A family of low dispersive and low dissipative explicit schemes for flow and noise computations

Bogey, Christophe; Bailly, Christophe

doi:10.1016/j.jcp.2003.09.003

Cited by 806 publications

(629 citation statements)

References 33 publications

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“…Schemes with such undesired property are very sensitive to mesh smoothness. Theses schemes require spatial meshes that are less than 8-10% nonuniform (see [4]; percentage denotes value of relation between lengths of neighboring cells). As the allowed rate of mesh refining/coarsening is exceeded, strong reflected parasite waves are generated by such schemes.…”

Section: Comparison Of Bicompact Schemes With Some Known Numerical Scmentioning

confidence: 99%

“…Moreover, these schemes have superior spectral resolution compared to classic symmetric finite difference schemes of the same order of accuracy [1][2][3]. However, the spatial stencil of well-known symmetric compact schemes contains no less than three integer nodes in each space dimension, therefore, these schemes can be used for computations only on uniform or weakly non-uniform meshes [1,4,5].…”

Section: Introductionmentioning

confidence: 99%

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Dispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equations

Rogov

2018

KIAM Prepr.

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(Online) Rogov B.V.Dispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equations Dispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equations Moscow -2018 Boris Vadimovich RogovDispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equationsThe Fourier analysis of fully discrete bicompact fourth-order spatial approximation schemes for hyperbolic equations is presented. This analysis is carried out on the example of a model linear advection equation. The results of Fourier analysis are presented as graphs of the dependence of the dispersion and dissipative characteristics of the bicompact schemes on the dimensionless wave number and the Courant number. The dispersion and dissipative properties of bicompact schemes are compared with those of other widely used difference schemes for hyperbolic equations. It is shown that bicompact schemes have one of the best spectral resolutions among the difference schemes being compared.

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Section: Comparison Of Bicompact Schemes With Some Known Numerical Scmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equations

Rogov

2018

KIAM Prepr.

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“…As in Refs. [3,4,6,7] we consider uniform grids, such that ∆x i = ∆x, and β i j = j − i. Moreover, for internal points, filters are symmetric, and M = N. In that case g i, j becomes independent of the position i of the internal point.…”

Section: Construction Of High-order Conservative Boundary Filtersmentioning

confidence: 99%

“…For the construction of internal filters, the filter coefficients are determined by imposing a number of constraints on the filter transfer function [3,4,6]. Firstly, normalization (12) leads to G(0) = 1.…”

Section: Construction Of High-order Conservative Boundary Filtersmentioning

confidence: 99%

Globally conservative high-order filters for large-eddy simulation and computational aero-acoustics

Wu¹,

Meyers²

2011

Computers & Fluids

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In computational aero-acoustics, large-eddy simulations (LES) or direct numerical simulations (DNS) are often employed for flow computations in the source region. As part of the numerical implementation or required modeling, explicit spatial filters are frequently employed. For instance, in LES spatial filters are employed in the formulation of various subgrid-scale (SGS) models such as the dynamic model or the variational multi-scale (VMS) Smagorinsky model; both in LES or DNS, spatial high-pass filters are often used to remove undesired grid-to-grid oscillations.Though these type of spatial filters adhere to local accuracy requirements, in practice, they often destroy global conservation properties in the presence of non-periodic boundaries conditions. This leads to the incorrect prediction of the flow properties near the hard boundaries, such as walls. In the current work, we present globally conservative high-order accurate filters, which combine traditional filters at the internal points with one-sided conservative filters near the wall boundary. We test these filters to remove grid-to-grid oscillations both in a channel-flow case and in 2D cavity flow. We find that the use of a non-conservative filter leads to erroneous predictions of the skin friction in channel flows up to 30%. In the cavity-flow simulations, the use of non-conservative filters to remove grid-to-grid oscillations leads to important shifts in the Strouhal number of the dominant mode, and a change of the flow pattern inside the cavity. In all cases, the use of conservative high-order filter formulations to remove grid-to-grid oscillations lead to very satisfactory results. Finally, in our channel-flow test case, we also illustrate the importance of using conservative filters for the formulation of the VMS Smagorinsky model.

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“…20 Fourth-order eleven-point centered finite differences are used for spatial discretization, and a second-order six-stage low-storage Runge-Kutta algorithm is implemented for time integration. 21 To circumvent the severe time-step restriction induced by the cylindrical coordinates, the derivatives in the azimuthal direction around the axis are calculated using every n-th grid point, from n = 2 up to n = 32 at the closest points to the axis. To remove grid-to-grid oscillations, a sixth-order eleven-point centered filtering designed to only damp the shortest waves discretized 22 is applied every time step to the flow variables.…”

Section: B Les Procedures and Parametersmentioning

confidence: 99%

Influence of the Nozzle-Exit Boundary-Layer Thickness on the Flow and Acoustic Fields of Initially Laminar Jets

Bailly

2009

15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference)

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Round jets originating from a pipe nozzle are computed by Large-Eddy Simulations (LES) to investigate the effects of the nozzle-exit conditions on the flow and sound fields of initially laminar jets. The jets are at Mach number 0.9 and Reynolds number 10 5 , and exhibit exit boundary layers characterized by Blasius velocity profiles, maximum rootmean-square axial velocity fluctuations between 0.2% and 1.9% of the jet velocity, and momentum thicknesses varying from 0.003 to 0.023 times the jet radius. The far-field noise is determined from the LES data on a cylindrical surface by solving the acoustic equations. Jets with thinner boundary layer develop earlier but at a slower rate, yielding longer potential cores and lower centerline turbulent intensities comparing well with measurements at high Reynolds numbers. In all jets the shear-layer transition is dominated by vortex rolling-ups and pairings, which generate strong components in the noise spectra. Just adding random disturbances of low magnitude in the nozzle however leads to weaker rolling-up and pairing processes, thus significantly reducing their contributions to the sound field. This high sensitivity to the initial conditions is in good agreement with experimental observations.

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A family of low dispersive and low dissipative explicit schemes for flow and noise computations

Cited by 806 publications

References 33 publications

Dispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equations

Dispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equations

Globally conservative high-order filters for large-eddy simulation and computational aero-acoustics

Influence of the Nozzle-Exit Boundary-Layer Thickness on the Flow and Acoustic Fields of Initially Laminar Jets

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