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Structural modeling

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:<math>
:<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>
</math>
Line 9: Line 9:
:<math>
:<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>
</math>

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}
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