Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier–Stokes equation

Balajewicz, Maciej; Dowell, Earl H.; Noack, Bernd R.

doi:10.1017/jfm.2013.278

Cited by 172 publications

(161 citation statements)

References 46 publications

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“…41 Having defined an acceptable number of modes, a Galerkin system of evolution equations is written for the modes in terms of advective and dissipative terms, with the latter modeled to prevent excessive energy build-up (some form of cascade is required). Approaches are inspired by an eddy-viscosity approach, 41 with more advanced closures incorporating linear approximations to the nonlinear terms 67 or nonlinear interactions directly, 68 and comparative analyses demonstrating the utility of these more advanced formulations. 42 While dyadic wavelet modes are locally correlated at singularities (providing the basis for multifractal methods 25 ), they provide an approximately orthogonal or orthonormal basis that is also conditioned on frequency.…”

Section: B Implications Of the Results For Reduced Order Modelingmentioning

confidence: 99%

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

2015

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This work explores the properties of the velocity increment distributions for wakes of contrasting local Reynolds number and nature of generation (a cylinder wake and a multiscale-forced case, respectively). It makes use of a technique called gradual wavelet reconstruction (GWR) to generate constrained randomizations of the original data, the nature of which is a function of a parameter, ϑ. This controls the proportion of the energy between the Markov-Einstein length (∼ 0.8 Taylor scales) and integral scale that is fixed in place in the synthetic data. The properties of the increments for these synthetic data are then compared to the original data as a function of ϑ. We write a Fokker-Planck equation for the evolution of the velocity increments as a function of spatial scale, r, and, in line with previous work, expand the drift and diffusion terms in terms up to fourth order in the increments and find no terms are relevant beyond the quadratic terms. Only the linear contribution to the expansion of the drift coefficient is non-zero and it exhibits a consistent scaling with ϑ for different flows above a low threshold. For the diffusion coefficient, we find a local Reynolds number independence in the relation between the constant term and ϑ for the multiscale-forced wakes. This term characterizes small scale structure and can be contrasted with the results for the Kolmogorov capacity of the zero-crossings of the velocity signals, which measures structure over all scales and clearly distinguishes between the types of forcing. Using GWR shows that results for the linear and quadratic terms in the expansion of the diffusion coefficient are significant, providing a new means for identifying intermittency and anomalous scaling in turbulence datasets. All our data showed a similar scaling behavior for these parameters irrespective of forcing type or Reynolds number, indicating a degree of universality to the anomalous scaling of turbulence. Hence, these terms are a useful metric for testing the efficacy of synthetic turbulence generation schemes used in large eddy simulation, and we also discuss the implications of our approach for reduced order modeling of the Navier-Stokes equations.

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Section: B Implications Of the Results For Reduced Order Modelingmentioning

confidence: 99%

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

2015

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“…Nonlinear models based on the Galerkin projection of filtered Navier-Stokes equations have been pursued by Wang et al (2011Wang et al ( , 2012). An approach of completely different nature is suggested by Balajewicz et al (2013). Here, no auxiliary subscale turbulence terms have been introduced in the Galerkin system, but the dissipative effects are incorporated in a generalized POD.…”

Section: Introductionmentioning

confidence: 99%

On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high-Reynolds-number flow over an Ahmed body

et al. 2014

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We investigate a hierarchy of eddy-viscosity terms in POD Galerkin models to account for a large fraction of unresolved fluctuation energy. These Galerkin methods are applied to Large Eddy Simulation data for a flow around the vehicle-like bluff body called Ahmed body. This flow has three challenges for any reduced-order model: a high Reynolds number, coherent structures with broadband frequency dynamics, and meta-stable asymmetric base flow states. The Galerkin models are found to be most accurate with modal eddy viscosities as proposed by Rempfer & Fasel (1994). Robustness of the model solution with respect to initial conditions, eddy viscosity values and model order is only achieved for state-dependent eddy viscosities as proposed by Noack, Morzyński & Tadmor (2011). Only the POD system with state-dependent modal eddy viscosities can address all challenges of the flow characteristics. All parameters are analytically derived from the Navier-Stokes based balance equations with the available data. We arrive at simple general guidelines for robust and accurate POD models which can be expected to hold for a large class of turbulent flows.

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“…They generally fail, however, in the numerical simulation of convection-dominated flows [8][9][10][11][12][13][14][15]. Indeed, to ensure a low computational cost, only the first few POD modes are generally used in the ROM.…”

Section: Introductionmentioning

confidence: 99%

“…The resulting low-dimensional ROM, however, generally yields poor results in the numerical simulation of convection-dominated flows, often in the form of numerical oscillations (see, e.g., [3,4,8,9,14,[16][17][18]). In the ROM literature, a common explanation for this failure of standard ROMs is the violation of the concept of energy cascade [3,8,9,14,18,19]. Indeed, in [20] it was shown that the concept of energy cascade is also valid in a POD setting: The main role of the neglected POD modes is to drain energy from the ROM.…”

Section: Introductionmentioning

confidence: 99%

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Approximate deconvolution reduced order modeling

Xie

Wells

Wang

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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Highlights• A new large eddy simulation reduced order model (LES-ROM) framework.• A new approximate deconvolution ROM (AD-ROM) not of eddy viscosity type.• Successful application of AD-ROM to 3D flow past cylinder at Re = 1000. AbstractThis paper proposes a large eddy simulation reduced order model (LES-ROM) framework for the numerical simulation of convection-dominated flows. In this LES-ROM framework, the proper orthogonal decomposition (POD) is used to define the ROM basis and a ROM differential filter is used to define the large ROM structures. An approximate deconvolution (AD) approach is used to solve the ROM closure problem and develop a new AD-ROM. This AD-ROM is tested in the numerical simulation of the three-dimensional flow past a circular cylinder at a Reynolds number Re = 1000.

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Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier–Stokes equation

Cited by 172 publications

References 46 publications

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high-Reynolds-number flow over an Ahmed body

Approximate deconvolution reduced order modeling

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