01746nas a2200217 4500008004100000020001400041245012200055210006900177260001600246520096600262653003001228653003001258653004101288653002501329653001801354100002701372700001901399700001701418700002101435856007201456 2021 eng d a0898-122100aA Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier–Stokes problems0 aReduced Order Cut Finite Element method for geometrically parame c2021/08/12/3 a
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.
10aCut Finite Element Method10aNavier–Stokes equations10aParameter–dependent shape geometry10aReduced Order Models10aUnfitted mesh1 aKaratzas, Efthymios, N1 aNonino, Monica1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.sciencedirect.com/science/article/pii/S0898122121002790