  The discrete direct deconvolution model (D3M) is developed for the large-eddy
simulation (LES) of turbulence. The D3M is a discrete approximation of previous
direct deconvolution model studied by Chang et al. ["The effect of sub-filter
scale dynamics in large eddy simulation of turbulence," Phys. Fluids 34, 095104
(2022)]. For the first type model D3M-1, the original Gaussian filter is
approximated by local discrete formulation of different orders, and direct
inverse of the discrete filter is applied to reconstruct the unfiltered flow
field. The inverse of original Gaussian filter can be also approximated by
local discrete formulation, leading to a fully local model D3M-2. Compared to
traditional models including the dynamic Smagorinsky model (DSM) and the
dynamic mixed model (DMM), the D3M-1 and D3M-2 exhibit much larger correlation
coefficients and smaller relative errors in the a priori studies. In the a
posteriori validations, both D3M-1 and D3M-2 can accurately predict turbulence
statistics, including velocity spectra, probability density functions (PDFs) of
sub-filter scale (SFS) stresses and SFS energy flux, as well as time-evolving
kinetic energy spectra, momentum thickness, and Reynolds stresses in turbulent
mixing layer. Moreover, the proposed model can also well capture spatial
structures of the Q-criterion iso surfaces. Thus, the D3M holds potential as an
effective SFS modeling approach in turbulence simulations.
