01567nas a2200217   4500008004100000020001400041245011400055210007100169260001600240300001100256520078900267653002401056653003001080653003601110653002401146653004201170100002301212700002101235700002101256856007201277       2022                        eng d  a0045-793000aA POD-Galerkin reduced order model for the Navier–Stokes equations in stream function-vorticity formulation0 aPODGalerkin reduced order model for the Navier–Stokes equations   c2022/06/14/  a1055363 a<p>We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier–Stokes equations in the stream function-vorticity formulation. Unlike previous works, we choose different reduced coefficients for the vorticity and stream function fields. In addition, for parametric studies we use a global POD basis space obtained from a database of time dependent full order snapshots related to sample points in the parameter space. We test the performance of our ROM strategy with the well-known vortex merger benchmark and a more complex case study featuring the geometry of the North Atlantic Ocean. Accuracy and efficiency are assessed for both time reconstruction and physical parametrization.</p>10aGalerkin projection10aNavier–Stokes equations10aProper orthogonal decomposition10aReduced order model10aStream function-vorticity formulation1 aGirfoglio, Michele1 aQuaini, Annalisa1 aRozza, Gianluigi  uhttps://www.sciencedirect.com/science/article/pii/S004579302200164501539nas a2200133   4500008004100000245006800041210006500109490000800174520100800182100002301190700002101213700002101234856015001255       2021                        eng d00aA POD-Galerkin reduced order model for a LES filtering approach0 aPODGalerkin reduced order model for a LES filtering approach0 v4363 a<p>We propose a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for an implementation of the Leray model that combines a two-step algorithm called Evolve-Filter (EF) with a computationally efficient finite volume method. The main novelty of the proposed approach relies in applying spatial filtering both for the collection of the snapshots and in the reduced order model, as well as in considering the pressure field at reduced level. In both steps of the EF algorithm, velocity and pressure fields are approximated by using different POD basis and coefficients. For the reconstruction of the pressures fields, we use a pressure Poisson equation approach. We test our ROM on two benchmark problems: 2D and 3D unsteady flow past a cylinder at Reynolds number 0≤Re≤100. The accuracy of the reduced order model is assessed against results obtained with the full order model. For the 2D case, a parametric study with respect to the filtering radius is also presented.</p>1 aGirfoglio, Michele1 aQuaini, Annalisa1 aRozza, Gianluigi  uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85102138957&doi=10.1016%2fj.jcp.2021.110260&partnerID=40&md5=73115708267e80754f343561c26f4744