Reduced order methods for laminar and turbulent flows in a finite volume setting: projection-based methods and data-driven techniques

This dissertation presents a family of Reduced Order Models (ROMs) which is specifically designed to deal with both laminar and turbulent flows in a finite volume full order setting. Several aspects associated with the reduction of the incompressible Navier–Stokes equations have been investigated. The first of them is related to the need of an accurate reduced pressure reconstruction. This issue has been studied with the help of two main approaches which consist in the use of the Pressure Poisson Equation (PPE) at the reduced order level and also the employment of the supremizer stabilization method. A second aspect is connected with the enforcement of non-homogeneous Dirichlet boundary conditions at the inlet boundary at the reduced order level. The solutions to address this aspect include two methods, namely, the lifting function method and the penalty method. Different solutions for the treatment of turbulence at the reduced order level have been proposed. We have developed a unified reduction approach which is capable of dealing with turbulent flows based on the Reynolds Averaged Navier–Stokes (RANS) equations complemented by any Eddy Viscosity Model (EVM). The turbulent ROM developed is versatile in the sense that it may be applied on the FOM solutions obtained by different turbulent closure models or EVMs. This is made possible thanks to the formulation of the ROM which merges projection-based techniques with data-driven reduction strategies. In particular, the work presents a mixed strategy that exploits a data-driven reduction method to approximate the eddy viscosity solution manifold and a classical POD-Galerkin projection approach for the velocity and the pressure fields. The newly proposed turbulent ROM has been validated on benchmark test cases in both steady and unsteady settings with Reynolds up to Re 10 to 5.