  In this work, we perform an aposteriori error analysis on implicit and
explicit large eddy simulation closure models for solving the Burgers
turbulence problem. Our closure modeling efforts include both functional and
structural models equipped with various low-pass filters. We introduce discrete
binomial smoothing filters and an enhanced version of the Van Cittert algorithm
to accelerate the convergence of approximate deconvolution processes including
regularization and relaxation filtering approaches. Our implicit modeling
efforts consist of various high-order schemes including compact and non-compact
fifth-order upwind schemes as well as weighted essential non-oscillatory (WENO)
and compact reconstructed WENO (CRWENO) schemes, and the resulting schemes are
shown to effectively converge to the direct numerical simulation (DNS) for
increasing resolutions. Comparing with DNS and underresolved DNS computations,
our numerical assessments illustrate the ability of these methods to capture
the energy content near grid cut-off scale.
