Dynamic inverse modeling and its testing in large-eddy simulations of the mixing layer

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Abstract
We propose new identities for dynamic subgrid modeling in large-eddy simulation involving an explicit filter and its inverse. Exact defiltering of a class of numerical realizations of the top-hat filter is developed. The approach is applied to large-eddy simulation of the temporal mixing layer. Smagorinsky’s model is adopted as base model and the results are compared to the standard dynamic eddy-viscosity model as well as to filtered DNS (direct numerical simulation) results. The difference between the results of the two models for the present application is found to be quite small. This is explained by performing a sensitivity analysis with respect to the dynamic coefficient, which hints towards a “self-restoring” response underlying the observed robustness of the physical predictions. Using DNS data the validity of the assumption that the model coefficients are independent of filter width is tested and found to favor the inverse modeling procedure. The computational effort of the dynamic inverse model is 15% smaller than of the standard dynamic eddy-viscosity model.