Structural modeling

(Difference between revisions)

Revision as of 22:06, 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

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

@@ Line 2: / Line 2: @@
 :<math>
-\tau_{ij} = \widetilde{\bar{u}_i} \widetilde{\bar{u}_j} - \widetilde{\bar{u}_i \bar{u}_j}
+\tau_{ij} = L_{ij} = \widetilde{\bar{u}_i} \widetilde{\bar{u}_j} - \widetilde{\bar{u}_i \bar{u}_j}
 </math>
@@ Line 9: / Line 9: @@
 :<math>
-\tau_{ij} = \frac{\Delta^2}{12} \frac{\partial \bar{u}_i}{\partial x_{k}} \frac{\partial \bar{u}_j}{\partial x_{k}}
+\tau_{ij} = G_{ij} = \frac{\Delta^2}{12} \frac{\partial \bar{u}_i}{\partial x_{k}} \frac{\partial \bar{u}_j}{\partial x_{k}}
+</math>
+Mixed models, which are based on linear combinations of the eddy-viscosity and structural types
+:<math>
+\tau_{ij} = G_{ij}-2\nu_{sgs} S_{ij}
+</math>
+or
+:<math>
+\tau_{ij} = L_{ij}-2\nu_{sgs} S_{ij}
 </math>