Stable Spectral Difference Approach Using Raviart-Thomas Elements for 3D Computations on Tetrahedral Grids

Veilleux, Adèle; Puigt, Guillaume; Deniau, Hugues; Daviller, Guillaume

doi:10.1007/s10915-022-01790-2

Cited by 8 publications

(6 citation statements)

References 39 publications

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“…Moreover, Veilleux et 1.3 High-order methods for combustion al. [55] extended the SDRT method on triangle elements up to 6 th order and on tetrahedral elements up to 3 rd order [56].…”

Section: The Spectral Difference Methodsmentioning

confidence: 99%

Extension of the Spectral Difference Method to Combustion

Marchal

Deniau²,

Boussuge³

et al. 2021

SSRN Journal

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“…Moreover, Veilleux et 1.3 High-order methods for combustion al. [55] extended the SDRT method on triangle elements up to 6 th order and on tetrahedral elements up to 3 rd order [56].…”

Section: The Spectral Difference Methodsmentioning

confidence: 99%

Extension of the Spectral Difference Method to Combustion

Marchal

Deniau²,

Boussuge³

et al. 2021

SSRN Journal

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“…We used bilinear interpolation to project the low-order solution onto the high-order domain. The high-fidelity simulations are run with Jaguar [32,33,34,35], a high-order spectral difference flow solver collaboratively developed by CERFACS and ONERA. At first, Jaguar is run without any forcing applied to it for long enough to evacuate initial transients.…”

Section: Simulation Conditionsmentioning

confidence: 99%

Coherent structure tracking of the second Mack mode in transitional hypersonic boundary layers

Hammachi,

Piot,

Deniau

et al. 2024

J. Phys.: Conf. Ser.

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The natural transition of hypersonic boundary layers (HBLs) is often expressed in terms of discrete modes and their linear stability. A frequent interpretation revolves around fast and slow acoustic modes interacting in the vicinity of the vortical/entropic branches of the continuous spectrum found from stability analyses. Yet several transition scenarios are contingent upon factors such as the spectral content of the free-stream disturbances, or the interactions between the discrete modes within the boundary layer and the free-stream disturbances near the leading edge which can be decomposed into vortical, acoustic and entropic nature based on the fluid-thermodynamic (FT) components. Yet the interpretations of linear stability applied to discrete modes can lead to semantic conflicts with the terminology of FT components. To clarify the current description of the processes involved, this study chooses an approach aimed at characterizing the dynamics of the second Mack mode in transitional HBLs through coherent structure tracking. The method involves decomposing the flow perturbations into acoustic, vortical and entropic content, and following their associated coherent structures over time. For this purpose, direct numerical simulations are carried out to investigate the dynamics of the second Mack mode instability in two-dimensional HBLs, considering a flow at Mach 6 over a cooled and an insulated wall. It is found that vortical structures coexist at different heights along the wall surface, forming alternating sign doublets around the critical layer and above the relative sonic line. These structures are found to merge in the region of maximum second Mack mode instability.

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“…To access such data, DNS were conducted with the spectral difference Navier-Stokes solver named JAGUAR (Chapelier, Lodato & Jameson 2016) and developed at ONERA and CERFACS. The code is designed to handle triangle (Veilleux et al 2022a) or tetrahedral elements (Veilleux et al 2022b) but all the presented computations were performed with a fourth-order discretisation scheme using hexahedral elements. Time integration is made with a low-dissipation low-dispersion sixth-order Runge-Kutta scheme.…”

Section: The Dns Computations For Validationmentioning

confidence: 99%

“…2022 a ) or tetrahedral elements (Veilleux et al. 2022 b ) but all the presented computations were performed with a fourth-order discretisation scheme using hexahedral elements. Time integration is made with a low-dissipation low-dispersion sixth-order Runge–Kutta scheme.…”

Section: Navier–stokes Computationsmentioning

confidence: 99%

About the role of the Hanratty correction in the linear response of a turbulent flow bounded by a wavy wall

Chedevergne¹,

Stuck²,

Olazabal-Loumé³

et al. 2023

J. Fluid Mech.

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Scallop patterns forming on erodible surfaces were studied historically using a linear analysis of the inner region of a turbulent boundary layer growing on a corrugated wall. Experimental observations show a phase shift between the shear stress at the wall and the wall oscillation that depends on the wavenumber. An ad hoc correction applied to the turbulent closure and due to Hanratty et al. (Thorsness et al., Chem. Engng Sci., vol. 33, issue 5, 1978, pp. 579–592; Abrams & Hanratty, J. Fluid Mech., vol. 151, issue 1, 1985, p. 443; Frederick & Hanratty, Exp. Fluids, vol. 6, issue 7, 1988, pp. 477–486) was systematically used to recover the reference experimental results. In this study, Reynolds-averaged Navier–Stokes (RANS) and direct numerical simulations (DNS) were performed and revealed the role of the Boussinesq assumption in the results obtained. We show that the Hanratty correction acts as a palliative to the misrepresentation of Reynolds stresses due to the use of the Boussinesq hypothesis. The RANS calculations based on a turbulence model using a second-order moment closure recovered the expected results obtained in the reference DNS calculations, in particular with respect to wall heat transfer. The analysis of these results highlights the critical importance of the anisotropy of the diagonal Reynolds stresses on the prediction of wall transfer under these conditions and their implication in the occurrence of scalloping.

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Stable Spectral Difference Approach Using Raviart-Thomas Elements for 3D Computations on Tetrahedral Grids

Cited by 8 publications

References 39 publications

Extension of the Spectral Difference Method to Combustion

Extension of the Spectral Difference Method to Combustion

Coherent structure tracking of the second Mack mode in transitional hypersonic boundary layers

About the role of the Hanratty correction in the linear response of a turbulent flow bounded by a wavy wall

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