A family of dynamic finite difference schemes for large-eddy simulation

Fauconnier, Dieter; Langhe, Chris De; Dick, Erik

doi:10.1016/j.jcp.2008.11.014

Cited by 21 publications

(46 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In comparison with the upwind schemes, the TVD scheme and the WENO scheme, the amplitude of these disturbances is much smaller. Looking at the dispersion property, the mean modified wavenumber μ κ (κ) does not collapse with the characteristic of the 6 th -order tridiagonal compact scheme, which is in contrast to the conclusion from the analytical single-wave analysis in the work of Fauconnier et al [6]. In the high wavenumber range, the mean dispersion relation μ κ (κ) displays a pretty good behaviour, as it is better than that of the 6 th -order central scheme, although, it does not reach the accuracy of the 6 th -order tridiagonal compact scheme.…”

Section: Discussioncontrasting

confidence: 83%

“…The last nonlinear finite difference scheme that is investigated in this work, is the central nonlinear DFD scheme of Fauconnier et al [6]. This scheme is defined by…”

Section: Thementioning

confidence: 99%

“…This leads to values around f = 0.21. It was shown in [6], that for f = 0.2, the nonlinear DFD scheme has the same modified wavenumber as the standard 6 th -order tridiagonal compact scheme, for a single-wave field. Therefore, we will adopt f = 0.2 in this work.…”

Section: Thementioning

confidence: 99%

“…Therefore, we will adopt f = 0.2 in this work. For more information about the mathematical derivation and justification of the nonlinear DFD scheme, we refer to Fauconnier et al [6]. This scheme does not depend on a transporting velocity, and thus remains nonlinear in each point for a constant transport velocity v. We emphasize that, in contrast to the upwind schemes, the TVD scheme and the WENO scheme, the DFD scheme (26) consists of a central discretization operator in combination with a dispersive correction operator.…”

Section: Thementioning

confidence: 99%

See 3 more Smart Citations

On the spectral and conservation properties of nonlinear discretization operators

Fauconnier

Dick

2011

Journal of Computational Physics

View full text Add to dashboard Cite

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.

show abstract

Section: Discussioncontrasting

confidence: 83%

“…The last nonlinear finite difference scheme that is investigated in this work, is the central nonlinear DFD scheme of Fauconnier et al [6]. This scheme is defined by…”

Section: Thementioning

confidence: 99%

Section: Thementioning

confidence: 99%

Section: Thementioning

confidence: 99%

See 2 more Smart Citations

On the spectral and conservation properties of nonlinear discretization operators

Fauconnier

Dick

2011

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…So by careful designed SGS model, low order discretization scheme can also obtain reasonable result. Fauconnier et al (Fauconnier et al 2009) also point out that low-order methods may have advantages over high order scheme because the dissipation error of SGS model can cancel part of the numerical errors resulting in a reduction of the total errors on some quantities. Of course the disadvantage is that the accuracy of small scales is not controlled.…”

Section: Introductionmentioning

confidence: 99%

Study of Some Key Issues for Applying LES to Real Engineering Problems

Yang¹

2011

Computational Simulations and Applications

View full text Add to dashboard Cite

Balancing aspects of numerical dissipation, dispersion, and aliasing in time‐accurate simulations

Edoh

Mundis

Karagozian

et al. 2020

Numerical Methods in Fluids

View full text Add to dashboard Cite

The current study looks at the selection of scheme elements that are well-suited for long-time integration of unsteady flows in the absence or under-resolution of physical diffusion. A concerted assembly of numerical components are chosen relative to a target aliasing limit, which is taken as a best-case scenario for overall spectral resolvability. High-order and optimized difference stencils are employed in order to achieve accuracy; meanwhile, quasi skew-symmetric splitting techniques for nonlinear transport terms are used in order to greatly improve robustness. Finally, tunable and scale-discriminant artificial-dissipation methods are incorporated for de-aliasing purposes and as a means of further enhancing both accuracy and stability. Central finite difference methods are considered, and spectral characterizations of the scheme components are presented. Canonical test cases (the isentropic vortex [IV] and Taylor-Green vortex problems) are chosen in order to highlight the benefits associated with the proposed approach for enhancing overall algorithm robustness and accuracy.

show abstract

A family of dynamic finite difference schemes for large-eddy simulation

Cited by 21 publications

References 30 publications

On the spectral and conservation properties of nonlinear discretization operators

On the spectral and conservation properties of nonlinear discretization operators

Study of Some Key Issues for Applying LES to Real Engineering Problems

Balancing aspects of numerical dissipation, dispersion, and aliasing in time‐accurate simulations

Contact Info

Product

Resources

About