Data enhanced reduced order methods for turbulent flows

This chapter 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. We focus on reduced order models constructed by means of Proper Orthogonal Decomposition with Galerkin approach, enhanced with two different stabilization techniques: (i) the supremizer enrichment approach, (ii) the pressure Poisson equation approach. The available data collected from the offline simulation are used to construct two types of correction/closure terms added in the reduced system: the purely data-driven terms, which model the interaction between the resolved and the unresolved scales, and the physics-based data-driven terms, which introduce the turbulence modeling through the reduced eddy viscosity field. The numerical investigation of the turbulent flow past a circular cylinder at Re=50000 shows that the numerical method here introduced yields significantly more accurate velocity and pressure approximations than the standard reduced order method.