Title | A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier–Stokes problems |
Publication Type | Journal Article |
Year of Publication | 2021 |
Authors | Karatzas, EN, Nonino, M, Ballarin, F, Rozza, G |
Journal | Computer & Mathematics With Applications |
Date Published | 2021/08/12/ |
ISBN Number | 0898-1221 |
Keywords | Cut 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. |
URL | https://www.sciencedirect.com/science/article/pii/S0898122121002790 |
Short Title | Computers & Mathematics with Applications |
A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier–Stokes problems
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