Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate the Kolmogorov N−width decay thereby obtaining smaller linear subspaces with improved accuracy. These methods however must rely on the knowledge of the characteristic speeds in phase space of the solution, limiting their range of applicability to problems with explicit functional form for the advection field. In this work we approach the problem of automatically detecting the correct pre-processing transformation in a statistical learning framework by implementing a deep-learning architecture. The purely data-driven method allowed us to generalise the existing approaches of linear subspace manipulation to non-linear hyperbolic problems with unknown advection fields. The proposed algorithm has been validated against simple test cases to benchmark its performances and later successfully applied to a multiphase simulation. © 2022 Elsevier B.V.

10aAdvection10aComputational complexity10aDeep neural network10aDeep neural networks10aLinear subspace10aMultiphase simulations10aNon linear10aNonlinear hyperbolic equation10aPartial differential equations10aPhase space methods10aPre-processing10aPrincipal component analysis10areduced order modeling10aReduced order modelling10aReduced-order model10aShifted-POD1 aPapapicco, Davide1 aDemo, Nicola1 aGirfoglio, Michele1 aStabile, Giovanni1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85124488633&doi=10.1016%2fj.cma.2022.114687&partnerID=40&md5=12f82dcaba04c4a7c44f8e5b2010199702606nas a2200265 4500008004100000022001400041245009300055210006900148300001100217490000800228520174600236653003101982653003302013653001902046653002602065653002002091653003602111100002102147700002102168700001902189700002202208700001702230700002102247856007202268 2021 eng d a0045-793000aOn the comparison of LES data-driven reduced order approaches for hydroacoustic analysis0 acomparison of LES datadriven reduced order approaches for hydroa a1048190 v2163 aIn 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.

10aDynamic mode decomposition10aFfowcs Williams and Hawkings10aHydroacoustics10aLarge eddy simulation10aModel reduction10aProper orthogonal decomposition1 aGadalla, Mahmoud1 aCianferra, Marta1 aTezzele, Marco1 aStabile, Giovanni1 aMola, Andrea1 aRozza, Gianluigi uhttps://www.sciencedirect.com/science/article/pii/S004579302030389300548nas a2200169 4500008004100000245009600041210006900137260001200206300000800218490000600226100002200232700001900254700002200273700002000295700002100315856004200336 2021 eng d00aHybrid Neural Network Reduced Order Modelling for Turbulent Flows with Geometric Parameters0 aHybrid Neural Network Reduced Order Modelling for Turbulent Flow bMDPI AG a2960 v61 aZancanaro, Matteo1 aMrosek, Markus1 aStabile, Giovanni1 aOthmer, Carsten1 aRozza, Gianluigi uhttps://doi.org/10.3390/fluids608029600617nas a2200133 4500008004100000245014100041210006900182100002200251700001700273700002300290700002200313700002100335856012700356 2021 eng d00aThe Neural Network shifted-Proper Orthogonal Decomposition: a Machine Learning Approach for Non-linear Reduction of Hyperbolic Equations0 aNeural Network shiftedProper Orthogonal Decomposition a Machine 1 aPapapicco, Davide1 aDemo, Nicola1 aGirfoglio, Michele1 aStabile, Giovanni1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/neural-network-shifted-proper-orthogonal-decomposition-machine-learning-approach-non01919nas a2200181 4500008004100000245014700041210006900188260002500257300001200282490000700294520120500301100001701506700002201523700002301545700002101568700002001589856012801609 2021 eng d00aA novel iterative penalty method to enforce boundary conditions in Finite Volume POD-Galerkin reduced order models for fluid dynamics problems0 anovel iterative penalty method to enforce boundary conditions in bGlobal Science Press a34–660 v303 aA 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.1 aStar, Kelbij1 aStabile, Giovanni1 aBelloni, Francesco1 aRozza, Gianluigi1 aDegroote, Joris uhttps://www.math.sissa.it/publication/novel-iterative-penalty-method-enforce-boundary-conditions-finite-volume-pod-galerkin00579nas a2200169 4500008004100000245011300041210006900154260001000223300001600233490000800249100002700257700002100284700002400305700002100329700002200350856003700372 2021 eng d00aA numerical approach for heat flux estimation in thin slabs continuous casting molds using data assimilation0 anumerical approach for heat flux estimation in thin slabs contin bWiley a4541–45740 v1221 aMorelli, Umberto, Emil1 aBarral, Patricia1 aQuintela, Peregrina1 aRozza, Gianluigi1 aStabile, Giovanni uhttps://doi.org/10.1002/nme.671302164nas 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 aA 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-000588nas a2200169 4500008004100000245013500041210006900176260001000245300001600255490000700271100001700278700002300295700002200318700002100340700002000361856003700381 2021 eng d00aReduced order models for the incompressible Navier-Stokes equations on collocated grids using a `discretize-then-project' approach0 aReduced order models for the incompressible NavierStokes equatio bWiley a2694–27220 v931 aStar, Kelbij1 aSanderse, Benjamin1 aStabile, Giovanni1 aRozza, Gianluigi1 aDegroote, Joris uhttps://doi.org/10.1002/fld.499401497nas a2200169 4500008004100000245010500041210006900146520085900215100002101074700001601095700001701111700001901128700002301147700002201170700001701192856011801209 2020 eng d00aAdvances in reduced order methods for parametric industrial problems in computational fluid dynamics0 aAdvances in reduced order methods for parametric industrial prob3 aReduced 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.

1 aRozza, Gianluigi1 aMalik, M.H.1 aDemo, Nicola1 aTezzele, Marco1 aGirfoglio, Michele1 aStabile, Giovanni1 aMola, Andrea uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395686&partnerID=40&md5=fb0b1a3cfdfd35a104db9921bc9be67500632nas a2200169 4500008004100000020001800041245010800059210006900167260003100236300001100267100002100278700002100299700002200320700001900342700001700361856008400378 2020 eng d a978311067149000aBasic ideas and tools for projection-based model reduction of parametric partial differential equations0 aBasic ideas and tools for projectionbased model reduction of par aBerlin, BostonbDe Gruyter a1 - 471 aRozza, Gianluigi1 aHess, Martin, W.1 aStabile, Giovanni1 aTezzele, Marco1 aBallarin, F. uhttps://www.degruyter.com/view/book/9783110671490/10.1515/9783110671490-001.xml01480nas a2200145 4500008004100000022001400041245010300055210006900158300001100227490000800238520092500246100002201171700001801193856012301211 2020 eng d a0045-793000aBayesian identification of a projection-based reduced order model for computational fluid dynamics0 aBayesian identification of a projectionbased reduced order model a1044770 v2013 aIn 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.1 aStabile, Giovanni1 aRosic, Bojana uhttps://www.math.sissa.it/publication/bayesian-identification-projection-based-reduced-order-model-computational-fluid01178nas a2200157 4500008004100000245006900041210006700110300001100177490000800188520070800196100001900904700002200923700001700945700002100962856003700983 2020 eng d00aData-driven POD-Galerkin reduced order model for turbulent flows0 aDatadriven PODGalerkin reduced order model for turbulent flows a1095130 v4163 aIn 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 $Re=O(10^5)$.

1 aHijazi, Saddam1 aStabile, Giovanni1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/1907.0990901597nas a2200145 4500008004100000245008800041210006900129300001400198490000800212520112900220100002201349700002201371700002101393856003701414 2020 eng d00aEfficient Geometrical parametrization for finite-volume based reduced order methods0 aEfficient Geometrical parametrization for finitevolume based red a2655-26820 v1213 aIn 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

1 aStabile, Giovanni1 aZancanaro, Matteo1 aRozza, Gianluigi uhttps://arxiv.org/abs/1901.0637301671nas a2200181 4500008004100000020002200041245012000063210006900183260004400252300001400296520095800310100001901268700001701287700002201304700001701326700002101343856012501364 2020 eng d a978-3-030-30705-900aThe Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows0 aEffort of Increasing Reynolds Number in ProjectionBased Reduced aChambSpringer International Publishing a245–2643 aWe 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.

1 aHijazi, Saddam1 aAli, Shafqat1 aStabile, Giovanni1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/effort-increasing-reynolds-number-projection-based-reduced-order-methods-laminar-001480nas a2200157 4500008004100000245009400041210006900135490000600204520097900210100001901189700001701208700002201225700001701247700002101264856003701285 2020 eng d00aEnhancing CFD predictions in shape design problems by model and parameter space reduction0 aEnhancing CFD predictions in shape design problems by model and 0 v73 aIn 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.

1 aTezzele, Marco1 aDemo, Nicola1 aStabile, Giovanni1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/2001.0523701487nas a2200169 4500008004100000245008100041210006900122300001100191490000800202520096400210100002301174700002201197700001701219700002101236700002301257856003701280 2020 eng d00aA hybrid reduced order method for modelling turbulent heat transfer problems0 ahybrid reduced order method for modelling turbulent heat transfe a1046150 v2083 aA 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.

1 aGeorgaka, Sokratia1 aStabile, Giovanni1 aStar, Kelbij1 aRozza, Gianluigi1 aBluck, Michael, J. uhttps://arxiv.org/abs/1906.0872501405nas a2200169 4500008004100000020002200041245014800063210006900211260004400280300001400324520076900338100001901107700002201126700001701148700002101165856004901186 2020 eng d a978-3-030-48721-800aNon-intrusive Polynomial Chaos Method Applied to Full-Order and Reduced Problems in Computational Fluid Dynamics: A Comparison and Perspectives0 aNonintrusive Polynomial Chaos Method Applied to FullOrder and Re aChambSpringer International Publishing a217–2403 aIn 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.

1 aHijazi, Saddam1 aStabile, Giovanni1 aMola, Andrea1 aRozza, Gianluigi uhttps://doi.org/10.1007/978-3-030-48721-8_1001696nas 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 aThe 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=a8dcce1b53b8ee872d174bbc4c20caa301868nas a2200181 4500008004100000245012100041210006900162260003800231520122900269100002701498700002201525700001901547700002401566700002101590700001601611700002201627856003701649 2020 eng d00aA Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries0 aReduced Order Approach for the Embedded Shifted Boundary FEM and bSpringer International Publishing3 aA 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.

1 aKaratzas, Efthymios, N1 aStabile, Giovanni1 aAtallah, Nabib1 aScovazzi, Guglielmo1 aRozza, Gianluigi1 aFehr, Jörg1 aHaasdonk, Bernard uhttps://arxiv.org/abs/1807.0775301444nas a2200157 4500008004100000245010200041210006900143490000800212520080500220100002701025700002201052700001701074700002401091700002101115856015001136 2020 eng d00aA reduced-order shifted boundary method for parametrized incompressible Navier–Stokes equations0 areducedorder shifted boundary method for parametrized incompress0 v3703 aWe 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.

1 aKaratzas, Efthymios, N1 aStabile, Giovanni1 aNouveau, Leo1 aScovazzi, Guglielmo1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85087886522&doi=10.1016%2fj.cma.2020.113273&partnerID=40&md5=d864e4808190b682ecb1c8b27cda72d801425nas 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 aA 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-002191nas a2200169 4500008004100000245015000041210006900191300001200260490000800272520148000280100002701760700002201787700001701809700002401826700002101850856015001871 2019 eng d00aA reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow0 areduced basis approach for PDEs on parametrized geometries based a568-5870 v3473 aWe 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.

1 aKaratzas, Efthymios, N1 aStabile, Giovanni1 aNouveau, Leo1 aScovazzi, Guglielmo1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85060107322&doi=10.1016%2fj.cma.2018.12.040&partnerID=40&md5=1a3234f0cb000c91494d946428f8ebef01735nas a2200157 4500008004100000245007200041210006900113300001400182490000700196520114500203100002201348700001701370700001801387700002101405856015101426 2019 eng d00aA reduced order variational multiscale approach for turbulent flows0 areduced order variational multiscale approach for turbulent flow a2349-23680 v453 aThe 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.

1 aStabile, Giovanni1 aBallarin, F.1 aZuccarino, G.1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85068076665&doi=10.1007%2fs10444-019-09712-x&partnerID=40&md5=af0142e6d13bbc2e88c6f31750aef6ad01151nas a2200133 4500008004100000245012600041210006900167300001200236490000800248520056200256100002200818700002100840856015600861 2018 eng d00aFinite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier–Stokes equations0 aFinite volume PODGalerkin stabilised reduced order methods for t a273-2840 v1733 aIn 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.

1 aStabile, Giovanni1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85043366603&doi=10.1016%2fj.compfluid.2018.01.035&partnerID=40&md5=c15435ea3b632e55450da19ba2bb612500508nas a2200145 4500008004100000245008900041210006900130260002300199300001400222490000800236100002200244700002600266700001900292856005100311 2018 eng d00aA novel reduced order model for vortex induced vibrations of long flexible cylinders0 anovel reduced order model for vortex induced vibrations of long bElsevier {BV}cmay a191–2070 v1561 aStabile, Giovanni1 aMatthies, Hermann, G.1 aBorri, Claudio uhttps://doi.org/10.1016/j.oceaneng.2018.02.06400622nas a2200157 4500008004100000245010600041210006900147260001300216300001600229490000800245100002300253700002200276700001700298700001900315856013000334 2017 eng d00aCoupling effects on the dynamic response of moored floating platforms for offshore wind energy plants0 aCoupling effects on the dynamic response of moored floating plat bElsevier a3194–31990 v1991 aGiusti, Alessandro1 aStabile, Giovanni1 aMarino, Enzo1 aBorri, Claudio uhttps://www.math.sissa.it/publication/coupling-effects-dynamic-response-moored-floating-platforms-offshore-wind-energy-plants01724nas 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 aVortex 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-vortex00554nas a2200133 4500008004100000245007100041210006900112260006200181300001400243100002200257700002600279700001900305856009600324 2015 eng d00aA Reduced Order Model for the Simulation of Mooring Cable Dynamics0 aReduced Order Model for the Simulation of Mooring Cable Dynamics bSalvatore, Francesco; Broglia, Riccardo; Muscari, Roberto a387–4001 aStabile, Giovanni1 aMatthies, Hermann, G.1 aBorri, Claudio uhttps://www.math.sissa.it/publication/reduced-order-model-simulation-mooring-cable-dynamics00587nas a2200133 4500008004100000245011700041210006900158100001700227700001900244700002200263700001900285700001800304856013100322 2014 eng d00aCoupled dynamic simulations of offshore wind turbines: influence of wave modelling on the fatigue load assesment0 aCoupled dynamic simulations of offshore wind turbines influence 1 aMarino, Enzo1 aLugni, Claudio1 aStabile, Giovanni1 aBorri, Claudio1 aManuel, Lance uhttps://www.math.sissa.it/publication/coupled-dynamic-simulations-offshore-wind-turbines-influence-wave-modelling-fatigue-load00592nas a2200121 4500008004100000245016000041210006900201100001700270700001900287700002200306700001900328856012300347 2014 eng d00aCoupled dynamic simulations of offshore wind turbines using linear, weakly and fully nonlinear wave models: the limitations of the second-order wave theory0 aCoupled dynamic simulations of offshore wind turbines using line1 aMarino, Enzo1 aLugni, Claudio1 aStabile, Giovanni1 aBorri, Claudio uhttps://www.math.sissa.it/publication/coupled-dynamic-simulations-offshore-wind-turbines-using-linear-weakly-and-fully00631nas a2200145 4500008004100000245014200041210006900183260001400252300001400266100001700280700002200297700001900319700001900338856012800357 2013 eng d00aA comparative study about the effects of linear, weakly and fully nonlinear wave models on the dynamic response of offshore wind turbines0 acomparative study about the effects of linear weakly and fully n bCRC Press a389–3901 aMarino, Enzo1 aStabile, Giovanni1 aBorri, Claudio1 aLugni, Claudio uhttps://www.math.sissa.it/publication/comparative-study-about-effects-linear-weakly-and-fully-nonlinear-wave-models-dynamic