Multilevel Methods for the Simulation of Turbulence

Témam, Roger

doi:10.1006/jcph.1996.0177

Cited by 15 publications

(6 citation statements)

References 19 publications

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“…The simulations with these models can be accurate but expensive LES or cheap approximated DNS. The dynamics multilevel model [10,36,9] is an example of cheap DNS as it requires the same resolution as the corresponding DNS. Our 2D version of the RDT model [19] using a Lagrangian evolution of small-scale wave-packets is more flexible since the accuracy of the model is function of the number of modes used for the subfilter scales.…”

Section: Discussionmentioning

confidence: 99%

A LES-Langevin model for turbulence

Laval¹,

Dubrulle

2006

Eur. Phys. J. B

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We propose a new model of turbulence for use in large-eddy simulations (LES). The turbulent force, represented here by the turbulent Lamb vector, is divided in two contributions. The contribution including only subfilter fields is deterministically modeled through a classical eddy-viscosity. The other contribution including both filtered and subfilter scales is dynamically computed as solution of a generalized (stochastic) Langevin equation. This equation is derived using Rapid Distortion Theory (RDT) applied to the subfilter scales. The general friction operator therefore includes both advection and stretching by the resolved scale. The stochastic noise is derived as the sum of a contribution from the energy cascade and a contribution from the pressure. The LES model is thus made of an equation for the resolved scale, including the turbulent force, and a generalized Langevin equation integrated on a twice-finer grid. We compare the full model with several approximations. In the first one, the friction operator of the Langevin equation is simply replaced by an empirical constant, of the order of the resolved scale correlation time. In the second approximation, the integration is replaced by a condition of instantaneous adjustment to the stochastic force. In this approximation, our model becomes equivalent to the velocity-estimation model of Domaradzki et al. [7,5,8]. In the isotropic, homogeneous situations we study, both approximations provide satisfactory results, at a reduced computational cost. The model is finally validated by comparison to DNS and is tested against classical LES models for isotropic homogeneous turbulence, based on eddy viscosity. We show that even in this situation, where no walls are present, our inclusion of backscatter through the Langevin equation results in a better description of the flow.

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Section: Discussionmentioning

confidence: 99%

A LES-Langevin model for turbulence

Laval¹,

Dubrulle

2006

Eur. Phys. J. B

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“…II for additional details. R. Temam and his co-workers have also been very active in applying multi-scale approaches to turbulence modeling 6,7 and the interested reader should consult these references as well. Hughes et al 1 provide a comparison of their approach to that of the Temam group.…”

Section: B Review Of the Vms-les Methodsmentioning

confidence: 99%

Monitoring unresolved scales in multiscale turbulence modeling

2001

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This paper extends the two-level Variational MultiScale (VMS) method for Large-Eddy Simulation, introduced by Hughes et al. [Comput. Visual. Sci., 3:47-59 (2000)], to a threelevel approach that clarifies the role of unresolved scales of motion on the resolved scales.It is shown that the multi-scale framework does not obviate modeling on the large-scales, but that VMS allows for different modeling assumptions to be used on each scale range. In particular, one can choose to neglect the effect of the unresolved scales on the large scales which is reasonable for sufficiently large scale separation.

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“…We next turn to some concrete examples. In particular we consider stochastic versions of a meteorological model developed by Lorenz in [14] and of a simple model for turbulent flow proposed by Temam in [20]. In each case we exhibit the renormalization group which decouples the two scale inherent in the original system.…”

Section: The Renormalization Group With Stochastic Forcing 1243mentioning

confidence: 99%

Singular perturbation systems with stochastic forcing and the renormalization group method

Glatt-Holtz¹,

Ziane²

2010

Discrete &Amp; Continuous Dynamical Systems - A

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This article examines a class of singular perturbation systems in the presence of a small white noise. Modifying the renormalization group procedure developed by Chen, Goldenfeld and Oono [6] , we derive an associated reduced system which we use to construct an approximate solution that separates scales. Rigorous results demonstrating that these approximate solutions remain valid with high probability on large time scales are established. As a special case we infer new small noise asymptotic results for a class of processes exhibiting a physically motivated cancellation property in the nonlinear term. These results are applied to some concrete perturbation systems arising in geophysical fluid dynamics and in the study of turbulence. For each system we exhibit the associated renormalization group equation which helps decouple the interactions between the different scales inherent in the original system.2000 Mathematics Subject Classification. 60H10.

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Multilevel Methods for the Simulation of Turbulence

Cited by 15 publications

References 19 publications

A LES-Langevin model for turbulence

A LES-Langevin model for turbulence

Monitoring unresolved scales in multiscale turbulence modeling

Singular perturbation systems with stochastic forcing and the renormalization group method

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