Analysis and Modelling of the Commutation Error

Klein, Markus; Germano, Massimo

doi:10.3390/fluids6010015

Cited by 5 publications

(1 citation statement)

References 34 publications

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“…Numerical errors associated with LES have been studied extensively, including the effects of filter commutativity (Vasilyev, Lund & Moin 1998; Haselbacher & Vasilyev 2003; van der Bos & Geurts 2005; Klein & Germano 2020), discretisation error (Ghosal 1996; Geurts 2009; Viré & Knaepen 2009), truncation error (Kravchenko & Moin 1997), numerical dispersion and dissipation (Mittal & Moin 1997; Yalla, Oliver & Moser 2021), the averaging effects for the dynamic models (Lilly 1992; Meneveau, Lund & Cabot 1996), grid anisotropy (Rozema et al. 2015; Schumann, Toosi & Larsson 2020) and grid-independent LES (Bose et al.…”

Section: Discussionmentioning

confidence: 99%

Optimising subgrid-scale closures for spectral energy transfer in turbulent flows

Nabavi,

Kim

2024

J. Fluid Mech.

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Subgrid-scale (SGS) modelling is formulated using a local transport of spectral kinetic energy estimated by a wavelet multiresolution analysis. Using a spectrally and spatially local decomposition by wavelet, the unresolved inter-scale energy transfer and modelled SGS dissipation are evaluated to enforce explicitly and optimally their balance a priori over a range of large-eddy simulation (LES) filter widths. The formulation determines SGS model constants that optimally describe the spectral energy balance between the resolved and unresolved scales at a given cutoff scale. The formulation is tested for incompressible homogeneous isotropic turbulence (HIT). One-parameter Smagorinsky- and Vreman-type eddy-viscosity closures are optimised for their model constants. The algorithm discovers the theoretical prediction of Lilly (The representation of small-scale turbulence in numerical simulation experiments. In Proceedings of the IBM Scientific Computing Symposium on Environmental Sciences, pp. 195–210) at a filter cutoff scale in the inertial subrange, whereas the discovered constants deviate from the theoretical value at other cutoff scales so that the spectral optimum is achieved. The dynamic Smagorinsky model used a posteriori shows a suboptimal behaviour at filter scales larger than those in the inertial subrange. A two-parameter Clark-type closure model is optimised. The optimised constants provide evidence that the nonlinear gradient model of Clark et al. (J. Fluid Mech., vol. 91, issue 1, 1979, pp. 1–16) is prone to numerical instability due to its model form, and combining the pure gradient model with a dissipative model such as the classic Smagorinsky model enhances numerical stability but the standard mixed model is not optimal in terms of spectral energy transfer. A posteriori analysis shows that the optimised SGS models produce accurate LES results.

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