Analysis of the impact of numerically induced high-order filters and regularization on LES modelling of an incompressible 3D Taylor-Green vortex flow undergoing laminar-turbulent transition

This study presents a comprehensive investigation into the effects of numerically induced filters and explicit regularization on large eddy simulation (LES) of the three-dimensional periodic Taylor-Green vortex (TGV) flow during the laminar-to-turbulent transition at $Re$=1600. Three subgrid-scale (SGS) modeling approaches are analyzed: (i) classical eddy-viscosity models, (ii) implicit LES (ILES), and (iii) the approximate deconvolution model (ADM), including the Layton-Lewandowski model. Simulations are performed using an in-house compact finite-difference code that enables systematic variation of derivative discretization schemes (from 2nd- to 10th-order) and interpolation methods (from 4th- to 10th-order). The accuracy of the numerical code is validated through comparisons with reference data and simulations of a laminar variant of TGV flow ($Re$=1600), for which an analytical solution is available. Theoretical analysis reveals that filters associated with first-order derivative discretization introduce dissipative effects without inducing numerical diffusion, while second-order derivative discretization suppresses small-scale viscous dissipation, potentially leading to instability. Three solution variants are examined: non-dissipative interpolation (N-DI), dissipative interpolation (DI), and non-dissipative interpolation with explicit regularization (N-DI-R). The results demonstrate that the overall effect of discretization-induced filtering is non-dissipative, and it does not decrease the effective Reynolds number. In effect, for the chosen TGV settings ($Re$ and a coarse mesh with 643 nodes), the simulations using the N-DI method are unstable without SGS models or when SGS models are used with standard filter widths and constants. In contrast, the DI and N-DI-R approaches stabilize the solution and serve as effective dissipation mechanisms within the ILES framework. It is shown that applying ADM requires the introduction of additional dissipation, either embedded in the solution algorithm (via interpolation) or through explicit regularization. The results further underscore the importance of selecting appropriate filters for the deconvolution procedure ($\mathscr{G}_{EF}$) and for computing the SGS tensor ($\mathscr{G}_\Delta$). Using numerically induced filters as $\mathscr{G}_{EF}$ proves beneficial primarily when $\mathscr{G}_\Delta$ is of low order. As the order of $\mathscr{G}_\Delta$ increases, the choice of the filter for $\mathscr{G}_{EF}$ becomes less important. The most accurate LES-ADM results are approximately twice as accurate as those obtained with classical SGS models, regardless of $\mathscr{G}_{EF}$, though still slightly less accurate than those from the Layton-Lewandowski model or the ILES approach. Verification of these findings for a higher $Re$ and different density meshes is planned for the near future.

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