Massimo Germano contributed a relation between unresolved stresses at different filtering scales that became a basis for the dynamic subgrid-scale model. A participant account of the 1990 Center for Turbulence Research summer program credits his identity with initiating the collaboration with Ugo Piomelli, Parviz Moin and William H. Cabot.[ref]
Thirty years of Dynamic Modeling by Ugo Piomelli and Parviz Moin. Page3: Germano's identity and the collaboration
The physical issue is that filtering a product differs from multiplying filtered quantities. In large eddy simulation, this creates subgrid-scale stress. Using a second filter exposes a relationship between stresses at two scales; an exact algebraic relation then helps constrain an approximate physical closure.[ref]
A dynamic subgrid-scale eddy viscosity model by Massimo Germano and others (1990). Section2: grid and test filters, stress identity and dynamic coefficient
For an original scalar illustration, average four equally weighted velocities . Their overall mean square is , and the square of their mean is , giving variance . Group them as and . The group means are , whose variance is ; each group's internal variance is . Thus total variance separates variation between coarse groups from variation within them. An identity among averages is exact even when a model for missing variations is approximate.
The dynamic model's success therefore does not turn every closure assumption into an identity. Separating those two ingredients makes the contribution reusable: exact relations provide constraints, while predictions still require tests against adequately resolved observations or computations.
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