A spectral element reduced basis method in parametric CFD

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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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Hess, M. W., & Rozza, G. (2019). A spectral element reduced basis method in parametric CFD. In Lecture Notes in Computational Science and Engineering (Vol. 126, pp. 693–701). Springer Verlag. https://doi.org/10.1007/978-3-319-96415-7_64

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