Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data

Wang, Jianxun; Wu, Jinlong

doi:10.1103/physrevfluids.2.034603

Cited by 522 publications

(340 citation statements)

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“…In terms of computational performance, point-to-point mapping requires less training time for learning SGS stresses from resolved flow variables. This approach is particularly attractive for complex or unstructured mesh and has been applied in many studies [35,36,49,50,72]. As illustrated in these works, our analysis with simple input features like resolved velocities and their derivatives also shows that the input features are critical for effective learning of SGS stresses for point-to-point mapping approach.…”

Section: Point-to-point Mappingmentioning

confidence: 67%

A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence

Pawar

San

Rasheed

et al. 2020

Theor. Comput. Fluid Dyn.

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In the present study, we investigate different data-driven parameterizations for large eddy simulation of two-dimensional turbulence in the a priori settings. These models utilize resolved flow field variables on the coarser grid to estimate the subgrid-scale stresses. We use data-driven closure models based on localized learning that employs multilayer feedforward artificial neural network (ANN) with point-to-point mapping and neighboring stencil data mapping, and convolutional neural network (CNN) fed by data snapshots of the whole domain. The performance of these data-driven closure models is measured through a probability density function and is compared with the dynamic Smagorinksy model (DSM). The quantitative performance is evaluated using the cross-correlation coefficient between the true and predicted stresses. We analyze different frameworks in terms of the amount of training data, selection of input and output features, their characteristics in modeling with accuracy, and training and deployment computational time. We also demonstrate computational gain that can be achieved using the intelligent eddy viscosity model that learns eddy viscosity computed by the DSM instead of subgrid-scale stresses. We detail the hyperparameters optimization of these models using the grid search algorithm.Keywords Turbulence closure · Deep learning · Neural networks · Subgrid scale modeling · Large eddy simulation 1 Introduction Direct numerical simulation (DNS) of complex fluid flows encountered in many engineering and geophysical applications is computationally unmanageable because of the need to resolve a wide range of spatiotemporal scales. Large eddy simulation (LES) and Reynolds Averaged Navier-Stokes (RANS) modeling are two most commonly used mathematical modeling frameworks that give accurate predictions by considering the interaction between the unresolved and grid-resolved scales. The development of these models is termed as the turbulence closure problem and has been a long-standing challenge in fluid mechanics community [1][2][3][4].In LES, we filter the Navier-Stokes equations using a low-pass filtering operator that separates the motion into small and large scales, and in turn, produces modified equations which are computationally faster to solve than actual Navier-Stokes equations [5][6][7]. The interaction between grid-resolved and unresolved scales is then taken into account by introducing subgrid-scale stress (SGS) term in the modified equation. The main task of the SGS model is to provide mean dissipation that corresponds to the transfer of energy from resolved scales to unresolved scales (the production of energy at large scales is balanced by the dissipation of energy at small scales based on Kolmogorov's theory of turbulence). The dissipation effect of unresolved scales can be included utilizing an eddy viscosity parameterization obtained through grid-resolved quantities. These approaches are called as functional approaches which assume isotropy of small scales to present the average dissipation of t...

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Section: Point-to-point Mappingmentioning

confidence: 67%

A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence

Pawar

San

Rasheed

et al. 2020

Theor. Comput. Fluid Dyn.

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“…From these mean pressure and velocity fields, various other features can be derived. Table 2 shows a set of five hand-crafted mean flow features following that of Ling and Templeton [58] and Wang et al [11]. In a typical RANS simulation, these quantities would be available, and such mean flow features have been used to predict the reliability of linear eddy viscosity models [58], the discrepancies of the RANS-modeled Reynolds stresses [11,59].…”

Section: Data Analysis Machine Learning and Interpretationmentioning

confidence: 99%

“…Table 2 shows a set of five hand-crafted mean flow features following that of Ling and Templeton [58] and Wang et al [11]. In a typical RANS simulation, these quantities would be available, and such mean flow features have been used to predict the reliability of linear eddy viscosity models [58], the discrepancies of the RANS-modeled Reynolds stresses [11,59]. They can also be used to predict Reynolds stress itself or the eddy viscosity [60] without relying on any baseline RANS models [13].…”

Section: Data Analysis Machine Learning and Interpretationmentioning

confidence: 99%

“…Here we use an example to illustrate the possible usage of our dataset for training and testing data-driven models. To this end, machine learning models are constructed to predict Reynolds stress anisotropy based on the mean flow features q shown in Table 2, which is a subset of what were used in [11]. The original features that are based on quantities from RANS solvers (e.g., turbulent kinetic energy k and dissipation rate ε) are omitted here as no RANS simulations are performed in this work.…”

Section: Problem Formulationmentioning

confidence: 99%

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Flows over periodic hills of parameterized geometries: A dataset for data-driven turbulence modeling from direct simulations

Xiao

Laizet

et al. 2020

Computers & Fluids

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Computational fluid dynamics models based on Reynolds-averaged Navier-Stokes equations with turbulence closures still play important roles in engineering design and analysis. However, the development of turbulence models has been stagnant for decades. With recent advances in machine learning, data-driven turbulence models have become attractive alternatives worth further explorations. However, a major obstacle in the development of data-driven turbulence models is the lack of training data. In this work, we survey currently available public turbulent flow databases and conclude that they are inadequate for developing and validating data-driven models. Rather, we need more benchmark data from systematically and continuously varied flow conditions (e.g., Reynolds number and geometry) with maximum coverage in the parameter space for this purpose.To this end, we perform direct numerical simulations of flows over periodic hills with varying slopes, resulting in a family of flows over periodic hills which ranges from incipient to mild and massive separations. We further demonstrate the use of such a dataset by training a machine learning model that predicts Reynolds stress anisotropy based on a set of mean flow features. We expect the generated dataset, along with its design methodology and the example application presented herein, will facilitate development and comparison of future data-driven turbulence models. entists and engineers. Turbulent flows are typical multi-scale physical systems that are characterized by a wide range of spatial and temporal scales. When predicting such systems, first-principle-based simulations are prohibitively expensive, and the small-scale processes must be modeled. For simulating turbulent flows, this is done by solving the Reynolds-Averaged Navier-Stokes (RANS) equations with the unresolved processes represented by turbulence model closures.While the past two decades have witnessed a rapid development of high-fidelity turbulence simulation methods such as large eddy simulations (LES), they are still too expensive for practical systems such as the flow around an commercial airplane [1]. It is expect that using LES for engineering design will remain infeasible for decades to come. On the other hand, attempts in combining models of different fidelity levels (e.g., hybrid LES/RANS models) have shown promises, but how to achieve consistencies in the hierarchical coupling of models is still a challenge and a topic of ongoing research. Consequently, Reynolds-Averaged Navier-Stokes (RANS) equations are still the workhorse tool in engineering computational fluid dynamics for simulating turbulent flows.It is well known that RANS turbulence models have large model-form uncertainties for a wide range of flows [2], which diminish the predictive capabilities of the RANS-based CFD models.Development of turbulence models has been stagnant for decades, which is evident from the fact that currently used turbulence models (e.g., k-ε, k-ω, and Spalart-Allmaras models [3-5]) were all developed decades ag...

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“…Thus, physical constraints have been used for decades in the computational fluid dynamics community (see, eg, Arakawa's pioneering work as well as more recent developments). More recently, physical constraints have started to be used in standard (ie, without ROM) LES closure modeling (see, eg, the works of Duraisamy et al and Wang et al). Finally, physical constraints have also been used in standard ROM (ie, without closure modeling) .…”

Section: Introductionmentioning

confidence: 99%

Physically constrained data‐driven correction for reduced‐order modeling of fluid flows

Mohebujjaman

Rebholz

Iliescu

2018

Numerical Methods in Fluids

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Summary We have recently proposed a data‐driven correction reduced‐order model (DDC‐ROM) framework for the numerical simulation of fluid flows, which can be formally written as follows. The new DDC‐ROM was constructed by using reduced‐order model spatial filtering and data‐driven reduced‐order model closure modeling (for the Correction term) and was successfully tested in the numerical simulation of a two‐dimensional channel flow past a circular cylinder at Reynolds numbers Re = 100,Re = 500, and Re = 1000. In this paper, we propose a physically constrained DDC‐ROM (CDDC‐ROM), which aims at improving the physical accuracy of the DDC‐ROM. The new physical constraints require that the CDDC‐ROM operators satisfy the same type of physical laws (ie, the Correction term's linear component should be dissipative, and the Correction term's nonlinear component should conserve energy) as those satisfied by the fluid flow equations. To implement these physical constraints, in the data‐driven modeling step, we replace the unconstrained least squares problem with a constrained least squares problem. We perform a numerical investigation of the new CDDC‐ROM and standard DDC‐ROM for a two‐dimensional channel flow past a circular cylinder at Reynolds numbers Re = 100,Re = 500, and Re = 1000. To this end, we consider a reproductive regime as well as a predictive (ie, cross‐validation) regime in which we use as little as 50% of the original training data. The numerical investigation clearly shows that the new CDDC‐ROM is significantly more accurate than the DDC‐ROM in both regimes.

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Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data

Cited by 522 publications

References 54 publications

A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence

A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence

Flows over periodic hills of parameterized geometries: A dataset for data-driven turbulence modeling from direct simulations

Physically constrained data‐driven correction for reduced‐order modeling of fluid flows

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