Large-Eddy Simulation Models with Analytically-Derived Dynamic Coefficients Using Stokes Flow Regularization

Large eddy simulations (LES) are commonly used for turbulent flows to save on computational cost compared to DNS that requires resolving the Kolmogorov scale. A common approach to LES modeling is obtained from the filtering theory. For example, popular "dynamic" models use the Germano identity to determine model coefficients on the fly with a test filter calculation. In this work, the LES theory is re-imagined using Stokes Flow Regularization (SFR), a physics-inspired coarsening procedure. As a first demonstration of SFR-based LES modeling, an alternative to the Germano identity is introduced which allows for a dynamic and local determination of model coefficients via pen-and-paper analysis, without the need for a test filter. This new dynamic procedure will be demonstrated to generate equilibrium and non-equilibrium eddy viscosity and mixed model closures for the residual stress tensor. The models are tested a posteriori using DNS data to demonstrate the efficacy of the SFR-based dynamic procedure and the range of performance based on the assumed model form and grid resolution.