Data Enhanced Reduced Order Methods for Turbulent Flows

This Thesis focuses on the combination of reduced order models and data-driven techniques applied to the study of turbulent flows in order to improve the pressure and velocity accuracy of standard reduced order methods. The full order model is based on the incompressible Navier-Stokes equations; the reduced order model is constructed by means of Proper Orthogonal Decomposition with Galerkin approach. The available data are used to construct different correction/closure terms, which are added to the reduced equations in order to model the interaction between the resolved and the unresolved scales. Both supremizer enrichment approach and Poisson equation approach have been considered for pressure treatment at the reduced level. The effect of the data-driven correction terms on both resolution systems has been studied and compared. The numerical investigation of the turbulent flow past a circular cylinder at Re=50000 shows that our method yields significantly more accurate velocity and pressure approximations than the standard reduced order method. In particular, the velocity correction introduced in the momentum equation improves both the velocity and pressure fields. In addition, the pressure corrections developed, which --- to the best of my knowledge --- have been introduced here for the first time, further improve the pressure accuracy.