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Lagrangian large eddy simulations via physics-informed machine learning

High-Reynolds number homogeneous isotropic turbulence (HIT) is fully described within the Navier–Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, know...

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Autores principales: Tian, Yifeng, Woodward, Michael, Stepanov, Mikhail, Fryer, Chris, Hyett, Criston, Livescu, Daniel, Chertkov, Michael
Formato: Online Artículo Texto
Lenguaje:English
Publicado: National Academy of Sciences 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10450849/
https://www.ncbi.nlm.nih.gov/pubmed/37585463
http://dx.doi.org/10.1073/pnas.2213638120
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author Tian, Yifeng
Woodward, Michael
Stepanov, Mikhail
Fryer, Chris
Hyett, Criston
Livescu, Daniel
Chertkov, Michael
author_facet Tian, Yifeng
Woodward, Michael
Stepanov, Mikhail
Fryer, Chris
Hyett, Criston
Livescu, Daniel
Chertkov, Michael
author_sort Tian, Yifeng
collection PubMed
description High-Reynolds number homogeneous isotropic turbulence (HIT) is fully described within the Navier–Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as large eddy simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about effects of subgrid scales on the resolved scales. Here, we take an alternative approach and design LES heuristics stated in terms of Lagrangian particles moving with the flow. Our Lagrangian LES, thus L-LES, is described by equations generalizing the weakly compressible smoothed particle hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from direct numerical simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The subgrid-scale contributions are modeled separately with physical constraints to account for the effects from unresolved scales. We build the resulting model under the differentiable programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our L-LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.
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spelling pubmed-104508492023-08-26 Lagrangian large eddy simulations via physics-informed machine learning Tian, Yifeng Woodward, Michael Stepanov, Mikhail Fryer, Chris Hyett, Criston Livescu, Daniel Chertkov, Michael Proc Natl Acad Sci U S A Physical Sciences High-Reynolds number homogeneous isotropic turbulence (HIT) is fully described within the Navier–Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as large eddy simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about effects of subgrid scales on the resolved scales. Here, we take an alternative approach and design LES heuristics stated in terms of Lagrangian particles moving with the flow. Our Lagrangian LES, thus L-LES, is described by equations generalizing the weakly compressible smoothed particle hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from direct numerical simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The subgrid-scale contributions are modeled separately with physical constraints to account for the effects from unresolved scales. We build the resulting model under the differentiable programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our L-LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers. National Academy of Sciences 2023-08-16 2023-08-22 /pmc/articles/PMC10450849/ /pubmed/37585463 http://dx.doi.org/10.1073/pnas.2213638120 Text en Copyright © 2023 the Author(s). Published by PNAS. https://creativecommons.org/licenses/by-nc-nd/4.0/This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND) (https://creativecommons.org/licenses/by-nc-nd/4.0/) .
spellingShingle Physical Sciences
Tian, Yifeng
Woodward, Michael
Stepanov, Mikhail
Fryer, Chris
Hyett, Criston
Livescu, Daniel
Chertkov, Michael
Lagrangian large eddy simulations via physics-informed machine learning
title Lagrangian large eddy simulations via physics-informed machine learning
title_full Lagrangian large eddy simulations via physics-informed machine learning
title_fullStr Lagrangian large eddy simulations via physics-informed machine learning
title_full_unstemmed Lagrangian large eddy simulations via physics-informed machine learning
title_short Lagrangian large eddy simulations via physics-informed machine learning
title_sort lagrangian large eddy simulations via physics-informed machine learning
topic Physical Sciences
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10450849/
https://www.ncbi.nlm.nih.gov/pubmed/37585463
http://dx.doi.org/10.1073/pnas.2213638120
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