Pseudo-DNS modeling of turbulent flows Development of Reduced Order Modeling strategies for simulations at microscale level

This thesis is dedicated to the enhancement of the Pseudo-DNS numerical model for the simulations of unstable flows. In essence, it is a multiscale method with two levels, coarse and fine, which allows to resolve flows with instabilities/turbulence efficiently. This can be done by establishing a database containing some flow variables obtained in the fine scale simulations, and then using them in the coarse scale ones. The fine scale simulations can be pre-computed offline on a Representative Volume Element (RVE) with the application of the Main-Secondary Multi-Point Constraint method (MPC) for the periodicity imposition. The main objective of this thesis is to develop a Reduced Order Model (ROM) for the fine scale simulations to speed up these computations while preserving the reliability of the solution. The first step is dedicated to collecting data from the Full Order Model (FOM) of the fine problem, with different parameters, to study the possibilities of reduction of the model. Then a ROM approach specifically tailored for the problem at hand is defined and, in particular, the application of the MPC to the reduced model is approached. Several strategies are developed at the theoretical level and subsequently tested on a simplified problem. While some of them are inspired by existing literature, a novel approach is also proposed.