Predictive large-eddy-simulation wall modeling via physics-informed neural networks

Yang, Xiang; Zafar, Suhaib; Wang, J.-X.; Xiao, Heng

doi:10.1103/physrevfluids.4.034602

Cited by 215 publications

(90 citation statements)

References 84 publications

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“…Carton de Wiart et al (2018) investigated the performance of WMLES in an ample set of cases including acceleration in the streamwise direction, and showed that WMLES is capable of predicting the wall stress with a reasonable degree of accuracy. Yang et al (2019) also attained good results using wall modelling via physics-informed neural networks, while Bae et al (2018a) employed a novel parameter-free dynamic wall model to predict the wall stress in a flow configuration similar to the present set-up.…”

Section: Applications To Wall-modelled Lesmentioning

confidence: 86%

Non-equilibrium three-dimensional boundary layers at moderate Reynolds numbers

et al. 2019

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Non-equilibrium wall turbulence with mean-flow three-dimensionality is ubiquitous in geophysical and engineering flows. Under these conditions, turbulence may experience a counter-intuitive depletion of the turbulent stresses, which has important implications for modelling and control. Yet, current turbulence theories have been established mainly for statistically two-dimensional equilibrium flows and are unable to predict the reduction in the Reynolds stress magnitude. In the present work, we propose a multiscale model which explains the response of non-equilibrium wall-bounded turbulence under the imposition of three-dimensional strain. The analysis is performed via direct numerical simulation of transient three-dimensional turbulent channels subjected to a sudden lateral pressure gradient at friction Reynolds numbers up to 1,000. We show that the flow regimes and scaling properties of the Reynolds stress are consistent with a model comprising momentum-carrying eddies with sizes and time scales proportional to their distance to the wall. We further demonstrate that the reduction in Reynolds stress follows a spatially and temporally self-similar evolution caused by the relative horizontal displacement between the core of the momentum-carrying eddies and the flow layer underneath. Inspection of the flow energetics reveals that this mechanism is associated with lower levels of pressurestrain correlation which ultimately inhibits the generation of Reynolds stress. Finally, we assess the ability of the state-of-the-art wall-modelled large-eddy simulation to predict non-equilibrium, three-dimensional flows.

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Section: Applications To Wall-modelled Lesmentioning

confidence: 86%

Non-equilibrium three-dimensional boundary layers at moderate Reynolds numbers

et al. 2019

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“…Probably, these extremes were hard to predict accurately because of their high stochastic nature and inherent rare occurrence. Yang et al (2019) identified this issue in the context of an ANN-based LES wall model, and found that this issue persisted even when the errors were weighted inversely proportional to their PDF (i.e. giving extreme values larger weights in the loss function).…”

Section: Performancementioning

confidence: 99%

“…Several other efforts in literature experimented with similar approaches in LES SGS modelling (Beck et al, 2019;Cheng et al, 2019;Gamahara and Hattori, 2017;Maulik et al, 2019;Milano and Koumoutsakos, 2002;Sarghini et al, 2003;Vollant et al, 2017;Wang et al, 2018;Xie et al, 2019;Yang et al, 2019;Zhou et al, 2019). Most of them used DNS fields as a basis, and subsequently applied a downscaling procedure to generate consistent pairs of coarse-grained fields (that are assumed to represent the fields that a LES code would generate) and the quantity of interest (e.g.…”

mentioning

confidence: 99%

“…There are also studies that attempted similar methods in cases that better represent ABLs. Some of them focused on LES wall modelling specifically (Milano and Koumoutsakos, 2002;Yang et al, 2019), which is challenging on its own because of the many unresolved near-wall motions that the wall model has to take into account. Sarghini et al (2003) and Gamahara and Hattori (2017), in turn, focused on SGS modelling in the whole turbulent channel flow.…”

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confidence: 99%

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Development of a large-eddy simulation subgrid model based on artificial neural networks: a case study of turbulent channel flow

Stoffer¹,

Leeuwen²,

Podareanu³

et al. 2020

Preprint

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Abstract. Atmospheric boundary layers and other wall-bounded flows are often simulated with the large-eddy simulation (LES) technique, which relies on subgrid-scale (SGS) models to parameterize the smallest scales. These SGS models often make strong simplifying assumptions. Also, they tend to interact with the discretization errors introduced by the popular LES approach where a staggered finite-volume grid acts as an implicit filter. We therefore developed an alternative LES SGS model based on artificial neural networks (ANNs) for the computational fluid dynamics code MicroHH (v2.0), which can be run in direct numerical simulation (DNS) and LES mode. We used a turbulent channel flow (with a friction Reynolds number Reτ = 590) as a test case. The developed SGS model has been designed to require fewer simplifying assumptions, and to compensate for the instantaneous discretization errors introduced by the staggered finite-volume grid. We trained the ANNs based on instantaneous flow fields from a direct numerical simulation (DNS) of the selected channel flow. In general, we found excellent agreement between the ANN predicted SGS fluxes and the SGS fluxes derived from DNS for flow fields not used during training (with the correlation coefficient ρ mostly varying between 0.6 and 1.0), showing the potential ANNs may have to construct highly accurate SGS models. However, we observed an artificial build-up of turbulence kinetic energy at high wave modes when we directly incorporated our ANN SGS model into a LES simulation of the selected channel flow, eventually resulting in numeric instability. We hypothesized that error accumulation and aliasing errrors, were both important contributors to the observed instability. Several obstacles therefore remain before the a priori promise of our ANN LES SGS model, can be successfully leveraged in practical applications.

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“…Our unsupervised learning method is also highly complementary with the significant body of work applying machine learning methods for more accurate predictions of specific physical systems, such as multiscale hydrodynamic systems [51] and turbulence modeling [52][53][54][55]. These methods often combine a known physics model with a machine learned correction or parametrize an unknown part of the physics model using neural networks.…”

Section: Discussionmentioning

confidence: 99%

Extracting Interpretable Physical Parameters from Spatiotemporal Systems Using Unsupervised Learning

Kim

Soljačić

2020

Phys. Rev. X

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Experimental data are often affected by uncontrolled variables that make analysis and interpretation difficult. For spatiotemporal systems, this problem is further exacerbated by their intricate dynamics. Modern machine learning methods are particularly well suited for analyzing and modeling complex datasets, but to be effective in science, the result needs to be interpretable. We demonstrate an unsupervised learning technique for extracting interpretable physical parameters from noisy spatiotemporal data and for building a transferable model of the system. In particular, we implement a physics-informed architecture based on variational autoencoders that is designed for analyzing systems governed by partial differential equations. The architecture is trained end to end and extracts latent parameters that parametrize the dynamics of a learned predictive model for the system. To test our method, we train our model on simulated data from a variety of partial differential equations with varying dynamical parameters that act as uncontrolled variables. Numerical experiments show that our method can accurately identify relevant parameters and extract them from raw and even noisy spatiotemporal data (tested with roughly 10% added noise). These extracted parameters correlate well (linearly with R 2 > 0.95) with the ground truth physical parameters used to generate the datasets. We then apply this method to nonlinear fiber propagation data, generated by an ab initio simulation, to demonstrate its capabilities on a more realistic dataset. Our method for discovering interpretable latent parameters in spatiotemporal systems will allow us to better analyze and understand real-world phenomena and datasets, which often have unknown and uncontrolled variables that alter the system dynamics and cause varying behaviors that are difficult to disentangle.

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Predictive large-eddy-simulation wall modeling via physics-informed neural networks

Cited by 215 publications

References 84 publications

Non-equilibrium three-dimensional boundary layers at moderate Reynolds numbers

Non-equilibrium three-dimensional boundary layers at moderate Reynolds numbers

Development of a large-eddy simulation subgrid model based on artificial neural networks: a case study of turbulent channel flow

Extracting Interpretable Physical Parameters from Spatiotemporal Systems Using Unsupervised Learning

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