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Wall-adapting local eddy-viscosity (WALE) model

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In the WALE model the eddy viscosity is modeled by:

 \mu_{t} = \rho \Delta _s^2 \frac{(S_{ij}^{d} S_{ij}^{d})^{3/2}}{(\overline{S}_{ij} \overline{S}_{ij})^{5/2} + (S_{ij}^{d} S_{ij}^{d})^{5/4}}

  \Delta _s = C_w V^{1/3}

 S_{ij}^{d} = \frac{1}{2} \left( \overline{g}_{ij}^{2} + \overline{g}_{ji}^{2}  \right) - \frac{1}{3} \delta_{ij} \overline{g}_{kk}^{2}

  \overline{g}_{ij} = \frac{\partial \overline{u_i}}{\partial x_{j}}

 \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)

Where the constant  C_w = 0.325

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