Subgrid modelling for two-dimensional turbulence using neural networks

Maulik, R.; San, O.; Rasheed, A.; Vedula, P.

doi:10.1017/jfm.2018.770

Subgrid modelling for two-dimensional turbulence using neural networks

Journal Article · Thu Jan 10 00:00:00 EST 2019 · Journal of Fluid Mechanics

DOI:https://doi.org/10.1017/jfm.2018.770· OSTI ID:1593570

Maulik, R. ^[1]; ^[2]; Rasheed, A. ^[3]; Vedula, P. ^[4]

Oklahoma State Univ., Stillwater, OK (United States); Oklahoma State University Stillwater
Oklahoma State Univ., Stillwater, OK (United States)
SINTEF Digital, Trondheim (Norway)
Univ. of Oklahoma, Norman, OK (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Oklahoma State Univ., Stillwater, OK (United States)

Sponsoring Organization:: NVIDIA Corporation; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

Grant/Contract Number:: SC0019290

OSTI ID:: 1593570

Journal Information:: Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 858; ISSN 0022-1120

Publisher:: Cambridge University PressCopyright Statement

Country of Publication:: United States

Language:: English

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