Complexity reduction in parametric flow problems via nonintrusive proper generalised decomposition in openfoam

Abstract

he present thesis explores the viability of the proper generalised decomposition (PGD) as a tool for parametric studies in a daily industrial environment. Starting from the equations modelling incompressible flows, the separated formulation of the equations, the development of a parametric solver, the implementation in a commercial computational fluid dynamics (CFD) software, OpenFOAM, and a numerical validation are presented. The parametrised Stokes and Oseen flows are used as an initial step to test the applicability of the PGD to flow problems. The rationale for the construc- tion of a separable approximation is described and implemented in OpenFOAM. For the numerical validation of the developed strategy analytical test cases are solved. Then, the parametrised steady laminar incompressible Navier-Stokes equations are considered. The nonintrusive implementation of PGD in OpenFOAM is formulated, focusing on the seamless integration of a reduced order model (ROM) in the framework of an industrially validated CFD software. The proposed strategy exploits classical solution strategies in OpenFOAM to solve the PGD spatial iteration, while the parametric one is solved via a collocation approach. Such nonintrusiveness represents an important step towards the industrialisation of PGD-based approaches. The capabilities of the methodology are tested by applying it to benchmark tests in the literature and solving a parametrised flow control problem in a realistic geometry of interest for the automotive industry. Finally, the PGD framework is extended to turbulent Navier-Stokes problems. The separable form of an industrially popular turbulence model, namely Spalart-Allmaras model, is formulated and a PGD strategy for the construction of a parametric turbulent eddy viscosity is devised. Different im- plementation possibilities in the nonintrusive PGD for parametrised Navier- Stokes equations are explored and the proposed strategy is applied to well-documented turbulent flow control benchmark cases in both two and three dimensions.