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Numerical Methods for Flows pp 245–264Cite as

The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: From Laminar to Turbulent Flows

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE,volume 132)

Abstract

We 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.

Keywords

  • Stabilised RB methods
  • SUPG
  • Turbulence modelling
  • Projection based model reduction
  • Data driven model reduction
  • Viscous flows

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Acknowledgements

We acknowledge the support provided by the European Research Council Consolidator Grant project Advanced Reduced Order Methods with Applications in Computational Fluid Dynamics—GA 681447, H2020-ERC COG 2015 AROMA-CFD, and INdAM-GNCS.

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Authors and Affiliations

  1. mathLab, Mathematics Area, SISSA, Trieste, Italy

    Saddam Hijazi, Shafqat Ali, Giovanni Stabile, Francesco Ballarin & Gianluigi Rozza

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  1. Saddam Hijazi
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  2. Shafqat Ali
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  3. Giovanni Stabile
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  4. Francesco Ballarin
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  5. Gianluigi Rozza
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Corresponding author

Correspondence to Saddam Hijazi .

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Editors and Affiliations

  1. Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, Noord-Brabant, The Netherlands

    Prof. Dr. Harald van Brummelen

  2. Department of Mechanical and Aerospace Engineering, Sapienza University of Rome, Roma, Italy

    Assoc. Prof. Alessandro Corsini

  3. MOX - Department of Mathematics, Politecnico di Milano, Milano, Italy

    Assoc. Prof. Simona Perotto

  4. SISSA mathLab, Mathematics Area, International School for Advanced Studies, Trieste, Italy

    Prof. Dr. Gianluigi Rozza

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Hijazi, S., Ali, S., Stabile, G., Ballarin, F., Rozza, G. (2020). The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: From Laminar to Turbulent Flows. In: van Brummelen, H., Corsini, A., Perotto, S., Rozza, G. (eds) Numerical Methods for Flows. Lecture Notes in Computational Science and Engineering, vol 132. Springer, Cham. https://doi.org/10.1007/978-3-030-30705-9_22

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