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European Conference on Numerical Mathematics and Advanced Applications

ENUMATH 2017: Numerical Mathematics and Advanced Applications ENUMATH 2017 pp 693–701Cite as

A Spectral Element Reduced Basis Method in Parametric CFD

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 126))

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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Notes

  1. 1.

    See www.nektar.info.

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Acknowledgements

This work was supported by European Union Funding for Research and Innovation through the European Research Council (project H2020 ERC CoG 2015 AROMA-CFD project 681447, P.I. Prof. G. Rozza).

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Authors and Affiliations

  1. SISSA mathLab, International School for Advanced Studies, Trieste, Italy

    Martin W. Hess & Gianluigi Rozza

Authors
  1. Martin W. Hess
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  2. Gianluigi Rozza
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Corresponding author

Correspondence to Martin W. Hess .

Editor information

Editors and Affiliations

  1. University of Bergen, Bergen, Norway

    Florin Adrian Radu

  2. University of Bergen, Bergen, Norway

    Kundan Kumar

  3. University of Bergen, Bergen, Norway

    Inga Berre

  4. University of Bergen, Bergen, Norway

    Jan Martin Nordbotten

  5. Hasselt University, Diepenbeek, Belgium

    Iuliu Sorin Pop

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Hess, M.W., Rozza, G. (2019). A Spectral Element Reduced Basis Method in Parametric CFD. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_64

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