00561nas a2200121 4500008004100000245011500041210007100156100001700227700001800244700001900262700002100281856013700302 2024 eng d00aOptimisation–Based Coupling of Finite Element Model and Reduced Order Model for Computational Fluid Dynamics0 aOptimisation–Based Coupling of Finite Element Model and Reduced 1 aPrusak, Ivan1 aTorlo, Davide1 aNonino, Monica1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/optimisation%E2%80%93based-coupling-finite-element-model-and-reduced-order-model-computational00563nas a2200121 4500008004100000245013000041210006900171100001700240700001800257700001900275700002100294856012600315 2023 eng d00aAn optimisation-based domain-decomposition reduced order model for parameter-dependent non-stationary fluid dynamics problems0 aoptimisationbased domaindecomposition reduced order model for pa1 aPrusak, Ivan1 aTorlo, Davide1 aNonino, Monica1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/optimisation-based-domain-decomposition-reduced-order-model-parameter-dependent-non02085nas a2200253 4500008004100000020001400041245011800055210007300173260001600246300001400262490000800276520123400284653003301518653002501551653002001576653003601596653002801632100001701660700001901677700001801696700002401714700002101738856007201759 2023 eng d a0898-122100aAn optimisation–based domain–decomposition reduced order model for the incompressible Navier-Stokes equations0 aoptimisation–based domain–decomposition reduced order model for  c2023/12/01/ a172 - 1890 v1513 a

The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical models: domain–decomposition (DD) methods and reduced–order modelling (ROM). In particular, we consider an optimisation–based domain–decomposition algorithm for the parameter–dependent stationary incompressible Navier–Stokes equations. Firstly, the problem is described on the subdomains coupled at the interface and solved through an optimal control problem, which leads to the complete separation of the subdomain problems in the DD method. On top of that, a reduced model for the obtained optimal–control problem is built; the procedure is based on the Proper Orthogonal Decomposition technique and a further Galerkin projection. The presented methodology is tested on two fluid dynamics benchmarks: the stationary backward–facing step and lid-driven cavity flow. The numerical tests show a significant reduction of the computational costs in terms of both the problem dimensions and the number of optimisation iterations in the domain–decomposition algorithm.

10aComputational fluid dynamics10aDomain decomposition10aOptimal control10aProper orthogonal decomposition10aReduced order modelling1 aPrusak, Ivan1 aNonino, Monica1 aTorlo, Davide1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.sciencedirect.com/science/article/pii/S089812212300424801169nas a2200133 4500008004100000245014700041210007100188520056100259100001900820700002400839700002100863700001600884856013500900 2022 eng d00aProjection based semi–implicit partitioned Reduced Basis Method for non parametrized and parametrized Fluid–Structure Interaction problems0 aProjection based semi–implicit partitioned Reduced Basis Method 3 a

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.

1 aNonino, Monica1 aBallarin, Francesco1 aRozza, Gianluigi1 aMaday, Yvon uhttps://www.math.sissa.it/publication/projection-based-semi%E2%80%93implicit-partitioned-reduced-basis-method-non-parametrized-and01334nas a2200157 4500008004100000022001400041245010000055210007100155300000800226490000600234520083600240100001901076700001701095700002101112856004301133 2021 eng d a2311-552100aA Monolithic and a Partitioned, Reduced Basis Method for Fluid–Structure Interaction Problems0 aMonolithic and a Partitioned Reduced Basis Method for Fluid–Stru a2290 v63 a

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.

1 aNonino, Monica1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.mdpi.com/2311-5521/6/6/22901746nas 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