TY - JOUR T1 - A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier–Stokes problems JF - Computer & Mathematics With Applications Y1 - 2021 A1 - Efthymios N Karatzas A1 - Monica Nonino A1 - F. Ballarin A1 - Gianluigi Rozza KW - Cut Finite Element Method KW - Navier–Stokes equations KW - Parameter–dependent shape geometry KW - Reduced Order Models KW - Unfitted mesh AB -

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.

SN - 0898-1221 UR - https://www.sciencedirect.com/science/article/pii/S0898122121002790 JO - Computers & Mathematics with Applications ER -