In 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 $Re=O(10^5)$.

VL - 416 UR - https://arxiv.org/abs/1907.09909 ER - TY - JOUR T1 - Efficient Geometrical parametrization for finite-volume based reduced order methods JF - International Journal for Numerical Methods in Engineering Y1 - 2020 A1 - Giovanni Stabile A1 - Matteo Zancanaro A1 - Gianluigi Rozza AB -In 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

VL - 121 UR - https://arxiv.org/abs/1901.06373 ER - TY - UNPB T1 - Enhancing CFD predictions in shape design problems by model and parameter space reduction Y1 - 2020 A1 - Marco Tezzele A1 - Nicola Demo A1 - Giovanni Stabile A1 - Andrea Mola A1 - Gianluigi Rozza AB -In 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.

UR - https://arxiv.org/abs/2001.05237 ER - TY - JOUR T1 - A hybrid reduced order method for modelling turbulent heat transfer problems JF - Computers & Fluids Y1 - 2020 A1 - Sokratia Georgaka A1 - Giovanni Stabile A1 - Kelbij Star A1 - Gianluigi Rozza A1 - Michael J. Bluck AB -A 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.

VL - 208 UR - https://arxiv.org/abs/1906.08725 ER - TY - CONF T1 - Non-Intrusive Polynomial Chaos Method Applied to Problems in Computational Fluid Dynamics with a Comparison to Proper Orthogonal Decomposition T2 - QUIET Selected Contributions Y1 - 2020 A1 - Saddam Hijazi A1 - Giovanni Stabile A1 - Andrea Mola A1 - Gianluigi Rozza ED - van Brummelen, Harald ED - Corsini, Alessandro ED - Perotto, Simona ED - Rozza, Gianluigi AB -In 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.

JF - QUIET Selected Contributions PB - Springer International Publishing UR - https://arxiv.org/abs/1901.02285 ER - TY - UNPB T1 - A POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step Y1 - 2020 A1 - Kelbij Star A1 - Giovanni Stabile A1 - Gianluigi Rozza A1 - Joris Degroote AB -A Finite-Volume based POD-Galerkin reduced order modeling strategy for steady-state Reynolds averaged Navier–Stokes (RANS) simulation is extended for low-Prandtl number flow. The reduced order model is based on a full order model for which the effects of buoyancy on the flow and heat transfer are characterized by varying the Richardson number. The Reynolds stresses are computed with a linear eddy viscosity model. A single gradient diffusion hypothesis, together with a local correlation for the evaluation of the turbulent Prandtl number, is used to model the turbulent heat fluxes. The contribution of the eddy viscosity and turbulent thermal diffusivity fields are considered in the reduced order model with an interpolation based data-driven method. The reduced order model is tested for buoyancy-aided turbulent liquid sodium flow over a vertical backward-facing step with a uniform heat flux applied on the wall downstream of the step. The wall heat flux is incorporated with a Neumann boundary condition in both the full order model and the reduced order model. The velocity and temperature profiles predicted with the reduced order model for the same and new Richardson numbers inside the range of parameter values are in good agreement with the RANS simulations. Also, the local Stanton number and skin friction distribution at the heated wall are qualitatively well captured. Finally, the reduced order simulations, performed on a single core, are about $10^5$ times faster than the RANS simulations that are performed on eight cores.

UR - https://arxiv.org/abs/2003.01114 ER - TY - CONF T1 - A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries T2 - IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018 Y1 - 2020 A1 - Efthymios N. Karatzas A1 - Giovanni Stabile A1 - Nabib Atallah A1 - Guglielmo Scovazzi A1 - Gianluigi Rozza ED - Fehr, Jörg ED - Haasdonk, Bernard AB -A 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.

JF - IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018 PB - Springer International Publishing UR - https://arxiv.org/abs/1807.07753 ER - TY - JOUR T1 - Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems JF - Communications in Computational Physics Y1 - 2019 A1 - Sokratia Georgaka A1 - Giovanni Stabile A1 - Gianluigi Rozza A1 - Michael J. Bluck AB -A parametric reduced order model based on proper orthogonal decom- position with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power plants. Thermal mixing of different temperature coolants in T-junction pipes leads to tem- perature fluctuations and this could potentially cause thermal fatigue in the pipe walls. The novelty of this paper is the development of a parametric ROM considering the three dimensional, incompressible, unsteady Navier-Stokes equations coupled with the heat transport equation in a finite volume approximation. Two different paramet- ric cases are presented in this paper: parametrization of the inlet temperatures and parametrization of the kinematic viscosity. Different training spaces are considered and the results are compared against the full order model.

VL - 27 UR - https://arxiv.org/abs/1808.05175 ER - TY - ABST T1 - The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows Y1 - 2018 A1 - Saddam Hijazi A1 - Shafqat Ali A1 - Giovanni Stabile A1 - Francesco Ballarin A1 - Gianluigi Rozza ER - TY - JOUR T1 - Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier-Stokes equations JF - Computers & Fluids Y1 - 2018 A1 - Giovanni Stabile A1 - Gianluigi Rozza PB - Elsevier {BV} UR - https://doi.org/10.1016/j.compfluid.2018.01.035 ER - TY - JOUR T1 - A novel reduced order model for vortex induced vibrations of long flexible cylinders Y1 - 2018 A1 - Giovanni Stabile A1 - Hermann G. Matthies A1 - Claudio Borri PB - Elsevier {BV} VL - 156 UR - https://doi.org/10.1016/j.oceaneng.2018.02.064 ER - TY - ABST T1 - A Reduced Basis approach for PDEs on parametrized geometries based on the Shifted Boundary Finite Element Method and application to fluid dynamics Y1 - 2018 A1 - Efthymios N. Karatzas A1 - Giovanni Stabile A1 - Leo Nouveau A1 - Guglielmo Scovazzi A1 - Gianluigi Rozza ER - TY - ABST T1 - A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries Y1 - 2018 A1 - Efthymios N. Karatzas A1 - Giovanni Stabile A1 - N. Atallah A1 - Guglielmo Scovazzi A1 - Gianluigi Rozza ER - TY - JOUR T1 - Advances in Reduced order modelling for CFD: vortex shedding around a circular cylinder using a POD-Galerkin method JF - Communication in Applied Industrial Mathematics Y1 - 2017 A1 - Giovanni Stabile A1 - Saddam Hijazi A1 - Stefano Lorenzi A1 - Andrea Mola A1 - Gianluigi Rozza KW - finite volume, CFD KW - Reduced order methods AB -Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. In this work a Reduced Order Model (ROM) of the incompressible flow around a circular cylinder, built performing a Galerkin projection of the governing equations onto a lower dimensional space is presented. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) for this purpose the projection of the Governing equations (momentum equation and Poisson equation for pressure) is performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework are presented. The accuracy of the reduced order model is assessed against full order results.

UR - https://arxiv.org/abs/1701.03424 ER - TY - JOUR T1 - POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder JF - Communications in Applied and Industrial Mathematics Y1 - 2017 A1 - Giovanni Stabile A1 - Saddam Hijazi A1 - Andrea Mola A1 - Stefano Lorenzi A1 - Gianluigi Rozza PB - Walter de Gruyter {GmbH} VL - 8 UR - https://doi.org/10.1515/caim-2017-0011 ER -