The goal of this manuscript is to present a partitioned Model Order Reduction method that is based on a semi-implicit projection scheme to solve multiphysics problems. We implement a Reduced Order Method based on a Proper Orthogonal Decomposition, with the aim of addressing both time-dependent and time-dependent, parametrized Fluid-Structure Interaction problems, where the fluid is incompressible and the structure is thick and two dimensional.

%G eng %0 Journal Article %J Fluids %D 2021 %T A Monolithic and a Partitioned, Reduced Basis Method for Fluid–Structure Interaction Problems %A Monica Nonino %A F. Ballarin %A Gianluigi Rozza %XThe aim of this work is to present an overview about the combination of the Reduced Basis Method (RBM) with two different approaches for Fluid–Structure Interaction (FSI) problems, namely a monolithic and a partitioned approach. We provide the details of implementation of two reduction procedures, and we then apply them to the same test case of interest. We first implement a reduction technique that is based on a monolithic procedure where we solve the fluid and the solid problems all at once. We then present another reduction technique that is based on a partitioned (or segregated) procedure: the fluid and the solid problems are solved separately and then coupled using a fixed point strategy. The toy problem that we consider is based on the Turek–Hron benchmark test case, with a fluid Reynolds number Re=100.

%B Fluids %V 6 %P 229 %G eng %U https://www.mdpi.com/2311-5521/6/6/229 %R 10.3390/fluids6060229 %0 Journal Article %J Computer & Mathematics With Applications %D 2021 %T A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier–Stokes problems %A Efthymios N Karatzas %A Monica Nonino %A F. Ballarin %A Gianluigi Rozza %K Cut Finite Element Method %K Navier–Stokes equations %K Parameter–dependent shape geometry %K Reduced Order Models %K Unfitted mesh %XWe 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.

%B Computer & Mathematics With Applications %8 2021/08/12/ %@ 0898-1221 %G eng %U https://www.sciencedirect.com/science/article/pii/S0898122121002790 %! Computers & Mathematics with Applications