A Spectral Element Reduced Basis Method in Parametric CFD
This work addresses the need for efficient parametric CFD simulations, but the approach is incremental, combining existing methods (reduced basis and spectral element discretization) with multilevel static condensation.
The paper presents a reduced basis method for parametric CFD, specifically for Navier-Stokes equations in a channel with varying Reynolds numbers, achieving accurate steady-state solutions with a reduced order model that reduces computational time in many-query scenarios.
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 [1] 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.