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POD model order reduction with space-adapted snapshots for incompressible flows

  • We consider model order reduction based on proper orthogonal decomposition (POD) for unsteady incompressible Navier-Stokes problems, assuming that the snapshots are given by spatially adapted finite element solutions. We propose two approaches of deriving stable POD-Galerkin reduced-order models for this context. In the first approach, the pressure term and the continuity equation are eliminated by imposing a weak incompressibility constraint with respect to a pressure reference space. In the second approach, we derive an inf-sup stable velocity-pressure reduced-order model by enriching the velocity reduced space with supremizers computed on a velocity reference space. For problems with inhomogeneous Dirichlet conditions, we show how suitable lifting functions can be obtained from standard adaptive finite element computations. We provide a numerical comparison of the considered methods for a regularized lid-driven cavity problem.

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Metadaten
Author:Carmen Gräßle, Michael Hinze, Jens Lang, Sebastian Ullmann
DOI:https://doi.org/doi:10.1007/s10444-019-09716-7
Document Type:Article
Language:English
Date of Publication (online):2021/02/27
Date of first Publication:2019/09/01
Release Date:2021/02/27
Volume:Advances in Computational Mathematics
Issue:45
First Page:2401
Last Page:2428
Subprojects:B01
Licence (German):License LogoCreative Commons - CC0 1.0 - Universell - Public Domain Dedication