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Title: Data-driven deconvolution for large eddy simulations of Kraichnan turbulence

Abstract

In this article, we demonstrate the use of artificial neural networks as optimal maps which are utilized for convolution and deconvolution of coarse-grained fields to account for sub-grid scale turbulence effects. Here, we demonstrate that an effective eddy-viscosity is predicted by our purely data-driven large eddy simulation framework without explicit utilization of phenomenological arguments. In addition, our data-driven framework precludes the knowledge of true sub-grid stress information during the training phase due to its focus on estimating an effective filter and its inverse so that grid-resolved variables may be related to direct numerical simulation data statistically. The proposed predictive framework is also combined with a statistical truncation mechanism for ensuring numerical realizability in an explicit formulation. Through this, we seek to unite structural and functional modeling strategies for modeling non-linear partial differential equations using reduced degrees of freedom. Both a priori and a posteriori results are shown for a two-dimensional decaying turbulence case in addition to a detailed description of validation and testing. A hyperparameter sensitivity study also shows that the proposed dual network framework simplifies learning complexity and is viable with exceedingly simple network architectures. Our findings indicate that the proposed framework approximates a robust and stable sub-grid closuremore » which compares favorably to the Smagorinsky and Leith hypotheses for capturing the theoretical k-3 scaling in Kraichnan turbulence.« less

Authors:
 [1];  [1];  [2];  [3]
+ Show Author Affiliations
  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)
OSTI Identifier:
1593571
Grant/Contract Number:  
SC0019290
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Fluids
Additional Journal Information:
Journal Volume: 30; Journal Issue: 12; Journal ID: ISSN 1070-6631
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING

Citation Formats

Maulik, R., San, O., Rasheed, A., and Vedula, P. Data-driven deconvolution for large eddy simulations of Kraichnan turbulence. United States: N. p., 2018. Web. doi:10.1063/1.5079582.
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Maulik, R., San, O., Rasheed, A., & Vedula, P. Data-driven deconvolution for large eddy simulations of Kraichnan turbulence. United States. https://doi.org/10.1063/1.5079582
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Maulik, R., San, O., Rasheed, A., and Vedula, P. Fri . "Data-driven deconvolution for large eddy simulations of Kraichnan turbulence". United States. https://doi.org/10.1063/1.5079582. https://www.osti.gov/servlets/purl/1593571.
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@article{osti_1593571,
title = {Data-driven deconvolution for large eddy simulations of Kraichnan turbulence},
author = {Maulik, R. and San, O. and Rasheed, A. and Vedula, P.},
abstractNote = {In this article, we demonstrate the use of artificial neural networks as optimal maps which are utilized for convolution and deconvolution of coarse-grained fields to account for sub-grid scale turbulence effects. Here, we demonstrate that an effective eddy-viscosity is predicted by our purely data-driven large eddy simulation framework without explicit utilization of phenomenological arguments. In addition, our data-driven framework precludes the knowledge of true sub-grid stress information during the training phase due to its focus on estimating an effective filter and its inverse so that grid-resolved variables may be related to direct numerical simulation data statistically. The proposed predictive framework is also combined with a statistical truncation mechanism for ensuring numerical realizability in an explicit formulation. Through this, we seek to unite structural and functional modeling strategies for modeling non-linear partial differential equations using reduced degrees of freedom. Both a priori and a posteriori results are shown for a two-dimensional decaying turbulence case in addition to a detailed description of validation and testing. A hyperparameter sensitivity study also shows that the proposed dual network framework simplifies learning complexity and is viable with exceedingly simple network architectures. Our findings indicate that the proposed framework approximates a robust and stable sub-grid closure which compares favorably to the Smagorinsky and Leith hypotheses for capturing the theoretical k-3 scaling in Kraichnan turbulence.},
doi = {10.1063/1.5079582},
journal = {Physics of Fluids},
number = 12,
volume = 30,
place = {United States},
year = {Fri Dec 28 00:00:00 EST 2018},
month = {Fri Dec 28 00:00:00 EST 2018}
}
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https://doi.org/10.1063/1.5079582
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