Data-driven turbulence modeling

This chapter provides an introduction to data-driven techniques for the development and calibration of closure models for the Reynolds-Averaged Navier--Stokes (RANS) equations. RANS models are the workhorse for engineering applications of computational fluid dynamics (CFD) and are expected to play an important role for decades to come. However, RANS model inadequacies for complex, non-equilibrium flows and uncertainties in modeling assumptions and calibration data are still a major obstacle to the predictive capability of RANS simulations. In the following, we briefly recall the origin and limitations of RANS models, and then review their shortcomings and uncertainties. Then, we provide an introduction to data-driven approaches to RANS turbulence modeling. The latter can range from simple model parameter inference to sophisticated machine learning techniques. We conclude with some perspectives on current and future research trends.