Giere, Swetlana
[Verfasser:in]
;
swetlana.giere@wias-berlin.de
[Mitwirkende:r];
w
[Mitwirkende:r];
Volker John
[Mitwirkende:r];
Gabriel Barrenechea
[Mitwirkende:r]
Numerical and Analytical Aspects of POD-Based Reduced-Order Modeling in Computational Fluid Dynamics ; Numerische und analytische Aspekte der projektionsbasierten ordnungsreduzierten Modellierung im Rahmen der numerischen Strömungsmechanik
Titel:
Numerical and Analytical Aspects of POD-Based Reduced-Order Modeling in Computational Fluid Dynamics ; Numerische und analytische Aspekte der projektionsbasierten ordnungsreduzierten Modellierung im Rahmen der numerischen Strömungsmechanik
Beteiligte:
Giere, Swetlana
[Verfasser:in]
Erschienen:
Freie Universität Berlin: Refubium (FU Berlin), 2016
Anmerkungen:
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Beschreibung:
This thesis studies projection-based reduced-order models (ROMs) in the context of computational fluid dynamics. Proper Orthogonal Decomposition (POD) is employed to compute the reduced-order basis from snapshots, which are assumed to represent the finite element solution of a partial differential equation. All investigations involve either convection-diffusion-reaction equation or the incompressible Navier-Stokes equations. The main contribution of the thesis can be divided into three parts. Firstly, a Streamline-Upwind Petrov-Galerkin reduced-order model (SUPG-ROM) is investigated theoretically and numerically for convection-dominated convection-diffusion- reaction equations. Numerical analysis is utilized to propose the scaling of the stabilization parameter for the SUPG-ROM. Two approaches are used: One based on the underlying finite element discretization and the other one based on the POD truncation. The resulting SUPG-ROMs and the standard Galerkin ROM are studied numerically on several convection-dominated test problems aiming at answering several questions. One of the choices for the stabilization parameter is recommended. Secondly, an alternative approach for the computation of the ROM initial condition is derived for problems, for which the standard approach, that is usually used in the literature, results in the ROM initial condition being polluted by spurious oscillations. The principal idea of the method consists in modifying the conventional ROM initial condition in a post-processing step by a filtering procedure. Numerical studies are performed in order to investigate the influence of the filtered initial condition on the ROM results. With respect to the minimum and maximum values of the ROM solution, which characterize the under- and overshoots, ROM results could be partly significantly improved compared to the results obtained with the standard ROM initial condition. Thirdly, three velocity- pressure reduced-order models (vp-ROMs) for incompressible flows are investigated numerically. One ...