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},
}