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

Östh, Jan; Noack, Bernd R.; Krajnović, Siniša; Barros, Diogo; Borée, Jacques

doi:10.1017/jfm.2014.168

Cited by 165 publications

(123 citation statements)

References 56 publications

Supporting

Mentioning

122

Contrasting

Order By: Relevance

“…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. Thus, while POD enforces orthogonality but any scale separation is implicit, wavelets enforce the latter.…”

Section: B Implications Of the Results For Reduced Order Modelingmentioning

confidence: 99%

“…While our framework may be used for modeling purposes, 39 it is used here to study the properties of turbulence datasets (in a similar way to work examining the form of the intermittency in measured datasets 40 ). Hence, the intention is not to inform a reduced order model for the dynamics, 41,42 although at the end of the paper, we consider the implications of our work for such an approach.…”

Section: B Fokker-planck Equation For the Velocity Incrementsmentioning

confidence: 99%

See 1 more Smart Citation

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

2015

View full text Add to dashboard Cite

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.

show abstract

Section: B Implications Of the Results For Reduced Order Modelingmentioning

confidence: 99%

Section: B Fokker-planck Equation For the Velocity Incrementsmentioning

confidence: 99%

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

2015

View full text Add to dashboard Cite

show abstract

“…These modifications are difficult or even impossible in commercial software [29]. In addition, the intrusive ROM suffers from non-linear inefficiency and instability issues [47,43,37]. The methods of improving the stability of the ROM can be found in [32,56,48,23,24,52].…”

Section: Introductionmentioning

confidence: 99%

A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications

Xiao¹,

Fang²,

Pain³

et al. 2017

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

A novel parameterized non-intrusive reduced order model (P-NIROM) based on proper orthogonal decomposition (POD) has been developed. This P-NIROM is a generic and efficient approach for model reduction of parameterized partial differential equations (P-PDEs). Over existing parameterized reduced order models (P-ROM) (most of them are based on the reduced basis method), it is non-intrusive and independent on partial differential equations and computational codes. During the training process, the Smolyak sparse grid method is used to select a set of parameters over a specific parameterized space (Ω p ∈ R P ). For each selected parameter, the reduced basis functions are generated from the snapshots derived from a run of the high fidelity model. More generally, the snapshots and basis function sets for any parameters over Ω p can be obtained using an interpolation method. The P-NIROM can then be constructed by using our recently developed technique [50,53] where either the Smolyak or radial basis function (RBF) methods are used to generate a set of hyper-surfaces representing the underlying dynamical system over the reduced space.The new P-NIROM technique has been applied to parameterized Navier-Stokes equations and implemented with an unstructured mesh finite element model. The capability of this P-NIROM has been illustrated numerically by two test cases: flow past a cylinder and lock exchange case. The prediction capabilities of the P-NIROM have been evaluated by varying the viscosity, initial and boundary conditions. The results show that this P-NIROM has captured the quasi-totality of the details of the flow with CPU speedup of three orders of magnitude. An error analysis for the P-NIROM has been carried out.

show abstract

“…Reduced order models (ROMs) can be derived by a combination of POD and Galerkin projection methods. However, the use of POD/Galerkin methods raises numerical instability and non-linearity inefficiency problems [11,12,13,14]. Several methods have been presented to improve the numerical stability of ROMs, such as calibration [15,16], Fourier expansion [17], regularisation [18] and Petrov−Galerkin methods [2,19].…”

Section: Introductionmentioning

confidence: 99%

A non-intrusive reduced-order model for compressible fluid and fractured solid coupling and its application to blasting

Xiao¹,

Yang²,

Fang

et al. 2017

Journal of Computational Physics

View full text Add to dashboard Cite

This work presents the first application of a non-intrusive reduced order method to model solid interacting with compressible fluid flows to simulate crack initiation and propagation. In the high fidelity model, the coupling process is achieved by introducing a source term into the momentum equation, which represents the effects of forces of the solid on the fluid. A combined single and smeared crack model with the MohrCoulomb failure criterion is used to simulate crack initiation and propagation. The non-intrusive reduced order method is then applied to compressible fluid and fractured solid coupled modelling where the computational cost involved in the full high fidelity simulation is high. The non-intrusive reduced order model (NIROM) developed here is constructed through proper orthogonal decomposition (POD) and a radial basis function (RBF) multi-dimensional interpolation method.The performance of the NIROM for solid interacting with compressible fluid flows, in the presence of fracture models, is illustrated by two complex test cases: an immersed wall in a fluid and a blasting test case. The numerical simulation results show that the NIROM is capable of capturing the details of compressible fluids and fractured solids while the CPU time is reduced by several orders of magnitude. In addition, the issue of whether or not to subtract the mean from the snapshots before applying POD is discussed in this paper. It is shown that solutions of the NIROM, without mean subtracted before constructing the POD basis, captured more details than the NIROM with mean subtracted from snapshots.

show abstract

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

Cited by 165 publications

References 56 publications

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications

A non-intrusive reduced-order model for compressible fluid and fractured solid coupling and its application to blasting

Contact Info

Product

Resources

About