Conditioning and accurate solutions of Reynolds average Navier–Stokes equations with data-driven turbulence closures

Brener, Bernardo Pereira; Cruz, Matheus; Thompson, Roney L.; Anjos, Rodrigo P.

doi:10.1017/jfm.2021.148

Cited by 40 publications

(25 citation statements)

References 58 publications

(179 reference statements)

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“…Although prior assessments show that the discrepancy between ML predictions and high-fidelity data is pretty small, other derived flow variables of ultimate interest, such as velocity and pressure, are possibly far removed from the true values for flows with higher Reynolds numbers. Recently, a few studies 46,47 showed that embedding ML prediction, i.e. the Reynolds stress field, explicitly into RANS equations would inevitably result in the lack of accuracy of data-driven turbulence models.…”

Section: Dsr For Turbulence Model Developmentmentioning

confidence: 99%

See 1 more Smart Citation

Discovering explicit Reynolds-averaged turbulence closures for turbulent separated flows through deep learning-based symbolic regression with non-linear corrections

Tang,

Wang,

Wang

et al. 2023

Preprint

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Section: Dsr For Turbulence Model Developmentmentioning

confidence: 99%

“…To avoid being ill-conditioned, it is necessary to decompose the Reynolds stress before it is injected into RANS simulations, as is done herein. This strategy has been proven to be effective in improving the stability and accuracy of data-driven RANS simulations 19,46,47 .…”

Section: Dsr For Turbulence Model Developmentmentioning

confidence: 99%

Discovering explicit Reynolds-averaged turbulence closures for turbulent separated flows through deep learning-based symbolic regression with non-linear corrections

Tang,

Wang,

Wang

et al. 2023

Preprint

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“…where iM u  is the fluctuation velocity and iM u  is the average velocity. When combining the equation above and N-S equations, we can obtain the Reynolds equation [25].…”

Section: Basic Mathematical Model Of Flowfield Letmentioning

confidence: 99%

Mathematical Model for Excited State Fluid Dynamics

Yue,

Zhang,

Wei

2023

J. Phys.: Conf. Ser.

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The rational mechanic’s research method is synthesized with the help of mathematical means such as generalized function analysis and tensor analysis. The basic definition of the fluctuation velocity generation is based on phenomenological physics in this article. The basic control equations of general excited state fluid dynamics applicable to the flowfield are obtained based on the basic principles of quantum mechanical superposition states. The simplified basic equations of the excited State are finally obtained through time and space discretization. The basic theory of excited state fluid dynamics is established, providing new ideas for the innovation and application of flow control, fluid mechanical engineering design, and other aspects of research work.

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“…2019 b ; Brener et al. 2021). Such ill-conditioning is particularly prominent in high-Reynolds-number flows; even an apparently simple flow such as a plane channel flow can be extremely ill-conditioned (Wu et al.…”

Section: Introductionmentioning

confidence: 99%

Ensemble Kalman method for learning turbulence models from indirect observation data

et al. 2022

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In this work, we propose using an ensemble Kalman method to learn a nonlinear eddy viscosity model, represented as a tensor basis neural network, from velocity data. Data-driven turbulence models have emerged as a promising alternative to traditional models for providing closure mapping from the mean velocities to Reynolds stresses. Most data-driven models in this category need full-field Reynolds stress data for training, which not only places stringent demand on the data generation but also makes the trained model ill-conditioned and lacks robustness. This difficulty can be alleviated by incorporating the Reynolds-averaged Navier–Stokes (RANS) solver in the training process. However, this would necessitate developing adjoint solvers of the RANS model, which requires extra effort in code development and maintenance. Given this difficulty, we present an ensemble Kalman method with an adaptive step size to train a neural-network-based turbulence model by using indirect observation data. To our knowledge, this is the first such attempt in turbulence modelling. The ensemble method is first verified on the flow in a square duct, where it correctly learns the underlying turbulence models from velocity data. Then the generalizability of the learned model is evaluated on a family of separated flows over periodic hills. It is demonstrated that the turbulence model learned in one flow can predict flows in similar configurations with varying slopes.

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Conditioning and accurate solutions of Reynolds average Navier–Stokes equations with data-driven turbulence closures

Abstract: Abstract

Cited by 40 publications

References 58 publications

Discovering explicit Reynolds-averaged turbulence closures for turbulent separated flows through deep learning-based symbolic regression with non-linear corrections

Discovering explicit Reynolds-averaged turbulence closures for turbulent separated flows through deep learning-based symbolic regression with non-linear corrections

Mathematical Model for Excited State Fluid Dynamics

Ensemble Kalman method for learning turbulence models from indirect observation data

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