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Explicit reduced-order models for the stabilized finite element approximation of the incompressible Navier–Stokes equations

Authors

  • Joan Baiges,

    Corresponding author
    1. Universitat Politècnica de Catalunya, Jordi Girona 1-3, Edifici C1, 08034 Barcelona, Spain
    • Centre Internacional de Mètodes Numèrics a l'Enginyeria (CIMNE), Edifici C1, Campus Nord UPC C/ Gran Capità S/N 08034 Barcelona, Spain
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  • Ramon Codina,

    1. Centre Internacional de Mètodes Numèrics a l'Enginyeria (CIMNE), Edifici C1, Campus Nord UPC C/ Gran Capità S/N 08034 Barcelona, Spain
    2. Universitat Politècnica de Catalunya, Jordi Girona 1-3, Edifici C1, 08034 Barcelona, Spain
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  • Sergio Idelsohn

    1. Centre Internacional de Mètodes Numèrics a l'Enginyeria (CIMNE), Edifici C1, Campus Nord UPC C/ Gran Capità S/N 08034 Barcelona, Spain
    2. Institució Catalana de Recerca i Estudis Avanç̧ats, Barcelona, Spain
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Correspondence to: Joan Baiges, Dept. Resistència de Materials i Estructures a l'Enginyeria, Universitat Politècnica de Catalunya, Barcelona, Spain.

E-mail: jbaiges@cimne.upc.edu

SUMMARY

In this paper, we present an explicit formulation for reduced-order models of the stabilized finite element approximation of the incompressible Navier–Stokes equations. The basic idea is to build a reduced-order model based on a proper orthogonal decomposition and a Galerkin projection and treat all the terms in an explicit way in the time integration scheme, including the pressure. This is possible because the reduced model snapshots do already fulfill the continuity equation. The pressure field is automatically recovered from the reduced-order basis and solution coefficients. The main advantage of this explicit treatment of the incompressible Navier–Stokes equations is that it allows for the easy use of hyper-reduced order models, because only the right-hand side vector needs to be recovered by means of a gappy data reconstruction procedure. A method for choosing the optimal set of sampling points at the discrete level in the gappy procedure is also presented. Numerical examples show the performance of the proposed strategy. Copyright © 2013 John Wiley & Sons, Ltd.

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