# Large eddy simulation (LES)

The subgrid-scale turbulence models usually employ the Boussinesq hypothesis,that is computing subgrid-scale turbulent stresses from:

$\tau _{ij} - \frac{1}{3}\tau _{kk} \delta _{ij} = - 2\mu _t \bar S_{ij}$

where $\bar S_{ij}$ is the rate-of-strain tensor for the resolved scale defined by

$\bar S_{ij} = \frac{1}{2}\left( {\frac{{\partial \bar u_i }}{{\partial x_j }} + \frac{{\partial \bar u_j }}{{\partial x_i }}} \right)$

and $\mu _t$ is the subgrid-scale turbulent viscosity.