@article {2020, title = {A spectral element reduced basis method for navier{\textendash}stokes equations with geometric variations}, journal = {Lecture Notes in Computational Science and Engineering}, volume = {134}, year = {2020}, pages = {561-571}, abstract = {

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.

}, doi = {10.1007/978-3-030-39647-3_45}, author = {Martin W. Hess and Annalisa Quaini and Gianluigi Rozza} }