A painless intrusive polynomial chaos expansion approach to the CFD analysis and the adjoint-based optimization - Χατζημανωλάκης, Μιχαήλ (Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Μηχανολόγων Μηχανικών. Τομέας Ρευστών. Εργαστήριο Θερμικών Στροβιλομηχανών, 2018)
This diploma thesis proposes a method of Uncertainty Quantification (UQ) for use in aerodynamic analysis and optimization under uncertainties, based on the Polynomial Chaos Expansion (PCE) theory, namely its intrusive variant. Intrusive PCE is considered to be a computationally efficient UQ method; however, it asks for changes in the software used to solve the governing equations. Thus, it is a problem--specific approach. The alternative PCE variant, the non--intrusive one, is easier to implement, as it does not require any software changes but is computationally expensive for problems with many uncertain variables. The method proposed in this diploma thesis is an effort to combine the merits of the intrusive and non--intrusive PCE variants; a general approach is presented that requires very few software changes and is not specific to the equations governing a problem. At the same time, the proposed method is computationally efficient and robust. Though herein developed for the Navier--Stokes equations for compressible fluids, the proposed method can be extended to other disciplines governed by different systems of equations, in a straightforward manner. Over and above, the continuous adjoint formulation of the proposed method is developed, in order to compute the gradients of objective functions in aerodynamic shape optimization problems. Again, emphasis is laid on establishing a general approach that is easy to implement. Applications in aerodynamic analysis and optimization problems, that compare the method to its non--intrusive variant are presented.