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We consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14 259 degrees of freedom. The steady-state snapshot solu- tions define a reduced order space, which allows to accurately evaluate the steady- state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.
@inbook{HessRozza2017, author = {Hess, Martin W. and Rozza, Gianluigi}, year = {2018}, chapter = {A Spectral Element Reduced Basis Method in Parametric CFD}, booktitle = {Numerical Mathematics and Advanced Applications - ENUMATH 2017}, volume = {126}, publisher = {Springer}, preprint = {https://arxiv.org/abs/1712.06432}, }