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Multiscale spectral viscosity discretization methods for the Navier-Stokes equations

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Max Gunzburger

Florida State University

The objective of turbulence modeling is to capture the large scale structures in the flow without explicitly resolving the small scales structures that, over time, influence the large-scale structures. This is generally accomplished by adding regularization terms to the Navier-Stokes equations. We examine spectral viscosity models in which only the high-frequency spectral modes are regularized. The objective is to retain the large-scale dynamics while modeling turbulent fluctuationsa ccurately. We show that, unlike for the Navier-Stokes equations, there is no existence-uniqueness gap for the spectral viscosity
models. Spectral regularization introduces a host of parameters to the model. We rigorously justify effective choices of parameters.