Structural modeling

(Difference between revisions)

Revision as of 20:03, 25 June 2013

1. Those that use the physical hypothesis of scale similarity

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

2. Those derived by formal series expansions

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

3. 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

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

4. Dynamic structure models (non-viscosity version)

$\tau_{ij} = 2k_{sgs} \left(\frac{L_{ij}}{L_{kk}}\right)$

or

$\tau_{ij} = 2k_{sgs} \left(\frac{G_{ij}}{G_{kk}}\right)$

R. A. Clark and J. H. Ferziger and W. C. Reynolds (1979), "Evaluation of subgrid-scale models using an accurately simulated turbulent flow", J. Fluid Mech..

@@ Line 1: / Line 1: @@
-Those that use the physical hypothesis of scale similarity
+. Those that use the physical hypothesis of scale similarity
 :<math>
@@ Line 6: / Line 6: @@
-Those derived by formal series expansions
+. Those derived by formal series expansions
 :<math>
@@ Line 12: / Line 12: @@
 </math>
-Mixed models, which are based on linear combinations of the eddy-viscosity and structural types
+. Mixed models, which are based on linear combinations of the eddy-viscosity and structural types
 :<math>
@@ Line 22: / Line 22: @@
 </math>
-Dynamic structure models (non-viscosity version)
+. Dynamic structure models (non-viscosity version)
 :<math>
 \tau_{ij} = 2k_{sgs} \left(\frac{L_{ij}}{L_{kk}}\right)
@@ Line 30: / Line 30: @@
 \tau_{ij} = 2k_{sgs} \left(\frac{G_{ij}}{G_{kk}}\right)
 </math>
+== References ==
+*{{reference-paper|author=R. A. Clark and J. H. Ferziger and W. C. Reynolds|year=1979|title=Evaluation of subgrid-scale models using an accurately simulated turbulent flow|rest=J. Fluid Mech.}}