In this work, Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) methodologies are applied to hydroacoustic dataset computed using Large Eddy Simulation (LES) coupled with Ffowcs Williams and Hawkings (FWH) analogy. First, a low-dimensional description of the flow fields is presented with modal decomposition analysis. Sensitivity towards the DMD and POD bases truncation rank is discussed, and extensive dataset is provided to demonstrate the ability of both algorithms to reconstruct the flow fields with all the spatial and temporal frequencies necessary to support accurate noise evaluation. Results show that while DMD is capable to capture finer coherent structures in the wake region for the same amount of employed modes, reconstructed flow fields using POD exhibit smaller magnitudes of global spatiotemporal errors compared with DMD counterparts. Second, a separate set of DMD and POD modes generated using half the snapshots is employed into two data-driven reduced models respectively, based on DMD mid cast and POD with Interpolation (PODI). In that regard, results confirm that the predictive character of both reduced approaches on the flow fields is sufficiently accurate, with a relative superiority of PODI results over DMD ones. This infers that, discrepancies induced due to interpolation errors in PODI is relatively low compared with errors induced by integration and linear regression operations in DMD, for the present setup. Finally, a post processing analysis on the evaluation of FWH acoustic signals utilizing reduced fluid dynamic fields as input demonstrates that both DMD and PODI data-driven reduced models are efficient and sufficiently accurate in predicting acoustic noises.

%B Computers & Fluids %V 216 %P 104819 %G eng %U https://www.sciencedirect.com/science/article/pii/S0045793020303893 %R https://doi.org/10.1016/j.compfluid.2020.104819 %0 Journal Article %J Fluids %D 2021 %T Hybrid Neural Network Reduced Order Modelling for Turbulent Flows with Geometric Parameters %A Matteo Zancanaro %A Markus Mrosek %A Giovanni Stabile %A Carsten Othmer %A Gianluigi Rozza %B Fluids %I MDPI AG %V 6 %P 296 %G eng %U https://doi.org/10.3390/fluids6080296 %R 10.3390/fluids6080296 %0 Generic %D 2021 %T The Neural Network shifted-Proper Orthogonal Decomposition: a Machine Learning Approach for Non-linear Reduction of Hyperbolic Equations %A Davide Papapicco %A Nicola Demo %A Michele Girfoglio %A Giovanni Stabile %A Gianluigi Rozza %G eng %0 Journal Article %J Communications in Computational Physics %D 2021 %T A novel iterative penalty method to enforce boundary conditions in Finite Volume POD-Galerkin reduced order models for fluid dynamics problems %A Kelbij Star %A Giovanni Stabile %A Francesco Belloni %A Gianluigi Rozza %A Joris Degroote %X A Finite-Volume based POD-Galerkin reduced order model is developed for fluid dynamic problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the control function method, whose aim is to obtain homogeneous basis functions for the reduced basis space and the penalty method where the boundary conditions are enforced in the reduced order model using a penalty factor. The penalty method is improved by using an iterative solver for the determination of the penalty factor rather than tuning the factor with a sensitivity analysis or numerical experimentation. The boundary control methods are compared and tested for two cases: the classical lid driven cavity benchmark problem and a Y-junction flow case with two inlet channels and one outlet channel. The results show that the boundaries of the reduced order model can be controlled with the boundary control methods and the same order of accuracy is achieved for the velocity and pressure fields. Finally, the speedup ratio between the reduced order models and the full order model is of the order 1000 for the lid driven cavity case and of the order 100 for the Y-junction test case. %B Communications in Computational Physics %I Global Science Press %V 30 %P 34–66 %G eng %R https://doi.org/10.4208/cicp.OA-2020-0059 %0 Journal Article %J International Journal for Numerical Methods in Engineering %D 2021 %T A numerical approach for heat flux estimation in thin slabs continuous casting molds using data assimilation %A Umberto Emil Morelli %A Patricia Barral %A Peregrina Quintela %A Gianluigi Rozza %A Giovanni Stabile %B International Journal for Numerical Methods in Engineering %I Wiley %V 122 %P 4541–4574 %G eng %U https://doi.org/10.1002/nme.6713 %R 10.1002/nme.6713 %0 Journal Article %J Applied Mathematical Modelling %D 2021 %T A POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step %A Kelbij Star %A Giovanni Stabile %A Gianluigi Rozza %A Joris Degroote %XA 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.

%B Applied Mathematical Modelling %V 89 %P 486-503 %G eng %R 10.1016/j.apm.2020.07.029 %0 Journal Article %J International Journal for Numerical Methods in Fluids %D 2021 %T Reduced order models for the incompressible Navier-Stokes equations on collocated grids using a `discretize-then-project' approach %A Kelbij Star %A Benjamin Sanderse %A Giovanni Stabile %A Gianluigi Rozza %A Joris Degroote %B International Journal for Numerical Methods in Fluids %I Wiley %V 93 %P 2694–2722 %G eng %U https://doi.org/10.1002/fld.4994 %R 10.1002/fld.4994 %0 Conference Paper %B Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018 %D 2020 %T Advances in reduced order methods for parametric industrial problems in computational fluid dynamics %A Gianluigi Rozza %A M.H. Malik %A Nicola Demo %A Marco Tezzele %A Michele Girfoglio %A Giovanni Stabile %A Andrea Mola %XReduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of model order reduction techniques in various engineering and scientific applications including but not limited to mechanical, naval and aeronautical engineering. The focus here is kept limited to computational fluid mechanics and related applications. The advances in the reduced order modeling with proper orthogonal decomposition and reduced basis method are presented as well as a brief discussion of dynamic mode decomposition and also some present advances in the parameter space reduction. Here, an overview of the challenges faced and possible solutions are presented with examples from various problems.

%B Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395686&partnerID=40&md5=fb0b1a3cfdfd35a104db9921bc9be675 %0 Book Section %B Model Order Reduction, Volume 2 Snapshot-Based Methods and Algorithms %D 2020 %T Basic ideas and tools for projection-based model reduction of parametric partial differential equations %A Gianluigi Rozza %A Martin Hess %A Giovanni Stabile %A Marco Tezzele %A F. Ballarin %B Model Order Reduction, Volume 2 Snapshot-Based Methods and Algorithms %I De Gruyter %C Berlin, Boston %P 1 - 47 %@ 9783110671490 %G eng %U https://www.degruyter.com/view/book/9783110671490/10.1515/9783110671490-001.xml %R https://doi.org/10.1515/9783110671490-001 %0 Journal Article %J Computers & Fluids %D 2020 %T Bayesian identification of a projection-based reduced order model for computational fluid dynamics %A Giovanni Stabile %A Bojana Rosic %X In this paper we propose a Bayesian method as a numerical way to correct and stabilise projection-based reduced order models (ROM) in computational fluid dynamics problems. The approach is of hybrid type, and consists of the classical proper orthogonal decomposition driven Galerkin projection of the laminar part of the governing equations, and Bayesian identification of the correction term mimicking both the turbulence model and possible ROM-related instabilities given the full order data. In this manner the classical ROM approach is translated to the parameter identification problem on a set of nonlinear ordinary differential equations. Computationally the inverse problem is solved with the help of the Gauss-Markov-Kalman smoother in both ensemble and square-root polynomial chaos expansion forms. To reduce the dimension of the posterior space, a novel global variance based sensitivity analysis is proposed. %B Computers & Fluids %V 201 %P 104477 %G eng %R https://doi.org/10.1016/j.compfluid.2020.104477 %0 Journal Article %J Journal of Computational Physics %D 2020 %T Data-driven POD-Galerkin reduced order model for turbulent flows %A Saddam Hijazi %A Giovanni Stabile %A Andrea Mola %A Gianluigi Rozza %XIn this work we present a Reduced Order Model which is specifically designed to deal with turbulent flows in a finite volume setting. The method used to build the reduced order model is based on the idea of merging/combining projection-based techniques with data-driven reduction strategies. In particular, the work presents a mixed strategy that exploits a data-driven reduction method to approximate the eddy viscosity solution manifold and a classical POD-Galerkin projection approach for the velocity and the pressure fields, respectively. The newly proposed reduced order model has been validated on benchmark test cases in both steady and unsteady settings with Reynolds up to $Re=O(10^5)$.

%B Journal of Computational Physics %V 416 %P 109513 %G eng %U https://arxiv.org/abs/1907.09909 %R 10.1016/j.jcp.2020.109513 %0 Journal Article %J International Journal for Numerical Methods in Engineering %D 2020 %T Efficient Geometrical parametrization for finite-volume based reduced order methods %A Giovanni Stabile %A Matteo Zancanaro %A Gianluigi Rozza %XIn this work, we present an approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations. On the contrary to what is normally done in the framework of finite element reduced order methods, different geometries are not mapped to a common reference domain: the method relies on basis functions defined on an average deformed configuration and makes use of the Discrete Empirical Interpolation Method (D-EIM) to handle together non-affinity of the parametrization and non-linearities. In the first numerical example, different mesh motion strategies, based on a Laplacian smoothing technique and on a Radial Basis Function approach, are analyzed and compared on a heat transfer problem. Particular attention is devoted to the role of the non-orthogonal correction. In the second numerical example the methodology is tested on a geometrically parametrized incompressible Navier–Stokes problem. In this case, the reduced order model is constructed following the same segregated approach used at the full order level

%B International Journal for Numerical Methods in Engineering %V 121 %P 2655-2682 %G eng %U https://arxiv.org/abs/1901.06373 %R 10.1002/nme.6324 %0 Conference Paper %B Lecture Notes in Computational Science and Engineering %D 2020 %T The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows %A Saddam Hijazi %A Shafqat Ali %A Giovanni Stabile %A F. Ballarin %A Gianluigi Rozza %XWe present in this double contribution two different reduced order strategies for incompressible parameterized Navier-Stokes equations characterized by varying Reynolds numbers. The first strategy deals with low Reynolds number (laminar flow) and is based on a stabilized finite element method during the offline stage followed by a Galerkin projection on reduced basis spaces generated by a greedy algorithm. The second methodology is based on a full order finite volume discretization. The latter methodology will be used for flows with moderate to high Reynolds number characterized by turbulent patterns. For the treatment of the mentioned turbulent flows at the reduced order level, a new POD-Galerkin approach is proposed. The new approach takes into consideration the contribution of the eddy viscosity also during the online stage and is based on the use of interpolation. The two methodologies are tested on classic benchmark test cases.

%B Lecture Notes in Computational Science and Engineering %I Springer International Publishing %C Cham %P 245–264 %@ 978-3-030-30705-9 %G eng %R 10.1007/978-3-030-30705-9_22 %0 Journal Article %J Advanced Modeling and Simulation in Engineering Sciences %D 2020 %T Enhancing CFD predictions in shape design problems by model and parameter space reduction %A Marco Tezzele %A Nicola Demo %A Giovanni Stabile %A Andrea Mola %A Gianluigi Rozza %XIn this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality. The pipeline is based on high-fidelity simulations carried out by the application of finite volume method for turbulent flows, and automatic mesh morphing through radial basis functions interpolation technique. The proposed pipeline is able to save 1/3 of the overall computational resources thanks to the application of DMD. Moreover exploiting DyAS and performing the regression on a lower dimensional space results in the reduction of the relative error in the approximation of the time-varying lift coefficient by a factor 2 with respect to using only the DMD.

%B Advanced Modeling and Simulation in Engineering Sciences %V 7 %G eng %U https://arxiv.org/abs/2001.05237 %N 40 %R https://doi.org/10.1186/s40323-020-00177-y %0 Journal Article %J Computers & Fluids %D 2020 %T A hybrid reduced order method for modelling turbulent heat transfer problems %A Sokratia Georgaka %A Giovanni Stabile %A Kelbij Star %A Gianluigi Rozza %A Michael J. Bluck %XA parametric, hybrid reduced order model approach based on the Proper Orthogonal Decomposition with both Galerkin projection and interpolation based on Radial Basis Functions method is presented. This method is tested against a case of turbulent non-isothermal mixing in a T-junction pipe, a common ow arrangement found in nuclear reactor cooling systems. The reduced order model is derived from the 3D unsteady, incompressible Navier-Stokes equations weakly coupled with the energy equation. For high Reynolds numbers, the eddy viscosity and eddy diffusivity are incorporated into the reduced order model with a Proper Orthogonal Decomposition (nested and standard) with Interpolation (PODI), where the interpolation is performed using Radial Basis Functions. The reduced order solver, obtained using a k-ω SST URANS full order model, is tested against the full order solver in a 3D T-junction pipe with parametric velocity inlet boundary conditions.

%B Computers & Fluids %V 208 %P 104615 %G eng %U https://arxiv.org/abs/1906.08725 %R 10.1016/j.compfluid.2020.104615 %0 Book Section %B Quantification of Uncertainty: Improving Efficiency and Technology: QUIET selected contributions %D 2020 %T Non-intrusive Polynomial Chaos Method Applied to Full-Order and Reduced Problems in Computational Fluid Dynamics: A Comparison and Perspectives %A Saddam Hijazi %A Giovanni Stabile %A Andrea Mola %A Gianluigi Rozza %XIn this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the computational cost associated with each of the simulations required by the non-intrusive UQ algorithm used, we resort to a Reduced Order Model (ROM) based on Proper Orthogonal Decomposition (POD)-Galerkin approach. A first set of results is presented to characterize the accuracy of the POD-Galerkin ROM developed approach with respect to the Full Order Model (FOM) solver (OpenFOAM). A further analysis is then presented to assess how the UQ results are affected by substituting the FOM predictions with the surrogate ROM ones.

%B Quantification of Uncertainty: Improving Efficiency and Technology: QUIET selected contributions %I Springer International Publishing %C Cham %P 217–240 %@ 978-3-030-48721-8 %G eng %U https://doi.org/10.1007/978-3-030-48721-8_10 %R 10.1007/978-3-030-48721-8_10 %0 Journal Article %J Computers and Mathematics with Applications %D 2020 %T POD–Galerkin reduced order methods for combined Navier–Stokes transport equations based on a hybrid FV-FE solver %A S. Busto %A Giovanni Stabile %A Gianluigi Rozza %A M.E. Vázquez-Cendón %XThe 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.

%B Computers and Mathematics with Applications %V 79 %P 256-273 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85068068567&doi=10.1016%2fj.camwa.2019.06.026&partnerID=40&md5=a8dcce1b53b8ee872d174bbc4c20caa3 %R 10.1016/j.camwa.2019.06.026 %0 Conference Paper %B IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018 %D 2020 %T A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries %A Efthymios N Karatzas %A Giovanni Stabile %A Nabib Atallah %A Guglielmo Scovazzi %A Gianluigi Rozza %E Fehr, Jörg %E Bernard Haasdonk %XA model order reduction technique is combined with an embedded boundary finite element method with a POD-Galerkin strategy. The proposed methodology is applied to parametrized heat transfer problems and we rely on a sufficiently refined shape-regular background mesh to account for parametrized geometries. In particular, the employed embedded boundary element method is the Shifted Boundary Method (SBM) recently proposed. This approach is based on the idea of shifting the location of true boundary conditions to a surrogate boundary, with the goal of avoiding cut cells near the boundary of the computational domain. This combination of methodologies has multiple advantages. In the first place, since the Shifted Boundary Method always relies on the same background mesh, there is no need to update the discretized parametric domain. Secondly, we avoid the treatment of cut cell elements, which usually need particular attention. Thirdly, since the whole background mesh is considered in the reduced basis construction, the SBM allows for a smooth transition of the reduced modes across the immersed domain boundary. The performances of the method are verified in two dimensional heat transfer numerical examples.

%B IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018 %I Springer International Publishing %G eng %U https://arxiv.org/abs/1807.07753 %R 10.1007/978-3-030-21013-7_8 %0 Journal Article %J Computer Methods in Applied Mechanics and Engineering %D 2020 %T A reduced-order shifted boundary method for parametrized incompressible Navier–Stokes equations %A Efthymios N Karatzas %A Giovanni Stabile %A Leo Nouveau %A Guglielmo Scovazzi %A Gianluigi Rozza %XWe investigate a projection-based reduced order model of the steady incompressible Navier–Stokes equations for moderate Reynolds numbers. In particular, we construct an “embedded” reduced basis space, by applying proper orthogonal decomposition to the Shifted Boundary Method, a high-fidelity embedded method recently developed. We focus on the geometrical parametrization through level-set geometries, using a fixed Cartesian background geometry and the associated mesh. This approach avoids both remeshing and the development of a reference domain formulation, as typically done in fitted mesh finite element formulations. Two-dimensional computational examples for one and three parameter dimensions are presented to validate the convergence and the efficacy of the proposed approach.

%B Computer Methods in Applied Mechanics and Engineering %V 370 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85087886522&doi=10.1016%2fj.cma.2020.113273&partnerID=40&md5=d864e4808190b682ecb1c8b27cda72d8 %R 10.1016/j.cma.2020.113273 %0 Journal Article %J Communications in Computational Physics %D 2019 %T Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems %A Sokratia Georgaka %A Giovanni Stabile %A Gianluigi Rozza %A Michael J. Bluck %XA 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.

%B Communications in Computational Physics %V 27 %P 1–32 %G eng %U https://arxiv.org/abs/1808.05175 %R 10.4208/cicp.OA-2018-0207 %0 Conference Paper %B International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019 %D 2019 %T POD-Galerkin Reduced Order Model of the Boussinesq Approximation for Buoyancy-Driven Enclosed Flows %A Kelbij Star %A Giovanni Stabile %A Sokratia Georgaka %A Francesco Belloni %A Gianluigi Rozza %A Joris Degroote %B International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019 %@ 9780894487699 %G eng %0 Journal Article %J Computer Methods in Applied Mechanics and Engineering %D 2019 %T A reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow %A Efthymios N Karatzas %A Giovanni Stabile %A Leo Nouveau %A Guglielmo Scovazzi %A Gianluigi Rozza %XWe propose a model order reduction technique integrating the Shifted Boundary Method (SBM) with a POD-Galerkin strategy. This approach allows to deal with complex parametrized domains in an efficient and straightforward way. The impact of the proposed approach is threefold. First, problems involving parametrizations of complex geometrical shapes and/or large domain deformations can be efficiently solved at full-order by means of the SBM. This unfitted boundary method permits to avoid remeshing and the tedious handling of cut cells by introducing an approximate surrogate boundary. Second, the computational effort is reduced by the development of a Reduced Order Model (ROM) technique based on a POD-Galerkin approach. Third, the SBM provides a smooth mapping from the true to the surrogate domain, and for this reason, the stability and performance of the reduced order basis are enhanced. This feature is the net result of the combination of the proposed ROM approach and the SBM. Similarly, the combination of the SBM with a projection-based ROM gives the great advantage of an easy and fast to implement algorithm considering geometrical parametrization with large deformations. The transformation of each geometry to a reference geometry (morphing) is in fact not required. These combined advantages will allow the solution of PDE problems more efficiently. We illustrate the performance of this approach on a number of two-dimensional Stokes flow problems.

%B Computer Methods in Applied Mechanics and Engineering %V 347 %P 568-587 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85060107322&doi=10.1016%2fj.cma.2018.12.040&partnerID=40&md5=1a3234f0cb000c91494d946428f8ebef %R 10.1016/j.cma.2018.12.040 %0 Journal Article %J Advances in Computational Mathematics %D 2019 %T A reduced order variational multiscale approach for turbulent flows %A Giovanni Stabile %A F. Ballarin %A G. Zuccarino %A Gianluigi Rozza %XThe purpose of this work is to present different reduced order model strategies starting from full order simulations stabilized using a residual-based variational multiscale (VMS) approach. The focus is on flows with moderately high Reynolds numbers. The reduced order models (ROMs) presented in this manuscript are based on a POD-Galerkin approach. Two different reduced order models are presented, which differ on the stabilization used during the Galerkin projection. In the first case, the VMS stabilization method is used at both the full order and the reduced order levels. In the second case, the VMS stabilization is used only at the full order level, while the projection of the standard Navier-Stokes equations is performed instead at the reduced order level. The former method is denoted as consistent ROM, while the latter is named non-consistent ROM, in order to underline the different choices made at the two levels. Particular attention is also devoted to the role of inf-sup stabilization by means of supremizers in ROMs based on a VMS formulation. Finally, the developed methods are tested on a numerical benchmark.

%B Advances in Computational Mathematics %V 45 %P 2349-2368 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85068076665&doi=10.1007%2fs10444-019-09712-x&partnerID=40&md5=af0142e6d13bbc2e88c6f31750aef6ad %R 10.1007/s10444-019-09712-x %0 Journal Article %J Computers and Fluids %D 2018 %T Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier–Stokes equations %A Giovanni Stabile %A Gianluigi Rozza %XIn this work a stabilised and reduced Galerkin projection of the incompressible unsteady Navier–Stokes equations for moderate Reynolds number is presented. The full-order model, on which the Galerkin projection is applied, is based on a finite volumes approximation. The reduced basis spaces are constructed with a POD approach. Two different pressure stabilisation strategies are proposed and compared: the former one is based on the supremizer enrichment of the velocity space, and the latter one is based on a pressure Poisson equation approach.

%B Computers and Fluids %V 173 %P 273-284 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85043366603&doi=10.1016%2fj.compfluid.2018.01.035&partnerID=40&md5=c15435ea3b632e55450da19ba2bb6125 %R 10.1016/j.compfluid.2018.01.035 %0 Journal Article %D 2018 %T A novel reduced order model for vortex induced vibrations of long flexible cylinders %A Giovanni Stabile %A Hermann G. Matthies %A Claudio Borri %I Elsevier {BV} %V 156 %P 191–207 %8 may %G eng %U https://doi.org/10.1016/j.oceaneng.2018.02.064 %R 10.1016/j.oceaneng.2018.02.064 %0 Journal Article %J Procedia engineering %D 2017 %T Coupling effects on the dynamic response of moored floating platforms for offshore wind energy plants %A Giusti, Alessandro %A Giovanni Stabile %A Marino, Enzo %A Claudio Borri %B Procedia engineering %I Elsevier %V 199 %P 3194–3199 %G eng %R 10.1016/j.proeng.2017.09.527 %0 Journal Article %J Communications in Applied and Industrial Mathematics %D 2017 %T POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder %A Giovanni Stabile %A Saddam Hijazi %A Andrea Mola %A Stefano Lorenzi %A Gianluigi Rozza %XVortex 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.

%B Communications in Applied and Industrial Mathematics %V 8 %P 210-236 %G eng %R 10.1515/caim-2017-0011 %0 Conference Paper %B Computational Methods in Marine Engineering VI – MARINE2015 %D 2015 %T A Reduced Order Model for the Simulation of Mooring Cable Dynamics %A Giovanni Stabile %A Hermann G. Matthies %A Claudio Borri %B Computational Methods in Marine Engineering VI – MARINE2015 %I Salvatore, Francesco; Broglia, Riccardo; Muscari, Roberto %P 387–400 %G eng %0 Conference Paper %B XIII Conference of the Italian Association for Wind Engineering (In-Vento 2014) %D 2014 %T Coupled dynamic simulations of offshore wind turbines: influence of wave modelling on the fatigue load assesment %A Marino, Enzo %A Lugni, Claudio %A Giovanni Stabile %A Claudio Borri %A Manuel, Lance %B XIII Conference of the Italian Association for Wind Engineering (In-Vento 2014) %G eng %0 Conference Paper %B 9th International Conference on Structural Dynamics (EURODYN 2014) %D 2014 %T Coupled dynamic simulations of offshore wind turbines using linear, weakly and fully nonlinear wave models: the limitations of the second-order wave theory %A Marino, Enzo %A Lugni, Claudio %A Giovanni Stabile %A Claudio Borri %B 9th International Conference on Structural Dynamics (EURODYN 2014) %G eng %0 Book Section %B Research and Applications in Structural Engineering, Mechanics and Computation %D 2013 %T A comparative study about the effects of linear, weakly and fully nonlinear wave models on the dynamic response of offshore wind turbines %A Marino, Enzo %A Giovanni Stabile %A Claudio Borri %A Lugni, Claudio %B Research and Applications in Structural Engineering, Mechanics and Computation %I CRC Press %P 389–390 %G eng