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PDE Apps for Acoustic Ducts: A Parametrized Component-to-System Model-Order-Reduction Approach Read chapter Read first chapter

2019 | OriginalPaper | Chapter

A Spectral Element Reduced Basis Method in Parametric CFD

Authors : Martin W. Hess, Gianluigi Rozza

Published in: Numerical Mathematics and Advanced Applications ENUMATH 2017

Publisher: Springer International Publishing

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Abstract

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 solutions 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 (Karniadakis and Sherwin, Spectral/hp element methods for computational fluid dynamics, 2nd edn. Oxford University Press, Oxford, 2005) 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.

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previous chapter Parametric Model Reduction via Interpolating Orthonormal Bases
next chapter POD for Optimal Control of the Cahn-Hilliard System Using Spatially Adapted Snapshots
Footnotes
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Metadata
Title
A Spectral Element Reduced Basis Method in Parametric CFD
Authors
Martin W. Hess
Gianluigi Rozza
Copyright Year
2019
Book
Numerical Mathematics and Advanced Applications ENUMATH 2017

Print ISBN: 978-3-319-96414-0

Electronic ISBN: 978-3-319-96415-7

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-96415-7_64

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