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.

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/S004579302030389302168nas a2200157 4500008004100000245011600041210006900157300001200226490000700238520155800245100002101803700002201824700002101846700002001867856012301887 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, Sabrina, K1 aStabile, Giovanni1 aRozza, Gianluigi1 aDegroote, Joris uhttps://www.math.sissa.it/publication/pod-galerkin-reduced-order-model-turbulent-convective-buoyant-flow-sodium-over-001497nas 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=fb0b1a3cfdfd35a104db9921bc9be67501178nas 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/1901.0637301462nas a2200145 4500008004100000245009400041210006900135520097900204100001901183700001701202700002201219700001701241700002101258856003701279 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 3 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/1906.0872501437nas a2200157 4500008004100000245014800041210006900189300001200258490000800270520076900278100001901047700002201066700001701088700002101105856015301126 2020 eng d00aNon-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 a217-2400 v1373 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://www.scopus.com/inward/record.uri?eid=2-s2.0-85089617719&doi=10.1007%2f978-3-030-48721-8_10&partnerID=40&md5=7e599e0d34815c3af91d3c0c90b9e1d401465nas a2200193 4500008004100000245014700041210006900188260003800257520076900295100001901064700002201083700001701105700002101122700002601143700002401169700002001193700002101213856003701234 2020 eng d00aNon-Intrusive Polynomial Chaos Method Applied to Problems in Computational Fluid Dynamics with a Comparison to Proper Orthogonal Decomposition0 aNonIntrusive Polynomial Chaos Method Applied to Problems in Comp bSpringer International Publishing3 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, Gianluigi1 avan Brummelen, Harald1 aCorsini, Alessandro1 aPerotto, Simona1 aRozza, Gianluigi uhttps://arxiv.org/abs/1901.0228502038nas a2200133 4500008004100000245011600041210006900157520156100226100001701787700002201804700002101826700002001847856003701867 2020 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 buoyan3 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 $10^5$ times faster than the RANS simulations that are performed on eight cores.

1 aStar, Kelbij1 aStabile, Giovanni1 aRozza, Gianluigi1 aDegroote, Joris uhttps://arxiv.org/abs/2003.0111401696nas 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=a8dcce1b53b8ee872d174bbc4c20caa301869nas a2200181 4500008004100000245012100041210006900162260003800231520122900269100002801498700002201526700001901548700002401567700002101591700001601612700002201628856003701650 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, N.1 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/1808.0517502002nas a2200157 4500008004100000245010400041210006900145520138000214100001701594700002201611700002301633700001601656700002101672700002001693856013101713 2019 eng d00aPod-Galerkin reduced order model of the Boussinesq approximation for buoyancy-driven enclosed flows0 aPodGalerkin reduced order model of the Boussinesq approximation 3 aA parametric Reduced Order Model (ROM) for buoyancy-driven flow is developed for which the Full Order Model (FOM) is based on the finite volume approximation and the Boussinesq approximation is used for modeling the buoyancy. Therefore, there exists a two-way coupling between the incompressible Boussinesq equations and the energy equation. The reduced basis is constructed with a Proper Orthogonal Decomposition (POD) approach and to obtain the Reduced Order Model, a Galerkin projection of the governing equations onto the reduced basis is performed. The ROM is tested on a 2D differentially heated cavity of which the side wall temperatures are parametrized. The parametrization is done using a control function method. The aim of the method is to obtain homogeneous POD basis functions. The control functions are obtained solving a Laplacian function for temperature. Only one full order solution was required for the reduced basis creation. The obtained ROM is stable for different parameter sets for which the temperature difference between the walls is smaller than for the set in the FOM used for the POD basis creation. Then, the relative error between the FOM and the ROM for temperature is below 10−4 and for velocity below 10−1 for the vast part of the simulation time. Finally, the ROM is about 20 times faster than the FOM run on a single processor.

1 aStar, Kelbij1 aStabile, Giovanni1 aGeorgaka, Sokratia1 aBelloni, F.1 aRozza, Gianluigi1 aDegroote, Joris uhttps://www.math.sissa.it/publication/pod-galerkin-reduced-order-model-boussinesq-approximation-buoyancy-driven-enclosed-flows02191nas 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=1a3234f0cb000c91494d946428f8ebef01742nas a2200157 4500008004100000245007200041210006900113300001400182490000700196520114500203100002201348700002401370700001801394700002101412856015101433 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, Francesco1 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=af0142e6d13bbc2e88c6f31750aef6ad00590nas a2200133 4500008004100000245012000041210006900161100001900230700001700249700002200266700002400288700002100312856012300333 2018 eng d00aThe Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows0 aEffort of Increasing Reynolds Number in ProjectionBased Reduced 1 aHijazi, Saddam1 aAli, Shafqat1 aStabile, Giovanni1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/effort-increasing-reynolds-number-projection-based-reduced-order-methods-laminar01151nas 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=c15435ea3b632e55450da19ba2bb612500462nas a2200109 4500008004100000245012400041210006900165260002300234100002200257700002100279856005200300 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 bElsevier {BV}cfeb1 aStabile, Giovanni1 aRozza, Gianluigi uhttps://doi.org/10.1016/j.compfluid.2018.01.03500508nas 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.2018.02.06400631nas a2200133 4500008004100000245015100041210006900192100002800261700002200289700001700311700002400328700002100352856012400373 2018 eng d00aA Reduced Basis approach for PDEs on parametrized geometries based on the Shifted Boundary Finite Element Method and application to fluid dynamics0 aReduced Basis approach for PDEs on parametrized geometries based1 aKaratzas, Efthymios, N.1 aStabile, Giovanni1 aNouveau, Leo1 aScovazzi, Guglielmo1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-basis-approach-pdes-parametrized-geometries-based-shifted-boundary-finite00596nas a2200133 4500008004100000245012100041210006900162100002800231700002200259700001600281700002400297700002100321856012000342 2018 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 and1 aKaratzas, Efthymios, N.1 aStabile, Giovanni1 aAtallah, N.1 aScovazzi, Guglielmo1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-order-approach-embedded-shifted-boundary-fem-and-heat-exchange-system01821nas a2200181 4500008004100000024003700041245012000078210006900198520118600267653002301453653002601476100002201502700001901524700002101543700001701564700002101581856003701602 2017 eng d ahttps://arxiv.org/abs/1701.0342400aAdvances in Reduced order modelling for CFD: vortex shedding around a circular cylinder using a POD-Galerkin method0 aAdvances in Reduced order modelling for CFD vortex shedding arou3 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.

10afinite volume, CFD10aReduced order methods1 aStabile, Giovanni1 aHijazi, Saddam1 aLorenzi, Stefano1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/1701.0342400603nas a2200169 4500008004100000245012600041210006900167260003400236300001400270490000600284100002200290700001900312700001700331700002100348700002100369856004300390 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 bWalter de Gruyter {GmbH}cdec a210–2360 v81 aStabile, Giovanni1 aHijazi, Saddam1 aMola, Andrea1 aLorenzi, Stefano1 aRozza, Gianluigi uhttps://doi.org/10.1515/caim-2017-0011