We focus on steady and unsteady Navier-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 -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.

Karatzas, E. N., Nonino, M., Ballarin, F., Rozza, G., A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier-Stokes problems, <<COMPUTERS & MATHEMATICS WITH APPLICATIONS>>, 2022; (116): 140-160. [doi:10.1016/j.camwa.2021.07.016] [https://hdl.handle.net/10807/219044]

A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier-Stokes problems

Ballarin, Francesco;
2022

Abstract

We focus on steady and unsteady Navier-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 -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.
Inglese
Karatzas, E. N., Nonino, M., Ballarin, F., Rozza, G., A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier-Stokes problems, <<COMPUTERS & MATHEMATICS WITH APPLICATIONS>>, 2022; (116): 140-160. [doi:10.1016/j.camwa.2021.07.016] [https://hdl.handle.net/10807/219044]
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