Unlike standard large eddy simulation (LES) (for a review of LES for incompressible and compressible turbulence refer e.g. to [18, 7]), implicit LES (ILES) does not require an explicitly computed sub-grid scale (SGS) closure, but rather employs an inherent, usually nonlinear, regularization mechanism due to the nonlinear truncation error of the convective-flux discretization scheme as implicit SGS model. As finite-volume discretizations imply a top-hat filtered solution, regularized finitevolume reconstruction schemes were among the first ILES approaches, such as the flux-corrected transport (FCT) method , the piecewise parabolic method (PPM) . Although ILES is attractive due to its relative simplicity, numerical robustness and easy implementation, it often exhibits inferior performance to explicit LES  if the discretization scheme is not constructed properly. Some schemes, such as PPM, FCT, MUSCL  and WENO  methods, work reasonably well for ILES by being able to recover a Kolmogorov-range for high-Reynolds-number turbulence up to
is the Nyquist wavenumber of the underlying grid [9, 10, 21]. These promising results have led to further efforts on the physically-consistent design of discretization schemes for ILES. Physical consistency implies the correct and resolution-independent reproduction of the subgrid-scale (SGS) energy transfer mechanism of isotropic turbulence. Based on this notion the adaptive local deconvolution method (ALDM) has been developed [1, 11]. Approaches for decreasing excessive model dissipation for the solenoidal velocity field include the low-Mach number switch of , and the dilatation switch and shock sensor of .