A Spectral Element Reduced Basis Method in Parametric CFD

TL;DR

This paper develops a spectral element reduced basis method for parametric CFD, enabling efficient evaluation of steady-state solutions of Navier-Stokes equations across varying Reynolds numbers using a reduced order model.

Contribution

It introduces a reduced basis approach combined with spectral element discretization and multilevel static condensation to improve computational efficiency in parametric CFD simulations.

Findings

Accurate reduced order model for Navier-Stokes in channel flow

Enhanced computational times through multilevel static condensation

Effective parametric solution evaluation across Reynolds numbers

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 [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.