Structural modeling

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Those that use the physical hypothesis of scale similarity

$\tau_{ij} = L_{ij} = \widetilde{\bar{u}_i} \widetilde{\bar{u}_j} - \widetilde{\bar{u}_i \bar{u}_j}$

Those derived by formal series expansions

$\tau_{ij} = G_{ij} = \frac{\Delta^2}{12} \frac{\partial \bar{u}_i}{\partial x_{k}} \frac{\partial \bar{u}_j}{\partial x_{k}}$

Mixed models, which are based on linear combinations of the eddy-viscosity and structural types

$\tau_{ij} = G_{ij}-2\nu_{sgs} S_{ij}$

or

$\tau_{ij} = L_{ij}-2\nu_{sgs} S_{ij}$

Dynamic structure models

$\tau_{ij} = 2k_{sgs} \frac{L_{ij}}{L_{kk}}$

or

$\tau_{ij} = 2k_{sgs} \frac{G_{ij}}{G_{kk}}$