A Data-Driven Nonlinear Eddy Viscosity Model for Sub-Grid Scale Stress Closure

The growing popularity of machine learning in fluid mechanics research has unveiled the massive potential of Big Data in the turbulence modeling community to reduce model uncertainties. The vast amounts of previously unmanageable high-fidelity flow field simulation and experimental data are now being harnessed to systematically inform medium to lower-cost turbulence models, which often outperform current state-of-the-art approaches. Through the extraction of meaningful statistics from a nominal amount of open-source Direct Numerical Simulation data, we have constructed a data-driven framework to model the Sub-Grid Scale Stress (SGS) tensor to close the filtered Navier Stokes equations. Our proposed Nonlinear Eddy Viscosity (NLEV) model imbeds frame, Galilean, time, and dimensional invariance properties directly into the machine learning model by training over an integrity basis of invariant scalars and tensors. Unlike previous approaches, our NLEV model form has been extended to handle anisotropic filter widths. We demonstrate the robustness of our low-cost data-driven framework and show improved predictive performance over classical SGS models for Large Eddy Simulations in both a priori and a posteriori tests.