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.

ER - TY - JOUR T1 - A Monolithic and a Partitioned, Reduced Basis Method for Fluid–Structure Interaction Problems JF - Fluids Y1 - 2021 A1 - Monica Nonino A1 - F. Ballarin A1 - Gianluigi Rozza AB -The 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.

VL - 6 UR - https://www.mdpi.com/2311-5521/6/6/229 ER - 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 -