Possible modifications to implicit large-eddy simulation

Implicit large-eddy simulation (ILES) provides an advantage over more usual LES approaches in that its construction does not involve filtering of the governing equations and, as a consequence, removal of the need to develop sub-grid scale (SGS) models to represent artificial stresses arising from this filtering. At the same time, it is clear that ILES is simply an under-resolved direct numerical simulation with advanced treatments of advection terms to better control numerical stability via dissipation that otherwise would have been provided by a SGS model. As such it cannot be expected to accurately predict interactions of fluid turbulence with other physical phenomena ({\it e.g.}, heat and mass transfer, chemical kinetics) on subgrid scales---as is also true of usual forms of LES. In this talk we describe a straightforward technique, based on formal multi-scale methods, whereby SGS interactions can be introduced to enhance resolved-scale results computed as in ILES, and we discuss derivation of a class of efficient models based on the ``poor man's Navier--Stokes equation'' (McDonough, {\it Phys.Rev.\ E} {\bf 79}, 2009; McDonough and Huang, {\it Int.J.Numer.\ Meth.\ Fluids} {\bf 44}, 2004). Properties of these models will be presented for a moderate-$Re$ 3-D lid-driven cavity problem.