Model order reduction for compressible turbulent flows: hybrid approaches in physics and geometry parametrization

This thesis provides a dissertation about efficient and reliable methods developed to deal with fluid flows problems, discretized by the use of finite volume approaches. In general increasing complexity dynamics are taken into consideration and suited strategies are utilized to overcome arising hurdles. The basic idea behind this work is the construction of reduced order models capable of providing fully consistent solutions with respect to the high fidelity flow fields. Full order solutions are often obtained through the use of segregated solvers, employing slightly modified conservation laws so that they can be decoupled and then solved one at a time. Classical reduction architecture, on the contrary, rely on the Galerkin projection of a complete Navier-Stokes system to be projected all at once, causing a mild discrepancy with the high order solutions. In this thesis three different segregated reduced order algorithms are presented for the resolution of laminar, turbulent and compressible flows respectively. Turbulent flows are frequently approached by the employment of Reynolds averaged Navier-Stokes equations. Since this set of equations is not self closed, an additional modeling is required for some terms related with turbulence. In particular in this thesis we will rely on eddy viscosity models. Since there are a variety of different turbulence models for the approximation of this supplementary viscosity, one of the aims of this work is to provide reduced order models which are independent on this selection. This goal is reached by the application of hybrid methods where Navier-Stokes equations are projected in a standard way while the viscosity field gets approximated by the use of data-driven interpolation methods or by the evaluation of a properly trained neural network. By exploiting the aforementioned expedients it is possible to resolve fluid flow problems characterized by high Reynolds numbers and elevated Mach numbers in a less costly and more general way.