A Spectral Element Reduced Basis Method in Parametric CFD

Journal: 

Inbook: Numerical Mathematics and Advanced Applications - ENUMATH 2017

Date: 

2019

Authors: 

Hess, Martin W. and Rozza, Gianluigi

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.

 

@inbook{HessRozza2019,
author = {Hess, Martin W. and Rozza, Gianluigi},
editor = {Radu, Florin Adrian and Kumar, Kundan and Berre, Inga and Nordbotten, Jan Martin and Pop, Iuliu Sorin},
year = {2019},
chapter = {A Spectral Element Reduced Basis Method in Parametric CFD},
booktitle = {Numerical Mathematics and Advanced Applications - ENUMATH 2017},
volume = {126},
doi = {10.1007/978-3-319-96415-7_64}
pages = {693--701},
publisher = {Springer International Publishing},
}