Fidelity of numerical discretization for spectrally-optimized subgrid-scale closures

This study assesses the effects of numerical discretization on spectrally-optimal subgrid-scale (SGS) closures discovered using a wavelet optimization framework. Nabavi & Kim (J. Fluid Mech. 2024) proposed a framework that optimizes SGS closures containing unknown constants for spectral energy transfer. In large-eddy simulation, numerical errors are manifested as implicit SGS dissipation, exceeding modeled SGS dissipation at coarse grid resolution. This is particularly the case for discretization errors. This study examines how discretization errors affect the optimized model constants. Two types of discretization errors are assessed, namely those associated with discretizing the governing equations and wavelet energy fluxes. For forced homogeneous isotropic turbulence at Re_λ = 85, pseudospectral and 2nd-order finite difference discretizations are used to perform direct numerical simulation (DNS). In addition, spectral and 2nd-order finite difference discretizations are employed for wavelet analysis. The effects of wavelet flux discretization are substantial, but simulation discretization has no effects on the model constants. Spectral discretization using the top-hat filter is incompatible with the wavelet framework, whereas 2nd-order discretization produces physically consistent results.