  The goal of this paper is twofold: first, it investigates the effect of
low-pass spatial filters for approximate deconvolution large eddy simulation
(AD-LES) of turbulent incompressible flows. Second, it proposes the
hyper-differential filter as a means of increasing the accuracy of the AD-LES
model without increasing the computational cost. Box filters, Pad\'{e} filters,
and differential filters with a wide range of parameters are studied in the
AD-LES framework. The AD-LES model, in conjunction with these spatial filters,
is tested in the numerical simulation of the three-dimensional Taylor-Green
vortex problem. The numerical results are benchmarked against direct numerical
simulation (DNS) data. An under-resolved numerical simulation is also used for
comparison purposes. Four criteria are used to investigate the AD-LES model
equipped with these spatial filters: (i) the time series of the volume-averaged
enstrophy; (ii) the volume-averaged third-order structure function; (iii) the
$L^2$-norm of the velocity and vorticity errors; and (iv) the volume-averaged
velocity and vorticity correlation coefficients. According to these criteria,
the numerical results yield the following two conclusions: first, the AD-LES
model equipped with any of these spatial filters yields accurate results at a
fraction of the computational cost of DNS. Second, the most accurate results
are obtained with the hyper-differential filter, followed by the differential
filter. We demonstrate that the results highly depend on the selection of the
filtering procedure. Although a careful parameter choice makes each class of
filters used in this study competitive, it seems that filters whose transfer
function resembles that of the Fourier cut-off filter (such as the
hyper-differential filters) tend to perform best.
