Turbulence Modeling in the Age of Data

Duraisamy, Karthik; Iaccarino, Gianluca; Xiao, Heng

doi:10.1146/annurev-fluid-010518-040547

Cited by 1,087 publications

(561 citation statements)

References 81 publications

(74 reference statements)

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“…Interested readers are directed to Refs. [66][67][68][69][70] for more on the influence of ML on fluid mechanics, specifically turbulence modeling.…”

Section: Introductionmentioning

confidence: 99%

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

et al. 2019

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In this study, we present a non-intrusive reduced order modeling (ROM) framework for largescale quasi-stationary systems. The framework proposed herein exploits the time series prediction capability of long short-term memory (LSTM) recurrent neural network architecture such that: (i) in the training phase, the LSTM model is trained on the modal coefficients extracted from the highresolution data snapshots using proper orthogonal decomposition (POD) transform, and (ii) in the testing phase, the trained model predicts the modal coefficients for the total time recursively based on the initial time history. Hence, no prior information about the underlying governing equations is required to generate the ROM. To illustrate the predictive performance of the proposed framework, the mean flow fields and time series response of the field values are reconstructed from the predicted modal coefficients by using an inverse POD transform. As a representative benchmark test case, we consider a two-dimensional quasi-geostrophic (QG) ocean circulation model which, in general, displays an enormous range of fluctuating spatial and temporal scales. We first illustrate that the conventional Galerkin projection based reduced order modeling of such systems requires a high number of POD modes to obtain a stable flow physics. In addition, ROM-GP does not seem to capture the intermittent bursts appearing in the dynamics of the first few most energetic modes. However, the proposed non-intrusive ROM framework based on LSTM (ROM-LSTM) yields a stable solution even for a small number of POD modes. We also observe that the ROM-LSTM model is able to capture quasi-periodic intermittent bursts accurately, and yields a stable and accurate mean flow dynamics using the time history of a few previous time states, denoted as the lookback time-window in this paper. Throughout the paper, we demonstrate our findings in terms of time series evolution of the field values and mean flow patterns, which suggest that the proposed fully non-intrusive ROM framework is robust and capable of predicting noisy nonlinear fluid flows in an extremely efficient way compared to the conventional projection based ROM framework.

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“…Interested readers are directed to Refs. [66][67][68][69][70] for more on the influence of ML on fluid mechanics, specifically turbulence modeling.…”

Section: Introductionmentioning

confidence: 99%

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

et al. 2019

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“…Furthermore, the DDC-ROM is more robust to noise than standard DD-ROMs, since the DDC-ROM employs data-driven modeling (which is an inverse problem sensitive to noise) only to model the Correction term in (6), whereas the DD-ROMs use it to model all the ROM operators (compare (9) with (5)). We note that data-driven closure modeling for non-ROM settings is an extremely active research area (see, eg, the works of Duraisamy et al 28 and Ling et al 29 ). We also note that there are other DD-ROM closure models.…”

Section: Introductionmentioning

confidence: 88%

“…We note that data‐driven closure modeling for non‐ROM settings is an extremely active research area (see, eg, the works of Duraisamy et al and Ling et al). We also note that there are other DD‐ROM closure models .…”

Section: Introductionmentioning

confidence: 99%

“…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%

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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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“…Reduced basis method for optimal control of unsteady viscous flows. International Journal of Computational Fluid Dynamics, 15(2): [97][98][99][100][101][102][103][104][105][106][107][108][109][110][111][112][113]2001. Figure 31: The first local basis function for vorticity field from PID application over the first subinterval (i.e., for t κ (Np−1) ≤ t ≤ 40) for double shear layer problem using different number of intervals.…”

Section: Boussinesq Problemmentioning

confidence: 99%

Memory embedded non-intrusive reduced order modeling of non-ergodic flows

et al. 2019

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Generating a digital twin of any complex system requires modeling and computational approaches that are efficient, accurate, and modular. Traditional reduced order modeling techniques are targeted at only the first two but the novel non-intrusive approach presented in this study is an attempt at taking all three into account effectively compared to their traditional counterparts. Based on dimensionality reduction using proper orthogonal decomposition (POD), we introduce a long short-term memory (LSTM) neural network architecture together with a principal interval decomposition (PID) framework as an enabler to account for localized modal deformation, which is a key element in accurate reduced order modeling of convective flows. Our applications for convection dominated systems governed by Burgers, Navier-Stokes, and Boussinesq equations demonstrate that the proposed approach yields significantly more accurate predictions than the POD-Galerkin method, and could be a key enabler towards near real-time predictions of unsteady flows. and perhaps much beyond. With the recent wave of digitization, reduced order modeling can be viewed as one of the key enablers to bring the promise of the digital twinning concept closer to reality [38]. Therefore, there is a continuous demand for the development of accurate reduced order models for complex physical phenomena. In projection-based ROMs, the most widely used technique, the discrete high-dimensional operators are projected onto a lower-dimensional space, so that the problem can be solved more efficiently in this reduced space [39][40][41][42][43][44].One of the very early-developed and well-known approaches to build this reduced space is Fourier analysis. However, it assumes universal basis functions (or modes) which have no specific relation to the physical system. On the other hand, snapshot-based model reduction techniques tailor a reduced space that best fits the problem by extracting the underlying coherent structures that controls the major dynamical evolution we are interested in. Proper orthogonal decomposition (POD) is a very popular and well-established approach extracting the modes which most contributes to the total variance [45,46]. In fluid dynamics applications, where we are mostly interested in the velocity field, those modes contain the largest amount of kinetic energy [47,48]. That is why POD is usually classified as an energy-based decomposition method. Another popular approach for model order reduction is the dynamic mode decomposition (DMD) [49][50][51][52][53][54] which generates a number of modes, each characterized by an oscillating frequency and growth/decay rate. In the present study, we are interested in the application of POD for dimensionality reduction.POD generates a set of spatial orthonormal basis functions, each containing a significant amount of total energy. To obtain a reduced representation of a system, the first few modes are selected, and the remaining are truncated assuming their contribution to the system's behavior is minimum (i.e.,...

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Turbulence Modeling in the Age of Data

Cited by 1,087 publications

References 81 publications

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

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

Memory embedded non-intrusive reduced order modeling of non-ergodic flows

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