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We investigate a hierarchy of eddy-viscosity terms in POD Galerkin models toaccount for a large fraction of unresolved fluctuation energy. These Galerkinmethods are applied to Large Eddy Simulation data for a flow around thevehicle-like bluff body call Ahmed body. This flow has three challenges for anyreduced-order model: a high Reynolds number, coherent structures with broadbandfrequency dynamics, and meta-stable asymmetric base flow states. The Galerkinmodels are found to be most accurate with modal eddy viscosities as proposed byRempfer & Fasel (1994). Robustness of the model solution with respect toinitial conditions, eddy viscosity values and model order is only achieved forstate-dependent eddy viscosities as proposed by Noack, Morzynski & Tadmor(2011). Only the POD system with state-dependent modal eddy viscosities canaddress all challenges of the flow characteristics. All parameters areanalytically derived from the Navier-Stokes based balance equations with theavailable data. We arrive at simple general guidelines for robust and accuratePOD models which can be expected to hold for a large class of turbulent flows.

On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high Reynolds number flow over an Ahmed body