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

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.

10aGalerkin projection10aNavier–Stokes equations10aProper orthogonal decomposition10aReduced order model10aStream function-vorticity formulation1 aGirfoglio, Michele1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://www.sciencedirect.com/science/article/pii/S004579302200164501169nas 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-and00512nas a2200109 4500008004100000245010500041210006900146100002200215700001700237700002100254856012700275 2022 eng d00aA Proper Orthogonal Decomposition Approach for Parameters Reduction of Single Shot Detector Networks0 aProper Orthogonal Decomposition Approach for Parameters Reductio1 aMeneghetti, Laura1 aDemo, Nicola1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/proper-orthogonal-decomposition-approach-parameters-reduction-single-shot-detector-001539nas 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

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.

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=73115708267e80754f343561c26f474402164nas a2200157 4500008004100000245011600041210006900157300001200226490000700238520155800245100001701803700002201820700002101842700002001863856012301883 2021 eng d00aA POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step0 aPODGalerkin reduced order model of a turbulent convective buoyan a486-5030 v893 a

A Finite-Volume based POD-Galerkin reduced order modeling strategy for steady-state Reynolds averaged Navier–Stokes (RANS) simulation is extended for low-Prandtl number flow. The reduced order model is based on a full order model for which the effects of buoyancy on the flow and heat transfer are characterized by varying the Richardson number. The Reynolds stresses are computed with a linear eddy viscosity model. A single gradient diffusion hypothesis, together with a local correlation for the evaluation of the turbulent Prandtl number, is used to model the turbulent heat fluxes. The contribution of the eddy viscosity and turbulent thermal diffusivity fields are considered in the reduced order model with an interpolation based data-driven method. The reduced order model is tested for buoyancy-aided turbulent liquid sodium flow over a vertical backward-facing step with a uniform heat flux applied on the wall downstream of the step. The wall heat flux is incorporated with a Neumann boundary condition in both the full order model and the reduced order model. The velocity and temperature profiles predicted with the reduced order model for the same and new Richardson numbers inside the range of parameter values are in good agreement with the RANS simulations. Also, the local Stanton number and skin friction distribution at the heated wall are qualitatively well captured. Finally, the reduced order simulations, performed on a single core, are about 105 times faster than the RANS simulations that are performed on eight cores.

1 aStar, Kelbij1 aStabile, Giovanni1 aRozza, Gianluigi1 aDegroote, Joris uhttps://www.math.sissa.it/publication/pod-galerkin-reduced-order-model-turbulent-convective-buoyant-flow-sodium-over-001174nas a2200229 4500008004100000022001400041245003900055210003800094300001100132490000600143520051100149653002600660653002500686653003100711653001100742653004100753100001900794700001700813700001700830700002100847856007600868 2021 eng d a2665-963800aPyGeM: Python Geometrical Morphing0 aPyGeM Python Geometrical Morphing a1000470 v73 aPyGeM is an open source Python package which allows to easily parametrize and deform 3D object described by CAD files or 3D meshes. It implements several morphing techniques such as free form deformation, radial basis function interpolation, and inverse distance weighting. Due to its versatility in dealing with different file formats it is particularly suited for researchers and practitioners both in academia and in industry interested in computational engineering simulations and optimization studies.10aFree form deformation10aGeometrical morphing10aInverse distance weighting10aPython10aRadial basis functions interpolation1 aTezzele, Marco1 aDemo, Nicola1 aMola, Andrea1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pygem-python-geometrical-morphing01633nas a2200121 4500008004100000245014500041210006900186520106800255100002201323700001701345700002101362856012801383 2020 eng d00aPOD-Galerkin Model Order Reduction for Parametrized Nonlinear Time Dependent Optimal Flow Control: an Application to Shallow Water Equations0 aPODGalerkin Model Order Reduction for Parametrized Nonlinear Tim3 a

In this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal with is nonlinear and time dependent: this leads to very time consuming simulations which can be unbearable e.g. in a marine environmental monitoring plan application. Our aim is to show how reduced order modelling could help in studying different configurations and phenomena in a fast way. After building the optimality system, we rely on a POD-Galerkin reduction in order to solve the optimal control problem in a low dimensional reduced space. The presented theoretical framework is actually suited to general nonlinear time dependent optimal control problems. The proposed methodology is finally tested with a numerical experiment: the reduced optimal control problem governed by shallow waters equations reproduces the desired velocity and height profiles faster than the standard model, still remaining accurate.

1 aStrazzullo, Maria1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod-galerkin-model-order-reduction-parametrized-nonlinear-time-dependent-optimal-flow01839nas a2200133 4500008004100000245014300041210007100184490000700255520124500262100002201507700001701529700002101546856013801567 2020 eng d00aPOD–Galerkin Model Order Reduction for Parametrized Time Dependent Linear Quadratic Optimal Control Problems in Saddle Point Formulation0 aPOD–Galerkin Model Order Reduction for Parametrized Time Depende0 v833 a

In this work we deal with parametrized time dependent optimal control problems governed by partial differential equations. We aim at extending the standard saddle point framework of steady constraints to time dependent cases. We provide an analysis of the well-posedness of this formulation both for parametrized scalar parabolic constraint and Stokes governing equations and we propose reduced order methods as an effective strategy to solve them. Indeed, on one hand, parametrized time dependent optimal control is a very powerful mathematical model which is able to describe several physical phenomena, on the other, it requires a huge computational effort. Reduced order methods are a suitable approach to have rapid and accurate simulations. We rely on POD–Galerkin reduction over the physical and geometrical parameters of the optimality system in a space-time formulation. Our theoretical results and our methodology are tested on two examples: a boundary time dependent optimal control for a Graetz flow and a distributed optimal control governed by time dependent Stokes equations. With these two test cases the convenience of the reduced order modelling is further extended to the field of time dependent optimal control.

1 aStrazzullo, Maria1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod%E2%80%93galerkin-model-order-reduction-parametrized-time-dependent-linear-quadratic-optimal01696nas a2200157 4500008004100000245012100041210007300162300001200235490000700247520104800254100001401302700002201316700002101338700002701359856015201386 2020 eng d00aPOD–Galerkin reduced order methods for combined Navier–Stokes transport equations based on a hybrid FV-FE solver0 aPOD–Galerkin reduced order methods for combined Navier–Stokes tr a256-2730 v793 a

The purpose of this work is to introduce a novel POD–Galerkin strategy for the semi-implicit hybrid high order finite volume/finite element solver introduced in Bermúdez et al. (2014) and Busto et al. (2018). The interest is into the incompressible Navier–Stokes equations coupled with an additional transport equation. The full order model employed in this article makes use of staggered meshes. This feature will be conveyed to the reduced order model leading to the definition of reduced basis spaces in both meshes. The reduced order model presented herein accounts for velocity, pressure, and a transport-related variable. The pressure term at both the full order and the reduced order level is reconstructed making use of a projection method. More precisely, a Poisson equation for pressure is considered within the reduced order model. Results are verified against three-dimensional manufactured test cases. Moreover a modified version of the classical cavity test benchmark including the transport of a species is analysed.

1 aBusto, S.1 aStabile, Giovanni1 aRozza, Gianluigi1 aVázquez-Cendón, M.E. uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85068068567&doi=10.1016%2fj.camwa.2019.06.026&partnerID=40&md5=a8dcce1b53b8ee872d174bbc4c20caa301515nas a2200145 4500008004100000245009800041210006900139300001200208490000700220520092500227100002701152700001701179700002101196856015201217 2020 eng d00aProjection-based reduced order models for a cut finite element method in parametrized domains0 aProjectionbased reduced order models for a cut finite element me a833-8510 v793 a

This work presents a reduced order modeling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order models thanks to their capabilities to seamlessly handle large deformations of parametrized domains and in general to handle topological changes. The combination of embedded methods and reduced order models allows us to obtain fast evaluation of parametrized problems, avoiding remeshing as well as the reference domain formulation, often used in the reduced order modeling for boundary fitted finite element formulations. The resulting novel methodology is presented on linear elliptic and Stokes problems, together with several test cases to assess its capability. The role of a proper extension and transport of embedded solutions to a common background is analyzed in detail.

1 aKaratzas, Efthymios, N1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85070900852&doi=10.1016%2fj.camwa.2019.08.003&partnerID=40&md5=2d222ab9c7832955d155655d3c93e1b101425nas a2200169 4500008004100000022001400041245009200055210006900147300001100216490000700227520089500234100002301129700002201152700002101174700002301195856003701218 2019 eng d a1991-712000aParametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems0 aParametric PODGalerkin Model Order Reduction for UnsteadyState H a1–320 v273 a

A parametric reduced order model based on proper orthogonal decom- position with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power plants. Thermal mixing of different temperature coolants in T-junction pipes leads to tem- perature fluctuations and this could potentially cause thermal fatigue in the pipe walls. The novelty of this paper is the development of a parametric ROM considering the three dimensional, incompressible, unsteady Navier-Stokes equations coupled with the heat transport equation in a finite volume approximation. Two different paramet- ric cases are presented in this paper: parametrization of the inlet temperatures and parametrization of the kinematic viscosity. Different training spaces are considered and the results are compared against the full order model.

1 aGeorgaka, Sokratia1 aStabile, Giovanni1 aRozza, Gianluigi1 aBluck, Michael, J. uhttps://arxiv.org/abs/1808.0517500643nas a2200157 4500008004100000020001800041245010400059210006900163100001700232700002200249700002300271700002300294700002100317700002000338856012700358 2019 eng d a978089448769900aPOD-Galerkin Reduced Order Model of the Boussinesq Approximation for Buoyancy-Driven Enclosed Flows0 aPODGalerkin Reduced Order Model of the Boussinesq Approximation 1 aStar, Kelbij1 aStabile, Giovanni1 aGeorgaka, Sokratia1 aBelloni, Francesco1 aRozza, Gianluigi1 aDegroote, Joris uhttps://www.math.sissa.it/publication/pod-galerkin-reduced-order-model-boussinesq-approximation-buoyancy-driven-enclosed-001658nas a2200157 4500008004100000245009100041210006900132300001200201490000800213520106300221100001701284700001701301700002001318700002101338856014101359 2019 eng d00aA POD-selective inverse distance weighting method for fast parametrized shape morphing0 aPODselective inverse distance weighting method for fast parametr a860-8840 v1173 a

Efficient shape morphing techniques play a crucial role in the approximation of partial differential equations defined in parametrized domains, such as for fluid-structure interaction or shape optimization problems. In this paper, we focus on inverse distance weighting (IDW) interpolation techniques, where a reference domain is morphed into a deformed one via the displacement of a set of control points. We aim at reducing the computational burden characterizing a standard IDW approach without significantly compromising the accuracy. To this aim, first we propose an improvement of IDW based on a geometric criterion that automatically selects a subset of the original set of control points. Then, we combine this new approach with a dimensionality reduction technique based on a proper orthogonal decomposition of the set of admissible displacements. This choice further reduces computational costs. We verify the performances of the new IDW techniques on several tests by investigating the trade-off reached in terms of accuracy and efficiency.

1 aBallarin, F.1 aD'Amario, A.1 aPerotto, Simona1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85056396233&doi=10.1002%2fnme.5982&partnerID=40&md5=6aabcbdc9a0da25e36575a0ebfac034f00402nas a2200133 4500008004100000245004500041210004400086300000800130490000600138100001700144700001900161700002100180856006700201 2018 eng d00aPyDMD: Python Dynamic Mode Decomposition0 aPyDMD Python Dynamic Mode Decomposition a5300 v31 aDemo, Nicola1 aTezzele, Marco1 aRozza, Gianluigi uhttps://joss.theoj.org/papers/734e4326edd5062c6e8ee98d03df9e1d01724nas a2200169 4500008004100000245012600041210006900167300001200236490000600248520107700254100002201331700001901353700001701372700002101389700002101410856012301431 2017 eng d00aPOD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder0 aPODGalerkin reduced order methods for CFD using Finite Volume Di a210-2360 v83 a

Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. In this work a Reduced Order Model (ROM) of the incompressible flow around a circular cylinder, built performing a Galerkin projection of the governing equations onto a lower dimensional space is presented. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) for this purpose the projection of the Governing equations (momentum equation and Poisson equation for pressure) is performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework are presented. The accuracy of the reduced order model is assessed against full order results.

1 aStabile, Giovanni1 aHijazi, Saddam1 aMola, Andrea1 aLorenzi, Stefano1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod-galerkin-reduced-order-methods-cfd-using-finite-volume-discretisation-vortex02275nas a2200145 4500008004100000245009200041210006900133260006800202520165800270100002101928700001901949700001701968700002101985856012302006 2016 en d00aPOD-Galerkin Method for Finite Volume Approximation of Navier-Stokes and RANS Equations0 aPODGalerkin Method for Finite Volume Approximation of NavierStok bComputer Methods in Applied Mechanics and Engineering, Elsevier3 aNumerical simulation of fluid flows requires important computational efforts but it is essential in engineering applications. Reduced Order Model (ROM) can be employed whenever fast simulations are required, or in general, whenever a trade-off between computational cost and solution accuracy is a preeminent issue as in process optimization and control. In this work, the efforts have been put to develop a ROM for Computational Fluid Dynamics (CFD) application based on Finite Volume approximation, starting from the results available in turbulent Reynold-Averaged Navier Stokes simulations in order to enlarge the application field of Proper Orthogonal Decomposition – Reduced Order Model (POD – ROM) technique to more industrial fields. The approach is tested in the classic benchmark of the numerical simulation of the 2D lid-driven cavity. In particular, two simulations at Re = 103 and Re = 105 have been considered in order to assess both a laminar and turbulent case. Some quantities have been compared with the Full Order Model in order to assess the performance of the proposed ROM procedure i.e., the kinetic energy of the system and the reconstructed quantities of interest (velocity, pressure and turbulent viscosity). In addition, for the laminar case, the comparison between the ROM steady-state solution and the data available in literature has been presented. The results have turned out to be very satisfactory both for the accuracy and the computational times. As a major outcome, the approach turns out not to be affected by the energy blow up issue characterizing the results obtained by classic turbulent POD-Galerkin methods.1 aLorenzi, Stefano1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod-galerkin-method-finite-volume-approximation-navier-stokes-and-rans-equations01495nas a2200121 4500008004100000245010500041210007100146260001000217520097200227100001701199700002101216856013601237 2016 en d00aPOD–Galerkin monolithic reduced order models for parametrized fluid-structure interaction problems0 aPOD–Galerkin monolithic reduced order models for parametrized fl bWiley3 aIn this paper we propose a monolithic approach for reduced order modelling of parametrized fluid-structure interaction problems based on a proper orthogonal decomposition (POD)–Galerkin method. Parameters of the problem are related to constitutive properties of the fluid or structural problem, or to geometrical parameters related to the domain configuration at the initial time. We provide a detailed description of the parametrized formulation of the multiphysics problem in its components, together with some insights on how to obtain an offline-online efficient computational procedure through the approximation of parametrized nonlinear tensors. Then, we present the monolithic POD–Galerkin method for the online computation of the global structural displacement, fluid velocity and pressure of the coupled problem. Finally, we show some numerical results to highlight the capabilities of the proposed reduced order method and its computational performances1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod%E2%80%93galerkin-monolithic-reduced-order-models-parametrized-fluid-structure-interaction