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Subgrid modelling for two-dimensional turbulence using neural networks

Published online by Cambridge University Press:  02 November 2018

R. Maulik ,
O. San Open the ORCID record for O. San [Opens in a new window] ,
A. Rasheed  and
P. Vedula
R. Maulik
Affiliation:
School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74078, USA
O. San*
Affiliation:
School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74078, USA
A. Rasheed
Affiliation:
CSE Group, Mathematics and Cybernetics, SINTEF Digital, N-7465 Trondheim, Norway
P. Vedula
Affiliation:
School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA
*
†Email address for correspondence: [email protected]
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Abstract

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.

JFM classification

Mathematical Foundations: Computational methods Geophysical and Geological Flows: Quasi-geostrophic flows Turbulent Flows: Turbulence modelling
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 858 , 10 January 2019 , pp. 122 - 144
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Copyright
© 2018 Cambridge University Press 

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