@article {2021, title = {A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier{\textendash}Stokes problems}, journal = {Computer \& Mathematics With Applications}, year = {2021}, month = {2021/08/12/}, abstract = {

We focus on steady and unsteady Navier{\textendash}Stokes flow systems in a reduced-order modeling framework based on Proper Orthogonal Decomposition within a levelset geometry description and discretized by an unfitted mesh Finite Element Method. This work extends the approaches of [1], [2], [3] to nonlinear CutFEM discretization. We construct and investigate a unified and geometry independent reduced basis which overcomes many barriers and complications of the past, that may occur whenever geometrical morphings are taking place. By employing a geometry independent reduced basis, we are able to avoid remeshing and transformation to reference configurations, and we are able to handle complex geometries. This combination of a fixed background mesh in a fixed extended background geometry with reduced order techniques appears beneficial and advantageous in many industrial and engineering applications, which could not be resolved efficiently in the past.

}, keywords = {Cut Finite Element Method, Navier{\textendash}Stokes equations, Parameter{\textendash}dependent shape geometry, Reduced Order Models, Unfitted mesh}, isbn = {0898-1221}, url = {https://www.sciencedirect.com/science/article/pii/S0898122121002790}, author = {Efthymios N Karatzas and Monica Nonino and F. Ballarin and Gianluigi Rozza} }