@article {2020, title = {A spectral element reduced basis method for navier{\textendash}stokes equations with geometric variations}, journal = {Lecture Notes in Computational Science and Engineering}, volume = {134}, year = {2020}, pages = {561-571}, abstract = {

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.

}, doi = {10.1007/978-3-030-39647-3_45}, author = {Martin W. Hess and Annalisa Quaini and Gianluigi Rozza} } @inbook {2019, title = {A Spectral Element Reduced Basis Method in Parametric CFD}, booktitle = {Numerical Mathematics and Advanced Applications - ENUMATH 2017}, volume = {126}, year = {2019}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, chapter = {A Spectral Element Reduced Basis Method in Parametric CFD}, 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 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.

}, doi = {10.1007/978-3-319-96415-7_64 pages = 693{\textendash}701}, url = {https://arxiv.org/abs/1712.06432}, author = {Martin W. Hess and Gianluigi Rozza}, editor = {Radu, Florin Adrian and Kumar, Kundan and Berre, Inga and Nordbotten, Jan Martin and Pop, Iuliu Sorin} } @article {2019, title = {A spectral element reduced basis method in parametric CFD}, journal = {Lecture Notes in Computational Science and Engineering}, volume = {126}, year = {2019}, pages = {693-701}, 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.

}, doi = {10.1007/978-3-319-96415-7_64}, url = {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}, author = {Martin W. Hess and Gianluigi Rozza} }