Large Eddy Simulations offer an alternative approach to turbulent flow simulations as compared to the RANS approach. In LES, the larger three-dimensional, unsteady eddies are resolved, whereas the effect of the smaller eddies is modeled. This requires the simulations to be three-dimensional and time dependent. The velocity, density and mass fraction fields are divided into resolved, (u,
ρ,
ωi), and unresolved, (
u', ρ', ω'i). The unresolved scales are assumed to be orthogonal to the inner-product space of the resolved scales and to vanish on
∂Ω, the boundaries of the domain
Ω.
where uτ is the friction velocity and

is the dimensionless mass fraction, given by