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 $Re=O(10^5)$.

%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 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 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 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