We consider the Navier-Stokes equations in a channel with a narrowing of varying height. The model is discretized with high-order spectral element ansatz functions, resulting in 6372 degrees of freedom. The steady-state snapshot solutions define a reduced order space through a standard POD procedure. The reduced order space allows to accurately and efficiently evaluate the steady-state solutions for different geometries. In particular, we detail different aspects of implementing the reduced order model in combination with a spectral element discretization. It is shown that an expansion in element-wise local degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

%B Lecture Notes in Computational Science and Engineering %V 134 %P 561-571 %G eng %R 10.1007/978-3-030-39647-3_45 %0 Book Section %B Numerical Mathematics and Advanced Applications - ENUMATH 2017 %D 2019 %T A Spectral Element Reduced Basis Method in Parametric CFD %A Martin W. Hess %A Gianluigi Rozza %E Radu, Florin Adrian %E Kumar, Kundan %E Berre, Inga %E Nordbotten, Jan Martin %E Pop, Iuliu Sorin %XWe 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.

%B Numerical Mathematics and Advanced Applications - ENUMATH 2017 %I Springer International Publishing %V 126 %G eng %U https://arxiv.org/abs/1712.06432 %& A Spectral Element Reduced Basis Method in Parametric CFD %R 10.1007/978-3-319-96415-7_64 pages = 693â€“701 %0 Journal Article %J Lecture Notes in Computational Science and Engineering %D 2019 %T A spectral element reduced basis method in parametric CFD %A Martin W. Hess %A Gianluigi Rozza %XWe 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.

%B Lecture Notes in Computational Science and Engineering %V 126 %P 693-701 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85060005503&doi=10.1007%2f978-3-319-96415-7_64&partnerID=40&md5=d1a900db8ddb92cd818d797ec212a4c6 %R 10.1007/978-3-319-96415-7_64