A Data-Driven k-Equation-Based Framework for Modeling Turbulence Using Sparse Regression

A novel framework for augmenting turbulence models with machine learning techniques is introduced. In particular, a one-equation linear eddy viscosity model is formulated by solving a transport equation for the turbulent kinetic energy, which provides a velocity scale, and training a regression function for a turbulent length scale. Sparsity-promoting regression is utilized to obtain interpretable, algebraic functions for the turbulent length scale directly from data. Additionally, a model in which a second length scale is trained to represent turbulent dissipation is also considered. The models are trained and tested on a set of parametrized periodic hill flows which exhibit massive separation. Model consistency is enforced by using a CFD-driven iterative process. CFD-driven cross-validation demonstrates that the proposed framework is capable of learning models which exhibit improved performance compared to a standard eddy viscosity model in geometries not included in their training set. In addition, the learned models are better able to capture the extent of the separated regions in three of the four testing cases. The need in future work to establish mesh independence of these preliminary results is highlighted.