Structural modeling

(Difference between revisions)

Revision as of 22:08, 24 June 2013

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

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

@@ Line 20: / Line 20: @@
 :<math>
 \tau_{ij} = L_{ij}-2\nu_{sgs} S_{ij}
+</math>
+Dynamic structure models
+:<math>
+\tau_{ij} = 2k_{sgs} \frac{L_{ij}}{L_{kk}}
+</math>
+or
+:<math>
+\tau_{ij} = 2k_{sgs} \frac{G_{ij}}{G_{kk}}
 </math>