Turbulence spectra characteristics of high order schemes for direct and large eddy simulation

Ladeinde, Foluso; Cai, Xiaodan; Visbal, Miguel R.; Gaitonde, Datta V.

doi:10.1016/s0168-9274(00)00019-2

Cited by 29 publications

(24 citation statements)

References 20 publications

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“…κ c < κ < κ max . This supports the conclusions of Ladeinde et al [8], who found that ENO and WENO schemes generate numerical turbulence, and Fauconnier et al [6] who found similar results for the nonlinear DFD scheme. The relative importance of these spurious modes in comparison with the regular modes, depends on the type of discretization.…”

Section: Discussionsupporting

confidence: 88%

“…In the case κ c /κ max = 1/2, one clearly notices the creation of spurious modes above the cutoff wavenumber κ c . This supports the conclusion of both Ladeinde et al [8], who stated that ENO and WENO schemes generate numerical turbulence, and Fauconnier et al [6] who found similar results for the nonlinear DFD scheme. For the TVD scheme and the WENO scheme, these spurious scales are approximately two magnitude smaller than the smallest scales at the cutoff wavenumber, whereas for the DFD scheme, the spurious modes are approximately four magnitudes smaller than the smallest scales at the cutoff wavenumber.…”

Section: Discussionsupporting

confidence: 86%

“…Aside from the analysis of the modified wavenumber, it is also interesting to investigate the impact of the nonlinearity on the energy spectrum of the synthetic field. This allows to study the energetic impact of the nonlinear mechanisms and to visualize the spurious scales that are generated by the nonlinear schemes at the tail of the energy spectrum [8,1]. In analogy with the analytical relation…”

Section: Methodsmentioning

confidence: 99%

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On the spectral and conservation properties of nonlinear discretization operators

Fauconnier

Dick

2011

Journal of Computational Physics

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Following the study of Pirozzoli [1], the objective of the present work is to provide a detailed theoretical analysis of the spectral properties and the conservation properties of nonlinear finite difference discretizations. First, a Nonlinear Spectral Analysis (NSA) is proposed in order to study the statistical behaviour of the modified wavenumber of a nonlinear finite difference operator, for a large set of synthetic scalar fields with prescribed energy spectrum and random phase. Second, the necessary conditions for local and global conservation of momentum and kinetic energy are derived and verified for nonlinear discretizations. Because the nonlinear mechanisms result in a violation of the energy conservation conditions, the NSA is used to quantify the energy imbalance. Third, the effect of aliasing errors due to the nonlinearity is analyzed. Finally, the theoretical observations are verified for two simple, thought relevant, numerical simulations.

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Section: Discussionsupporting

confidence: 88%

Section: Discussionsupporting

confidence: 86%

Section: Methodsmentioning

confidence: 99%

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On the spectral and conservation properties of nonlinear discretization operators

Fauconnier

Dick

2011

Journal of Computational Physics

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“…Domaradzki et al [6][7][8] and Bogey and Bailly [9,10] pointed out that the global amount of dissipation, as well as its spectral distribution, may be difficult to control in these methods. This has led to the development of other LES methodologies relying on high-order dissipation mechanisms, such as hyper-viscosity models [11,12], the relaxation term in the approximate deconvolution model (ADM) [13], or spectral-like/selective spatial filters [14].…”

Section: Introductionmentioning

confidence: 99%

On the performance of relaxation filtering for large-eddy simulation

Fauconnier

Bogey

Dick

2013

Journal of Turbulence

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“…The alternative is the use of high-order methods that allow reduction in the grid size while improving the precision of the simulation. This is already common practice in the compressible flow community where a large number of direct numerical simulations have been reported using sixth-order [1,2] or even higher-order methods [3]. However, the incompressibility condition imposed on flows in the low Mach number limit and the resulting velocity-pressure coupling appears to be a stumbling block for the development of high-order methods.…”

Section: Introductionmentioning

confidence: 99%

Study of a staggered fourth‐order compact scheme for unsteady incompressible viscous flows

Knikker

2008

Numerical Methods in Fluids

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SUMMARYThe objective of this paper is the development and assessment of a fourth-order compact scheme for unsteady incompressible viscous flows. A brief review of the main developments of compact and highorder schemes for incompressible flows is given. A numerical method is then presented for the simulation of unsteady incompressible flows based on fourth-order compact discretization with physical boundary conditions implemented directly into the scheme. The equations are discretized on a staggered Cartesian non-uniform grid and preserve a form of kinetic energy in the inviscid limit when a skew-symmetric form of the convective terms is used.The accuracy and efficiency of the method are demonstrated in several inviscid and viscous flow problems. Results obtained with different combinations of second-and fourth-order spatial discretizations and together with either the skew-symmetric or divergence form of the convective term are compared. The performance of these schemes is further demonstrated by two challenging flow problems, linear instability in plane channel flow and a two-dimensional dipole-wall interaction. Results show that the compact scheme is efficient and that the divergence and skew-symmetric forms of the convective terms produce very similar results. In some but not all cases, a gain in accuracy and computational time is obtained with a high-order discretization of only the convective and diffusive terms. Finally, the benefits of compact schemes with respect to second-order schemes is discussed in the case of the fully developed turbulent channel flow.

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Turbulence spectra characteristics of high order schemes for direct and large eddy simulation

Cited by 29 publications

References 20 publications

On the spectral and conservation properties of nonlinear discretization operators

On the spectral and conservation properties of nonlinear discretization operators

On the performance of relaxation filtering for large-eddy simulation

Study of a staggered fourth‐order compact scheme for unsteady incompressible viscous flows

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