Regularization modeling for large-eddy simulation

Geurts, Bernardus J.; Holm, Darryl D.

doi:10.1063/1.1529180

Cited by 178 publications

(173 citation statements)

References 12 publications

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“…3. This statement of the circulation theorem is also a mnemonic for deriving other regularized turbulence models of LANS-α type by specifying a different filtering kernel G α [10].…”

Section: As Expected the Lans-α Motion Equation Satisfies Thementioning

confidence: 99%

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Length-scale estimates for the LANS- equations in terms of the Reynolds number

Gibbon

Holm

2006

Physica D: Nonlinear Phenomena

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(2002) 289-306] for the Navier-Stokes equations, of obtaining estimates in terms of the Reynolds number Re, whose character depends on the fluid response, as opposed to the Grashof number, whose character depends on the forcing. Re is defined as Re = U /ν where U is a bounded spatio-temporally averaged Navier-Stokes velocity field and the characteristic scale of the forcing. It is found that the inverse Kolmogorov length is estimated by λ −1 k ≤ c ( /α) 1/4 Re 5/8 . Moreover, the estimate of Foias, Holm and Titi for the fractal dimension of the global attractor, in terms of Re, comes out to bewhere V α = L/( α) 1/2 3 and V = (L/ ) 3 . It is also shown that there exists a series of time-averaged inverse squared length scales whose members, κ 2 n,0 , are estimated as (n ≥ 1)The upper bound on the first member of the hierarchy κ 2 1,0 coincides with the inverse squared Taylor micro-scale to within log-corrections.

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“…3. This statement of the circulation theorem is also a mnemonic for deriving other regularized turbulence models of LANS-α type by specifying a different filtering kernel G α [10].…”

Section: As Expected the Lans-α Motion Equation Satisfies Thementioning

confidence: 99%

“…In this way, the classical Leray analysis of the Navier-Stokes equations finds itself a new role in the study of the analytical properties of turbulence models. Indeed, the Leray model itself was recently found to be a viable candidate for LES computational modeling of turbulence [10,17].…”

Section: As Expected the Lans-α Motion Equation Satisfies Thementioning

confidence: 99%

Length-scale estimates for the LANS- equations in terms of the Reynolds number

Gibbon

Holm

2006

Physica D: Nonlinear Phenomena

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“…Both these models are regularizations and conserve the total energy of the flow [8,17,18]. They do not, however, conserve the helicity nor the small-scale circulation.…”

Section: The Influence Of Circulation On Rigid Bodiesmentioning

confidence: 99%

“…Regularization modeling (of the SFS stress tensor) for Navier-Stokes [8,10,14,17,18,25,29,36,50], magnetohydrodynamics (MHD) [24], Boussinesq convection [53], and inviscid cases [33] promises several advantages. For Navier-Stokes, only weak, possibly non-unique solutions have been rigorously proven to exist, and this can impact the possibility of achieving a direct numerical solution (DNS), e.g., with Fourier methods [22].…”

Section: Introductionmentioning

confidence: 99%

The Effect of Subfilter-Scale Physics on Regularization Models

et al. 2010

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The subfilter-scale (SFS) physics of regularization models are investigated to understand the regularizations' performance as SFS models. Suppression of spectrally local SFS interactions and conservation of small-scale circulation in the Lagrangian-averaged Navier-Stokes α-model (LANS-α) is found to lead to the formation of rigid bodies. These contaminate the superfilter-scale energy spectrum with a scaling that approaches k +1 as the SFS spectra is resolved. The Clark-α and Leray-α models, truncations of LANS-α, do not conserve small-scale circulation and do not develop rigid bodies. LANS-α, however, is closest to Navier-Stokes in intermittency properties. All three models are found to be stable at high Reynolds number. Differences between L 2 and H 1 norm models are clarified. For magnetohydrodynamics (MHD), the presence of the Lorentz force as a source (or sink) for circulation and as a facilitator of both spectrally nonlocal large to small scale interactions as well as local SFS interactions prevents the formation of rigid bodies in Lagrangianaveraged MHD (LAMHD-α). LAMHD-α performs well as a predictor of superfilter-scale energy spectra and of intermittent current sheets at high Reynolds numbers. It may prove generally applicable as a MHD-LES.

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“…It is well-known that instabilities occur in the numerical implementation and that some kind of smoothing must be added in order to have effective simulations, see [17]. In particular, a filtered version of the Gradient method is called Rational or 4 Clark-α method, and the stress-tensor reads as…”

Section: An Anisotropic Large Eddy Simulation Modelmentioning

confidence: 99%

Horizontal Approximate Deconvolution for Stratified Flows: Analysis and Computations

Berselli

Iliescu

Özgökmen

2011

Quality and Reliability of Large-Eddy Simulations II

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Summary. In this paper we propose a new Large Eddy Simulation model derived by approximate deconvolution obtained by means of wave-number asymptotic expansions. This LES model is designed for oceanic flows and in particular to simulate mixing of fluids with different temperatures, density or salinity. The model -which exploits some ideas well diffused in the community-is based on a suitable horizontal filtering of the equations. We prove some a-priori estimates, showing certain mathematical properties and we present also the results of some preliminary numerical experiments.

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Regularization modeling for large-eddy simulation

Cited by 178 publications

References 12 publications

Length-scale estimates for the LANS- equations in terms of the Reynolds number

Length-scale estimates for the LANS- equations in terms of the Reynolds number

The Effect of Subfilter-Scale Physics on Regularization Models

Horizontal Approximate Deconvolution for Stratified Flows: Analysis and Computations

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