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Deep learning of the spanwise-averaged Navier–Stokes equations

Deep learning of the spanwise-averaged Navier–Stokes equations
Deep learning of the spanwise-averaged Navier–Stokes equations
Simulations of turbulent fluid flow around long cylindrical structures are computationally expensive because of the vast range of length scales, requiring simplifications such as dimensional reduction. Current dimensionality reduction techniques such as strip-theory and depth-averaged methods do not take into account the natural flow dissipation mechanism inherent in the small-scale three-dimensional (3-D) vortical structures. We propose a novel flow decomposition based on a local spanwise average of the flow, yielding the spanwise-averaged Navier-Stokes (SANS) equations. The SANS equations include closure terms accounting for the 3-D effects otherwise not considered in 2-D formulations. A supervised machine-learning (ML) model based on a deep convolutional neural network provides closure to the SANS system. A-priori results show up to 92% correlation between target and predicted closure terms; more than an order of magnitude better than the eddy viscosity model correlation. The trained ML model is also assessed for different Reynolds regimes and body shapes to the training case where, despite some discrepancies in the shear-layer region, high correlation values are still observed. The new SANS equations and ML closure model are also used for a-posteriori prediction. While we find evidence of known stability issues with long time ML predictions for dynamical systems, the closed SANS simulations are still capable of predicting wake metrics and induced forces with errors from 1-10%. This results in approximately an order of magnitude improvement over standard 2-D simulations while reducing the computational cost of 3-D simulations by 99.5%.
Fluid dynamics, Machine learning, Turbulence modelling, Wake flow
0021-9991
Font, Bernat
1c605529-b50d-4703-b8cc-4ccaa5dff7fc
Weymouth, Gabriel
b0c85fda-dfed-44da-8cc4-9e0cc88e2ca0
Nguyen, Vihn-Tan
fc1267b4-5e09-47aa-8048-6291869f0db9
Tutty, Owen
c9ba0b98-4790-4a72-b5b7-09c1c6e20375
Font, Bernat
1c605529-b50d-4703-b8cc-4ccaa5dff7fc
Weymouth, Gabriel
b0c85fda-dfed-44da-8cc4-9e0cc88e2ca0
Nguyen, Vihn-Tan
fc1267b4-5e09-47aa-8048-6291869f0db9
Tutty, Owen
c9ba0b98-4790-4a72-b5b7-09c1c6e20375

Font, Bernat, Weymouth, Gabriel, Nguyen, Vihn-Tan and Tutty, Owen (2021) Deep learning of the spanwise-averaged Navier–Stokes equations. Journal of Computational Physics, 434, [110199]. (doi:10.1016/j.jcp.2021.110199).

Record type: Article

Abstract

Simulations of turbulent fluid flow around long cylindrical structures are computationally expensive because of the vast range of length scales, requiring simplifications such as dimensional reduction. Current dimensionality reduction techniques such as strip-theory and depth-averaged methods do not take into account the natural flow dissipation mechanism inherent in the small-scale three-dimensional (3-D) vortical structures. We propose a novel flow decomposition based on a local spanwise average of the flow, yielding the spanwise-averaged Navier-Stokes (SANS) equations. The SANS equations include closure terms accounting for the 3-D effects otherwise not considered in 2-D formulations. A supervised machine-learning (ML) model based on a deep convolutional neural network provides closure to the SANS system. A-priori results show up to 92% correlation between target and predicted closure terms; more than an order of magnitude better than the eddy viscosity model correlation. The trained ML model is also assessed for different Reynolds regimes and body shapes to the training case where, despite some discrepancies in the shear-layer region, high correlation values are still observed. The new SANS equations and ML closure model are also used for a-posteriori prediction. While we find evidence of known stability issues with long time ML predictions for dynamical systems, the closed SANS simulations are still capable of predicting wake metrics and induced forces with errors from 1-10%. This results in approximately an order of magnitude improvement over standard 2-D simulations while reducing the computational cost of 3-D simulations by 99.5%.

Text
Font_et_al 2021 - Deep learning of the spanwise-averaged Navier-Stokes equations - Accepted Manuscript
Restricted to Repository staff only until 19 February 2022.
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More information

Accepted/In Press date: 10 February 2021
e-pub ahead of print date: 19 February 2021
Published date: 1 June 2021
Keywords: Fluid dynamics, Machine learning, Turbulence modelling, Wake flow

Identifiers

Local EPrints ID: 447044
URI: http://eprints.soton.ac.uk/id/eprint/447044
ISSN: 0021-9991
PURE UUID: c322d6cc-8732-4497-bb11-a163010e95f5
ORCID for Bernat Font: ORCID iD orcid.org/0000-0002-2136-3068
ORCID for Gabriel Weymouth: ORCID iD orcid.org/0000-0001-5080-5016

Catalogue record

Date deposited: 02 Mar 2021 17:31
Last modified: 09 Mar 2021 02:48

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Contributors

Author: Bernat Font ORCID iD
Author: Vihn-Tan Nguyen
Author: Owen Tutty

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