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Spatial Filtering for Reduced Order Modeling

  • L. C. BerselliEmail author
  • D. Wells
  • X. Xie
  • T. Iliescu
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 25)

Abstract

Spatial filtering has been central in the development of large eddy simulation reduced order models (LES-ROMs) (Wang et al. in Comput. Meth. Appl. Mech. Eng. 237–240:10–26, 2012, [9], Xie et al. in Data-driven filtered reduced order modeling of fluid flows, 2018, [11], Xie et al. in Comput. Methods Appl. Mech. Eng. 313:512–534, 2017, [12]) and regularized reduced order models (Reg-ROMs) (Iliescu et al. in Int. J. Numer. Anal. Mod. 2017, [4], Sabetghadam and Jafarpour in Appl. Math. Comput. 218:6012–6026, 2012, [7], Wells et al. in Int. J. Numer. Meth. Fluids 84:598–615, 2017, [10]) for efficient and relatively accurate numerical simulation of convection-dominated fluid flows. In this paper, we perform a numerical investigation of spatial filtering. To this end, we consider one of the simplest Reg-ROMs, the Leray ROM (L-ROM) (Iliescu et al. in Int. J. Numer. Anal. Mod. 2017, [4], Sabetghadam and Jafarpour in Appl. Math. Comput. 218:6012–6026, 2012, [7], Wells et al. in Int. J. Numer. Meth. Fluids 84:598–615, 2017, [10]), which uses ROM spatial filtering to smooth the flow variables and decrease the amount of energy aliased to the lower index ROM basis functions. We also propose a new form of ROM differential filter (Sabetghadam and Jafarpour in Appl. Math. Comput. 218:6012–6026, 2012, [7], Wells et al. in Int. J. Numer. Meth. Fluids 84:598–615, 2017, [10]) and use it as a spatial filter for the L-ROM. We investigate the performance of this new form of ROM differential filter in the numerical simulation of a flow past a circular cylinder at a Reynolds number \(Re=760\).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di PisaPisaItaly
  2. 2.Department of MathematicsUniversity of North Carolina at Chapel HillChapel HillUSA
  3. 3.Computational and Applied Mathematics GroupOak Ridge National LaboratoryOak RidgeUSA
  4. 4.Department of MathematicsVirginia TechBlacksburgUSA

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