An efficient spectral method based on an orthogonal decomposition of the velocity for transition analysis in wall bounded flow

Buffat, Marc; Penven, Lionel Le; Cadiou, Anne

doi:10.1016/j.compfluid.2010.11.003

Cited by 26 publications

(28 citation statements)

References 21 publications

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“…This method is based on the original approach of Moser, Moin & Leonard (1983). The further development of this method given by Buffat, Le Penven & Cadiou (2011) was used with rotational form for convective terms in order to ensure the energy conservation. For the computation of the Fourier transform of the nonlinear term the 3/2 de-aliasing rule is applied.…”

Section: Details Of the Numerical Simulationsmentioning

confidence: 99%

Acceleration in turbulent channel flow: universalities in statistics, subgrid stochastic models and an application

2013

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This paper focuses on the characterization and the stochastic modelling of the fluid acceleration in turbulent channel flow. In the first part, the acceleration is studied by direct numerical simulation (DNS) at three Reynolds numbers (Re * = u * h/ν = 180, 590 and 1000). It is observed that whatever the wall distance is, the norm of acceleration is log-normally distributed and that the variance of the norm is very close to its mean value. It is also observed that from the wall to the centreline of the channel, the orientation of acceleration relaxes statistically towards isotropy. On the basis of dimensional analysis, a universal scaling law for the acceleration norm is proposed. In the second part, in the framework of the norm/orientation decomposition, a stochastic model of the acceleration is introduced. The stochastic model for the norm is based on fragmentation process which evolves across the channel with the wall distance. Simultaneously the orientation is simulated by a random walk on the surface of a unit sphere. The process is generated in such a way that the mean components of the orientation vector are equal to zero, whereas with increasing wall distance, all directions become equally probable. In the third part, the models are assessed in the framework of large-eddy simulation with stochastic subgrid acceleration model (LES-SSAM), introduced recently by Sabel'nikov, Chtab-Desportes & Gorokhovski (Euro. Phys. J. B, vol. 80, 2011, p. 177-187), and designed to account for the intermittency at subgrid scales. Computations by LES-SSAM and its assessment using DNS data show that the prediction of important statistics to characterize the flow, such as the mean velocity, the energy spectra at small scales, the viscous and turbulent stresses, the distribution of the acceleration can be considerably improved in comparison with standard LES. In the last part of this paper, the advantage of LES-SSAM in accounting for the subgrid flow structure is demonstrated in simulation of particle-laden turbulent channel flows. Compared to standard LES, it is shown that for different Stokes numbers, the particle dynamics and the turbophoresis effect can be predicted significantly better when LES-SSAM is applied.

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Section: Details Of the Numerical Simulationsmentioning

confidence: 99%

Acceleration in turbulent channel flow: universalities in statistics, subgrid stochastic models and an application

2013

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“…These two classes of Chebyshev test functions have been proposed by Moser et al [33] to construct a divergence-free spectral approximation of periodic channel flows, and used by Buffat et al [9] to build an efficient spectral method based on an orthogonal decomposition of the velocity for transition analysis in wall-bounded flow. Using the set of test functions (18) and (19), we can take advantage of the decoupling of even and odd indices, and the matrix A p is the sum of two independent band matrices of size 5ð NÀ1 2 Þ for the Laplacian and 7ð NÀ1 2 Þ for the bi-Laplacian operator.…”

Section: Methodsmentioning

confidence: 99%

A spectral fictitious domain method with internal forcing for solving elliptic PDEs

Buffat¹,

Penven²

2011

Journal of Computational Physics

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“…DNS of spatially developing channel flows are performed with a spectral Galerkin method [1,8] for several Reynolds numbers Re h ranging from 1250 to 20,000. The computational domain starts at a small distance downstream from the origin of the boundary layers (at a location corresponding to a fixed Re x 0 = 40,000) and extends hundreds of time the channel half-width.…”

Section: Flow Configuration and Numerical Methodsmentioning

confidence: 99%

DNS of the Turbulent Flow Evolving in a Plane Channel from the Entry to the Fully Developed State

Capuano

Cadiou

Buffat

et al. 2016

Springer Proceedings in Physics

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Direct numerical simulation of the turbulent flow spatially developing in a plane channel is performed. The channel is long enough for the turbulence to achieve the statistically invariant state in space and time. Spatial evolution of statistical quantities and Reynolds stress budgets are calculated. Results are compared to the canonical flows consisting of the zero-pressure gradient turbulent boundary layer and of the periodical channel flow.

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An efficient spectral method based on an orthogonal decomposition of the velocity for transition analysis in wall bounded flow

Cited by 26 publications

References 21 publications

Acceleration in turbulent channel flow: universalities in statistics, subgrid stochastic models and an application

Acceleration in turbulent channel flow: universalities in statistics, subgrid stochastic models and an application

A spectral fictitious domain method with internal forcing for solving elliptic PDEs

DNS of the Turbulent Flow Evolving in a Plane Channel from the Entry to the Fully Developed State

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