  In this work, we will present a physically consistent theory to derive the
governing equations of the Large Eddy Simulation (LES) framework based on first
principles rather than the motivation to conduct computationally affordable
simulations of turbulent flows. Therefore, we assume that a coarse-grained
fluid element, subsequently called super fluid element, can be locally defined
comprising a large number of smaller elementary fluid elements. Then, similar
to non-equilibrium molecular dynamics (NEMD), in which the transport equations
of an elementary fluid element can be consistently reconstructed from the
local, collective dynamics of molecules, the transport equations of a super
fluid element can be derived from the local, collective dynamics of elementary
fluid elements. Interestingly, we find: (a) Favre filtering is a physical
consistency condition, (b) why Boussinesq's hypothesis in conjunction with eddy
viscosity models is commonly employed in LES and (c) that the LES framework
might be more than a numerical turbulence model for computational fluid
dynamics (CFD).
