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.

VL - 134 ER - TY - CHAP T1 - A Spectral Element Reduced Basis Method in Parametric CFD T2 - Numerical Mathematics and Advanced Applications - ENUMATH 2017 Y1 - 2019 A1 - Martin W. Hess A1 - Gianluigi Rozza ED - Radu, Florin Adrian ED - Kumar, Kundan ED - Berre, Inga ED - Nordbotten, Jan Martin ED - Pop, Iuliu Sorin AB -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.

JF - Numerical Mathematics and Advanced Applications - ENUMATH 2017 PB - Springer International Publishing VL - 126 UR - https://arxiv.org/abs/1712.06432 ER - TY - JOUR T1 - A spectral element reduced basis method in parametric CFD JF - Lecture Notes in Computational Science and Engineering Y1 - 2019 A1 - Martin W. Hess A1 - Gianluigi Rozza AB -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.

VL - 126 UR - 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 ER -