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arXiv · 1810.03892

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

Carmen Gräßle·Michael Hinze·Jens Lang·Sebastian Ullmann
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Abstract

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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Carmen Gräßle, Michael Hinze, Jens Lang, Sebastian Ullmann. 2018-10-09. POD model order reduction with space-adapted snapshots for incompressible flows. https://arxiv.org/abs/1810.03892

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