# Structural modeling

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 Revision as of 22:09, 24 June 2013 (view source)Media777 (Talk | contribs)← Older edit Revision as of 20:03, 25 June 2013 (view source)Media777 (Talk | contribs) Newer edit → Line 1: Line 1: - Those that use the physical hypothesis of scale similarity + 1. Those that use the physical hypothesis of scale similarity :$:[itex] Line 6: Line 6: - Those derived by formal series expansions + 2. Those derived by formal series expansions :[itex] :[itex] Line 12: Line 12:$ [/itex] - Mixed models, which are based on linear combinations of the eddy-viscosity and structural types + 3. Mixed models, which are based on linear combinations of the eddy-viscosity and structural types :$:[itex] Line 22: Line 22:$ [/itex] - Dynamic structure models (non-viscosity version) + 4. Dynamic structure models (non-viscosity version) :$:[itex] \tau_{ij} = 2k_{sgs} \left(\frac{L_{ij}}{L_{kk}}\right) \tau_{ij} = 2k_{sgs} \left(\frac{L_{ij}}{L_{kk}}\right) Line 30: Line 30: \tau_{ij} = 2k_{sgs} \left(\frac{G_{ij}}{G_{kk}}\right) \tau_{ij} = 2k_{sgs} \left(\frac{G_{ij}}{G_{kk}}\right)$ [/itex] + + == 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.}}

## 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

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

## References

• 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..