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

TitleA Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier–Stokes problems
Publication TypeJournal Article
Year of Publication2021
AuthorsKaratzas, EN, Nonino, M, Ballarin, F, Rozza, G
JournalComputer & Mathematics With Applications
Date Published2021/08/12/
ISBN Number0898-1221
KeywordsCut Finite Element Method; Navier–Stokes equations; Parameter–dependent shape geometry; Reduced Order Models; Unfitted mesh
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], [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.

URLhttps://www.sciencedirect.com/science/article/pii/S0898122121002790
Short TitleComputers & Mathematics with Applications

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