# Structural modeling

(Difference between revisions)
 Revision as of 20:03, 25 June 2013 (view source)Media777 (Talk | contribs)← Older edit Revision as of 20:06, 25 June 2013 (view source)Media777 (Talk | contribs) Newer edit → Line 1: Line 1: - 1. Those that use the physical hypothesis of scale similarity + 1. Those that use the physical hypothesis of scale similarity (Bardina et al., 1980) :[itex] :[itex] Line 6: Line 6: - 2. Those derived by formal series expansions + 2. Those derived by formal series expansions (Clark et al., 1979) :[itex] :[itex] Line 32: Line 32: == References == == References == + *{{reference-paper|author=J. Bardina and J. H. Ferziger and W. C. Reynolds|year=1980|title=Improved subgrid scale models for large eddy simulation|rest=AIAA Paper No. 80-1357}} *{{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.}} *{{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 20:06, 25 June 2013

1. Those that use the physical hypothesis of scale similarity (Bardina et al., 1980)

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

2. Those derived by formal series expansions (Clark et al., 1979)

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

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

• J. Bardina and J. H. Ferziger and W. C. Reynolds (1980), "Improved subgrid scale models for large eddy simulation", AIAA Paper No. 80-1357.
• 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..