J]Aerospace Science and Technology19971529730210.1016/S1270-9638(97)90051-1 – reference: WangJHuangJDuanLPrediction of Reynolds stresses in high-Mach-number turbulent boundary layers using physics-informed machine learning [J]Theoretical and Computational Fluid Dynamics2019331119392873610.1007/s00162-018-0480-2 – reference: WuJXiaoHPatersonE GPhysics-informed machine learning approach for augmenting turbulence models: A comprehensive framework [J]Physical Review Fluids2018307460210.1103/PhysRevFluids.3.074602 – reference: Xiao H., Wu J. L., Laizet S. et al. Flows over periodic hills of parameterized geometries: A dataset for data-driven turbulence modeling from direct simulations [J]. Computers and Fluids, 2019, Preprint arxiv: 1910.01264. – reference: DuraisamyKIaccarinoGXiaoHTurbulence modeling in the age of data [J]Annual Review of Fluid Mechanics201951357377396562310.1146/annurev-fluid-010518-040547 – reference: Zhang X., Michelen-Ströfer C., Xiao H. Regularization of ensemble kalman methods for inverse problems [J]. 2019 (Submitted). – reference: IAEA. Use of computational fluid dynamics codes for safety analysis of nuclear reac- tor systems [R]. Technical Report IAEA-TECDOC-1379, Pisa, Italy: International Atomic Energy Agency, 2002. – reference: WeatherittJSandbergR DThe development of algebraic stress models using a novel evolutionary algorithm [J]International Journal of Heat and Fluid Flow20176829831810.1016/j.ijheatfluidflow.2017.09.017 – reference: WuJSunRLaizetSRepresentation of stress tensor perturbations with application in machine-learning-assisted turbulence modeling [J]Computer Methods in Applied Mechanics and Engineering2019346707726391299110.1016/j.cma.2018.09.010 – reference: LingJTempletonJEvaluation of machine learning algorithms for prediction of regions of high Reynolds-averaged Navier-Stokes uncertainty [J]Physics of Fluids201527808510310.1063/1.4927765 – reference: Xiao H., Wu J., Laizet S. et al. Flow over periodic hills of parameterized geometries: Example code and dataset for data-driven turbulence modeling [EB/OL]. https://github.com/xiaoh/para-database-for-PIML, 2019. – reference: MoinPKimJTackling turbulence with supercomputers [J]Scientific American19972761465210.1038/scientificamerican0197-62 – reference: JohnsonF TTinocoE NYuN JThirty years of development and application of CFD at Boeing Commercial Airplanes, Seattle [J]Computers and Fluids200534101115115110.1016/j.compfluid.2004.06.005 – reference: LingJKurzawskiATempletonJReynolds averaged turbulence modelling using deep neural networks with embedded invariance [J]Journal of Fluid Mechanics2016807155166356930810.1017/jfm.2016.615 – reference: WuJWangJXiaoHA priori assessment of prediction confidence for data-driven turbulence modeling [J]Flow, Turbulence and Combustion2017991254610.1007/s10494-017-9807-0 – reference: XiaoHCinnellaPQuantification of model uncertainty in RANS simulations: A review [J]Progress in Aerospace Sciences201910813110.1016/j.paerosci.2018.10.001 – reference: Tracey B., Duraisamy K., Alonso J. J. A machine learning strategy to assist turbulence model development [C]. 53rd AIAA Aerospace Sciences Meeting, Kissimmee, USA, 2015, AIAA paper 2015-1287. – reference: XiaoHWuJWangJQuantifying and reducing model-form uncertainties in Reynolds-averaged Navier-Stokes equations: A data-driven, physics-based, Bayesian approach [J]Journal of Computational Physics2016324115136354033810.1016/j.jcp.2016.07.038 – reference: Xiao H., Wu J., Laizet S. et al. Flows over periodic hills of parameterized geometries: A dataset for data-driven turbulence modeling from direct simulations [J]. Fluid Dynamics, 2019 (Submitted). – reference: Michelén-Ströfer C., Zhang X., Xiao H. et al. Enforcing boundary conditions on physical fields in Bayesian inversion [J]. 2019 (Submitted). – reference: EmoryMLarssonJIaccarinoGModeling of structural uncertainties in Reynolds-averaged Navier-Stokes closures [J]Physics of Fluids2013251111082210.1063/1.4824659 – reference: SpalartP RPhilosophies and fallacies in turbulence modeling [J]Progress in Aerospace Sciences20157411510.1016/j.paerosci.2014.12.004 – reference: WangJWuJ LXiaoHPhysics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data [J]Physical Review Fluids20172303460310.1103/PhysRevFluids.2.034603 – reference: OliverT AMoserR DBayesian uncertainty quantification applied to RANS turbulence models [J]Journal of Physics: Conference Series2011318042032 – reference: Mahaffy J., Chung B., Song C. et al. Best practice guidelines for the use of CFD in nuclear reactor safety applications [R]. Technical Report, Organisation for Economic Cooperation and Development, 2007. – reference: SpalartP RAllmarasS RA one equation turbulence model for aerodynamic flows [J]Recherche Aerospatiale199411521 – reference: MenterF RTwo-equation eddy-viscosity turbulence models for engineering applications [J]AIAA Journal19943281598160510.2514/3.12149 – reference: WeatherittJSandbergRA novel evolutionary algorithm applied to algebraic modifications of the RANS stressstrain relationship [J]Journal of Computational Physics20163252237354683410.1016/j.jcp.2016.08.015 – reference: Kroll N., Rossow C., Schwamborn D. et al. MEGAFLOW: A numerical flow simulation tool for transport aircraft design [C]. ICAS Congress, Braunschweig, Germany, 2002, 1–105. – reference: ZhangZSongX DYeS RApplication of deep learning method to Reynolds stress models of channel flow based on reduced-order modeling of DNS data [J]Journal of Hydrodynamics2019311586510.1007/s42241-018-0156-9 – reference: Rumsey C. L. NASA Langley turbulence modeling portal [EB/OL]. https://turbmodels.larc.nasa.gov, 2018. – reference: Emory M., Pecnik R., Iaccarino G. Modeling structural uncertainties in Reynolds-averaged computations of shock/boundary layer interactions [C]. 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Orlando, FL, USA, 2011, AIAA paper 2011-479. – reference: ParishE JDuraisamyKA paradigm for data-driven predictive modeling using field inversion and machine learning [J]Journal of Computational Physics2016305758774342960510.1016/j.jcp.2015.11.012 – reference: ZhuLZhangWKouJMachine learning methods for turbulence modeling in subsonic flows around airfoils [J]Physics of Fluids201931101510510.1063/1.5061693 – reference: ZhangWZhuLLiuYProgresses in the application of machine learning in turbulence modeling [J]Acta Aerodynamica Sinica2019373444454(in Chinese) – reference: WuJMichelen-StröferCXiaoHPhysics-informed covariance kernel for model-form uncertainty quantification with application to turbulent flows [J]Computers and Fluids2019193104292401107010.1016/j.compfluid.2019.104292 – reference: LaunderBSharmaBApplication of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc [J]Letters in Heat and Mass Transfer19741213113710.1016/0094-4548(74)90150-7 – reference: BreuerMPellerNRappCFlow over periodic hills: Numerical and experimental study in a wide range of Reynolds numbers [J]Computers and Fluids200938243345710.1016/j.compfluid.2008.05.002 – reference: WuJXiaoHSunRReynolds-averaged Navier-Stokes equations with explicit data-driven Reynolds stress closure can be ill-conditioned [J]Journal of Fluid Mechanics2019869553586394409310.1017/jfm.2019.205 – reference: Oliver T., Moser R. Uncertainty quantification for RANS turbulence model predictions [C]. APS Division of Fluid Dynamics Meeting, Minneapolis, MN, USA, 2009. – reference: SinghA PMedidaSDuraisamyKMachine learning-augmented predictive modeling of turbulent separated flows over airfoils [J]AIAA Journal20175572215222710.2514/1.J055595 – volume: 68 start-page: 298 year: 2017 ident: 89_CR23 publication-title: International Journal of Heat and Fluid Flow doi: 10.1016/j.ijheatfluidflow.2017.09.017 – volume: 324 start-page: 115 year: 2016 ident: 89_CR25 publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2016.07.038 – volume: 346 start-page: 707 year: 2019 ident: 89_CR31 publication-title: Computer Methods in Applied Mechanics and Engineering doi: 10.1016/j.cma.2018.09.010 – volume: 33 start-page: 1 issue: 1 year: 2019 ident: 89_CR27 publication-title: Theoretical and Computational Fluid Dynamics doi: 10.1007/s00162-018-0480-2 – volume: 276 start-page: 46 issue: 1 year: 1997 ident: 89_CR4 publication-title: Scientific American doi: 10.1038/scientificamerican0197-62 – volume: 31 start-page: 58 issue: 1 year: 2019 ident: 89_CR21 publication-title: Journal of Hydrodynamics doi: 10.1007/s42241-018-0156-9 – volume: 318 start-page: 042032 year: 2011 ident: 89_CR9 publication-title: Journal of Physics: Conference Series – volume: 31 start-page: 015105 issue: 1 year: 2019 ident: 89_CR19 publication-title: Physics of Fluids doi: 10.1063/1.5061693 – volume: 51 start-page: 357 year: 2019 ident: 89_CR10 publication-title: Annual Review of Fluid Mechanics doi: 10.1146/annurev-fluid-010518-040547 – volume: 38 start-page: 433 issue: 2 year: 2009 ident: 89_CR33 publication-title: Computers and Fluids doi: 10.1016/j.compfluid.2008.05.002 – volume: 27 start-page: 085103 issue: 8 year: 2015 ident: 89_CR40 publication-title: Physics of Fluids doi: 10.1063/1.4927765 – ident: 89_CR6 – ident: 89_CR38 doi: 10.1016/j.cma.2020.113097 – volume: 1 start-page: 131 issue: 2 year: 1974 ident: 89_CR12 publication-title: Letters in Heat and Mass Transfer doi: 10.1016/0094-4548(74)90150-7 – volume: 2 start-page: 034603 issue: 3 year: 2017 ident: 89_CR26 publication-title: Physical Review Fluids doi: 10.1103/PhysRevFluids.2.034603 – volume: 1 start-page: 5 issue: 1 year: 1994 ident: 89_CR14 publication-title: Recherche Aerospatiale – volume: 108 start-page: 1 year: 2019 ident: 89_CR11 publication-title: Progress in Aerospace Sciences doi: 10.1016/j.paerosci.2018.10.001 – ident: 89_CR2 – volume: 1 start-page: 297 issue: 5 year: 1997 ident: 89_CR39 publication-title: Aerospace Science and Technology doi: 10.1016/S1270-9638(97)90051-1 – volume: 3 start-page: 074602 year: 2018 ident: 89_CR24 publication-title: Physical Review Fluids doi: 10.1103/PhysRevFluids.3.074602 – volume: 25 start-page: 110822 issue: 11 year: 2013 ident: 89_CR8 publication-title: Physics of Fluids doi: 10.1063/1.4824659 – volume: 807 start-page: 155 year: 2016 ident: 89_CR20 publication-title: Journal of Fluid Mechanics doi: 10.1017/jfm.2016.615 – ident: 89_CR35 – ident: 89_CR32 doi: 10.1016/j.compfluid.2020.104431 – ident: 89_CR17 doi: 10.2514/6.2015-1287 – volume: 37 start-page: 444 issue: 3 year: 2019 ident: 89_CR30 publication-title: Acta Aerodynamica Sinica – volume: 193 start-page: 104292 year: 2019 ident: 89_CR37 publication-title: Computers and Fluids doi: 10.1016/j.compfluid.2019.104292 – volume: 32 start-page: 1598 issue: 8 year: 1994 ident: 89_CR13 publication-title: AIAA Journal doi: 10.2514/3.12149 – volume: 869 start-page: 553 year: 2019 ident: 89_CR28 publication-title: Journal of Fluid Mechanics doi: 10.1017/jfm.2019.205 – ident: 89_CR36 doi: 10.1016/j.jcp.2020.109517 – volume: 34 start-page: 1115 issue: 10 year: 2005 ident: 89_CR5 publication-title: Computers and Fluids doi: 10.1016/j.compfluid.2004.06.005 – volume: 99 start-page: 25 issue: 1 year: 2017 ident: 89_CR29 publication-title: Flow, Turbulence and Combustion doi: 10.1007/s10494-017-9807-0 – ident: 89_CR3 – volume: 305 start-page: 758 year: 2016 ident: 89_CR18 publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2015.11.012 – volume: 55 start-page: 2215 issue: 7 year: 2017 ident: 89_CR16 publication-title: AIAA Journal doi: 10.2514/1.J055595 – volume: 325 start-page: 22 year: 2016 ident: 89_CR22 publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2016.08.015 – volume: 74 start-page: 1 year: 2015 ident: 89_CR15 publication-title: Progress in Aerospace Sciences doi: 10.1016/j.paerosci.2014.12.004 – ident: 89_CR1 – ident: 89_CR7 doi: 10.2514/6.2011-479 – ident: 89_CR41 doi: 10.1016/j.compfluid.2020.104431 – ident: 89_CR34 |
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| Title | Recent progress in augmenting turbulence models with physics-informed machine learning |
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