Machine-aided turbulence theory

Jiménez, Javier

doi:10.1017/jfm.2018.660

Cited by 56 publications

(66 citation statements)

References 19 publications

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“…General reviews can be found in [29,30] We discuss in this section how Monte-Carlo experimentation can be applied to test whether this vortex model is the only possible one for causality in two-dimensional decaying turbulence. The problem and the general procedure are described in [11,31], and there are few differences between the experiments here and in these references. The new material mostly refers to postprocessing the resulting data, and to how conclusions can be drawn from them.…”

Section: Introductionmentioning

confidence: 99%

“…Unless otherwise specified, all the cases discussed here have Fourier resolution 256 2 , with Re = q 0 L/ν = 2500, where ν is the kinematic viscosity. Further details can be found in [31]. Figure 2 is a typical initial vorticity field, with the 10×10 grid overlaid.…”

Section: Introductionmentioning

confidence: 99%

“…The properties of each cell used as diagnostic variables are the average cell enstrophy, ω 2 c = ω 2 c , defined by averaging over individual cells, the averaged kinetic energy, q 2 c = u 2 + v 2 c , and the average magnitude of the rate-of-strain tensor, S 2 c = S 2 c . The classification scheme in references [11,31] diagnosed significance using an optimal threshold computed for each of these variables in isolation. Each cell was classified as significant or not according to the flow behaviour at T ref , and the resulting labelled set was used to train the threshold in such a way that the number of misclassified events was minimised.…”

Section: Introductionmentioning

confidence: 99%

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Monte Carlo science

Jiménez

2020

Journal of Turbulence

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This paper explores how far the scientific discovery process can be automated. Using the identification of causally significant flow structures in two-dimensional turbulence as an example, it probes how far the usual procedure of planning experiments to test hypotheses can be substituted by 'blind' randomised experiments, and notes that the increased efficiency of computers is beginning to make such a 'Monte-Carlo' approach practical in fluid mechanics. The process of data generation, classification and model creation is described in some detail, stressing the importance of validation and verification. Although the purpose of the paper is to explore the procedure, rather than to model two-dimensional turbulence, it is encouraging that the Monte Carlo process naturally leads to the consideration of vortex dipoles as building blocks of the flow, on a par with the more conventional individual vortex cores. Although not completely novel, this 'spontaneous' discovery supports the claim that an important advantage of randomised experiments is to bypass researcher prejudice and alleviate paradigm lock. It is finally noted that the method can be extended to three-dimensional flows in practical times. * CONTACT Javier Jiménez.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Monte Carlo science

Jiménez

2020

Journal of Turbulence

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“…An emerging family of approaches uses various machine-learning techniques such as neural networks to deduce closure models with certain optimality properties from data. In this context we mention the investigations [15,26,34], whereas the state-ofthe-art in this field is discussed in the review papers [12,19,22]. Data-driven machinelearning methods, in addition to other data-driven techniques, have been utilized for computational prediction, modelling, and diagnosis of various turbulent flows [29,33,47].…”

Section: Introduction and Problem Statementmentioning

confidence: 99%

Optimal Closures in a Simple Model for Turbulent Flows

Matharu¹,

Protas²

2020

SIAM J. Sci. Comput.

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In this work we introduce a computational framework for determining optimal closures of the eddy-viscosity type for Large-Eddy Simulations (LES) of a broad class of PDE models, such as the Navier-Stokes equation. This problem is cast in terms of PDE-constrained optimization where an error functional representing the misfit between the target and predicted observations is minimized with respect to the functional form of the eddy viscosity in the closure relation. Since this leads to a PDE optimization problem with a nonstandard structure, the solution is obtained computationally with a flexible and efficient gradient approach relying on a combination of modified adjoint-based analysis and Sobolev gradients. By formulating this problem in the continuous setting we are able to determine the optimal closure relations in a very general form subject only to some minimal assumptions. The proposed framework is thoroughly tested on a model problem involving the LES of the 1D Kuramoto-Sivashinsky equation, where optimal forms of the eddy viscosity are obtained as generalizations of the standard Smagorinsky model. It is demonstrated that while the solution trajectories corresponding to the DNS and LES still diverge exponentially, with such optimal eddy viscosities the rate of divergence is significantly reduced as compared to the Smagorinsky model. By systematically finding optimal forms of the eddy viscosity within a certain general class of closure models, this framework can thus provide insights about the fundamental performance limitations of these models.

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“…In recent years, machine learning and data science have undergone rapid development thanks to increased data availability, boosted computing power and advanced algorithmic innovations. Many researchers have started to incorporate machine learning and data science techniques into modeling fluid systems (Brunton et al, 2016;Colabrese et al, 2017;Jiménez, 2018;Raissi et al, 2019). For RANS turbulence modeling, the task is to learn a good model for the Reynolds anisotropy tensor and considerable effort has been devoted to it (Tracey et al, 2015;Zhang and Duraisamy, 2015;Ling et al, 2016a,b;Wang et al, 2017;Wu et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Neural network models for the anisotropic Reynolds stress tensor in turbulent channel flow

Fang

Sondak

Protopapas

et al. 2019

Journal of Turbulence

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Reynolds-averaged Navier-Stokes (RANS) equations are presently one of the most popular models for simulating turbulence. Performing RANS simulation requires additional modeling for the anisotropic Reynolds stress tensor, but traditional Reynolds stress closure models lead to only partially reliable predictions. Recently, data-driven turbulence models for the Reynolds anisotropy tensor involving novel machine learning techniques have garnered considerable attention and have been rapidly developed.Focusing on modeling the Reynolds stress closure for the specific case of turbulent channel flow, this paper proposes three modifications to a standard neural network to account for the no-slip boundary condition of the anisotropy tensor, the Reynolds number dependence, and spatial non-locality. The modified models are shown to provide increased predicative accuracy compared to the standard neural network when they are trained and tested on channel flow at different Reynolds numbers. The best performance is yielded by the model combining the boundary condition enforcement and Reynolds number injection. This model also outperforms the Tensor Basis Neural Network (Ling et al., 2016b) on the turbulent channel flow dataset.

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Machine-aided turbulence theory

Cited by 56 publications

References 19 publications

Monte Carlo science

Monte Carlo science

Optimal Closures in a Simple Model for Turbulent Flows

Neural network models for the anisotropic Reynolds stress tensor in turbulent channel flow

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