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Title: Subgrid modelling for two-dimensional turbulence using neural networks

Abstract

Here in this investigation, a data-driven turbulence closure framework is introduced and deployed for the subgrid modelling of Kraichnan turbulence. The novelty of the proposed method lies in the fact that snapshots from high-fidelity numerical data are used to inform artificial neural networks for predicting the turbulence source term through localized grid-resolved information. In particular, our proposed methodology successfully establishes a map between inputs given by stencils of the vorticity and the streamfunction along with information from two well-known eddy-viscosity kernels. Through this we predict the subgrid vorticity forcing in a temporally and spatially dynamic fashion. Our study is both a priori and a posteriori in nature. In the former, we present an extensive hyper-parameter optimization analysis in addition to learning quantification through probability-density-function-based validation of subgrid predictions. In the latter, we analyse the performance of our framework for flow evolution in a classical decaying two-dimensional turbulence test case in the presence of errors related to temporal and spatial discretization. Statistical assessments in the form of angle-averaged kinetic energy spectra demonstrate the promise of the proposed methodology for subgrid quantity inference. In addition, it is also observed that some measure of a posteriori error must be considered during optimal modelmore » selection for greater accuracy. The results in this article thus represent a promising development in the formalization of a framework for generation of heuristic-free turbulence closures from data.« less

Authors:
 [1]; ORCiD logo [1];  [2];  [3]
  1. Oklahoma State Univ., Stillwater, OK (United States)
  2. SINTEF Digital, Trondheim (Norway)
  3. Univ. of Oklahoma, Norman, OK (United States)
Publication Date:
Research Org.:
Oklahoma State Univ., Stillwater, OK (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); NVIDIA Corporation
OSTI Identifier:
1593570
Grant/Contract Number:  
SC0019290; 268044/E20
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Fluid Mechanics
Additional Journal Information:
Journal Volume: 858; Journal ID: ISSN 0022-1120
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING

Citation Formats

Maulik, R., San, O., Rasheed, A., and Vedula, P. Subgrid modelling for two-dimensional turbulence using neural networks. United States: N. p., 2019. Web. doi:10.1017/jfm.2018.770.
Maulik, R., San, O., Rasheed, A., & Vedula, P. Subgrid modelling for two-dimensional turbulence using neural networks. United States. doi:10.1017/jfm.2018.770.
Maulik, R., San, O., Rasheed, A., and Vedula, P. Thu . "Subgrid modelling for two-dimensional turbulence using neural networks". United States. doi:10.1017/jfm.2018.770. https://www.osti.gov/servlets/purl/1593570.
@article{osti_1593570,
title = {Subgrid modelling for two-dimensional turbulence using neural networks},
author = {Maulik, R. and San, O. and Rasheed, A. and Vedula, P.},
abstractNote = {Here in this investigation, a data-driven turbulence closure framework is introduced and deployed for the subgrid modelling of Kraichnan turbulence. The novelty of the proposed method lies in the fact that snapshots from high-fidelity numerical data are used to inform artificial neural networks for predicting the turbulence source term through localized grid-resolved information. In particular, our proposed methodology successfully establishes a map between inputs given by stencils of the vorticity and the streamfunction along with information from two well-known eddy-viscosity kernels. Through this we predict the subgrid vorticity forcing in a temporally and spatially dynamic fashion. Our study is both a priori and a posteriori in nature. In the former, we present an extensive hyper-parameter optimization analysis in addition to learning quantification through probability-density-function-based validation of subgrid predictions. In the latter, we analyse the performance of our framework for flow evolution in a classical decaying two-dimensional turbulence test case in the presence of errors related to temporal and spatial discretization. Statistical assessments in the form of angle-averaged kinetic energy spectra demonstrate the promise of the proposed methodology for subgrid quantity inference. In addition, it is also observed that some measure of a posteriori error must be considered during optimal model selection for greater accuracy. The results in this article thus represent a promising development in the formalization of a framework for generation of heuristic-free turbulence closures from data.},
doi = {10.1017/jfm.2018.770},
journal = {Journal of Fluid Mechanics},
number = ,
volume = 858,
place = {United States},
year = {2019},
month = {1}
}

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Works referenced in this record:

Diffusion Approximation for Two-Dimensional Turbulence
journal, January 1968


Data-assisted reduced-order modeling of extreme events in complex dynamical systems
journal, May 2018


An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications
journal, October 2004


Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework
journal, July 2018


Nonlinear aeroelastic reduced order modeling by recurrent neural networks
journal, July 2014


Towards a mesoscale eddy closure
journal, January 2008


A neural network approach for the blind deconvolution of turbulent flows
journal, October 2017


Hidden physics models: Machine learning of nonlinear partial differential equations
journal, March 2018


Hybrid forecasting of chaotic processes: Using machine learning in conjunction with a knowledge-based model
journal, April 2018

  • Pathak, Jaideep; Wikner, Alexander; Fussell, Rebeckah
  • Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 28, Issue 4
  • DOI: 10.1063/1.5028373

Analysis of Subgrid-Scale Torque for Large-Eddy Simulation of Turbulence
journal, October 2003

  • Marshall, J. S.; Beninati, M. L.
  • AIAA Journal, Vol. 41, Issue 10
  • DOI: 10.2514/2.1903

Parameterization of mixed layer eddies. III: Implementation and impact in global ocean climate simulations
journal, January 2011


Subgrid‐scale backscatter in turbulent and transitional flows
journal, July 1991

  • Piomelli, Ugo; Cabot, William H.; Moin, Parviz
  • Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 7
  • DOI: 10.1063/1.857956

Determination of the Smagorinsky–Lilly constant CS
journal, May 1997

  • Canuto, V. M.; Cheng, Y.
  • Physics of Fluids, Vol. 9, Issue 5
  • DOI: 10.1063/1.869251

Unsteady Fluid Mechanics Applications of Neural Networks
journal, January 1997

  • Faller, William E.; Schreck, Scott J.
  • Journal of Aircraft, Vol. 34, Issue 1
  • DOI: 10.2514/2.2134

A dynamic subgrid‐scale eddy viscosity model
journal, July 1991

  • Germano, Massimo; Piomelli, Ugo; Moin, Parviz
  • Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 7
  • DOI: 10.1063/1.857955

A Dynamic LES Scheme for the Vorticity Transport Equation: Formulation anda PrioriTests
journal, September 1998

  • Mansfield, John R.; Knio, Omar M.; Meneveau, Charles
  • Journal of Computational Physics, Vol. 145, Issue 2
  • DOI: 10.1006/jcph.1998.6051

Neural networks based subgrid scale modeling in large eddy simulations
journal, January 2003


Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
journal, October 2016

  • Ling, Julia; Kurzawski, Andrew; Templeton, Jeremy
  • Journal of Fluid Mechanics, Vol. 807
  • DOI: 10.1017/jfm.2016.615

Smagorinsky constant in LES modeling of anisotropic MHD turbulence
journal, September 2007

  • Vorobev, Anatoliy; Zikanov, Oleg
  • Theoretical and Computational Fluid Dynamics, Vol. 22, Issue 3-4
  • DOI: 10.1007/s00162-007-0064-z

Inertial Ranges in Two-Dimensional Turbulence
journal, January 1967


High-order methods for decaying two-dimensional homogeneous isotropic turbulence
journal, June 2012


Neural Network Modeling for Near Wall Turbulent Flow
journal, October 2002

  • Milano, Michele; Koumoutsakos, Petros
  • Journal of Computational Physics, Vol. 182, Issue 1
  • DOI: 10.1006/jcph.2002.7146

Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data
journal, March 2017


Theoretically based optimal large-eddy simulation
journal, October 2009

  • Moser, Robert D.; Malaya, Nicholas P.; Chang, Henry
  • Physics of Fluids, Vol. 21, Issue 10
  • DOI: 10.1063/1.3249754

Theoretical comparison of subgrid turbulence in atmospheric and oceanic quasi-geostrophic models
journal, January 2016

  • Kitsios, Vassili; Frederiksen, Jorgen S.; Zidikheri, Meelis J.
  • Nonlinear Processes in Geophysics, Vol. 23, Issue 2
  • DOI: 10.5194/npg-23-95-2016

Optimal LES formulations for isotropic turbulence
journal, November 1999


Machine-Learning-Augmented Predictive Modeling of Turbulent Separated Flows over Airfoils
journal, July 2017

  • Singh, Anand Pratap; Medida, Shivaji; Duraisamy, Karthik
  • AIAA Journal, Vol. 55, Issue 7
  • DOI: 10.2514/1.J055595

A paradigm for data-driven predictive modeling using field inversion and machine learning
journal, January 2016


Approximate deconvolution large eddy simulation of a stratified two-layer quasigeostrophic ocean model
journal, March 2013


Deep neural networks for data-driven LES closure models
journal, December 2019


Deep learning in fluid dynamics
journal, January 2017


Learning partial differential equations via data discovery and sparse optimization
journal, January 2017

  • Schaeffer, Hayden
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 473, Issue 2197
  • DOI: 10.1098/rspa.2016.0446

Feedback Control of a Cylinder Wake Low-Dimensional Model
journal, July 2003

  • Cohen, Kelly; Siegel, Stefan; McLaughlin, Thomas
  • AIAA Journal, Vol. 41, Issue 7
  • DOI: 10.2514/2.2087

Neural network closures for nonlinear model order reduction
journal, January 2018


A dynamic localization model for large-eddy simulation of turbulent flows
journal, March 1995