A Legendre spectral viscosity (LSV) method applied to shock capturing for high-order flux reconstruction schemes

Sousa, Victor C. B.; Scalo, Carlo

doi:10.1016/j.jcp.2022.111157

Cited by 5 publications

(1 citation statement)

References 57 publications

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“…Recently, Sousa & Scalo (2022 b ) introduced the quasi-spectral viscosity (QSV) method, which is capable of unifying shock capturing and SFS modelling under a LES mathematical framework based on the concept that both hydrodynamic turbulence and shock formation are characterized by the energy cascade from large to small scales due to nonlinear interactions (Frisch 1995; Gupta & Scalo 2018), and they should be treated in a similar fashion. The QSV approach was also developed to be applicable to unstructured grids, via a block-spectral Legendre spectral decomposition (Sousa & Scalo 2022 a ).…”

Section: Introductionmentioning

confidence: 99%

Sub-filter-scale shear stress analysis in hypersonic turbulent Couette flow

Toki,

Sousa,

Chen

et al. 2024

J. Fluid Mech.

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Direct numerical simulations of hypersonic turbulent Couette flows are performed for top-wall Mach numbers of 6, 7 and 8, inspired by non-reactive high-enthalpy wind tunnel free-stream conditions, with the goal of analysing the physical processes driving the sub-filter-scale (SFS) stresses to inform development of large-eddy simulation techniques for hypersonic wall-bounded flows. Semi-local scaling laws collapse mean profiles and second-order turbulent statistics well, in spite of the strong wall-normal gradients of temperature and density. On the other hand, the SFS shear stresses exhibit an unexpected profile characterized by a region of pronounced shear stress deficit, which becomes more pronounced for higher Mach numbers. Instantaneous visualizations suggest that the SFS shear stress deficit is induced by the counter-gradient resolved momentum transport driven by residual velocity motions at the interface between high-density low-speed streaks being ejected away from the wall, and low-density high-speed ones replacing the displaced fluid, qualifying this as a compressibility effect. It is shown that the SFS shear stresses are primarily driven by second-order interactions between residual velocities, in spite of their triply nonlinear nature. This, in turn, motivated a statistical quadrant analysis revealing the presence of a SFS shear stress deficit, that is, SFS processes driving momentum transport of the resolved field towards the top wall. Additionally, higher-Reynolds-number simulations reveal that there is an upper limit of spatial filter widths to resolve large-scale structures, and such deficit is observable at any Reynolds number when a reasonable spatial filter is applied.

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