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Reduced-Order Modelling Strategies for the Finite Element Approximation of the Incompressible Navier-Stokes Equations

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Numerical Simulations of Coupled Problems in Engineering

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 33))

Abstract

In this chapter we present some Reduced-Order Modelling methods we have developed for the stabilized incompressible Navier-Stokes equations. In the first part of the chapter, we depart from the stabilized finite element approximation of incompressible flow equations and we build an explicit proper-orthogonal decomposition based reduced-order model. To do this, we treat the pressure and all the non-linear terms in an explicit way in the time integration scheme. This is possible due to the fact that the reduced model snapshots and basis functions do already fulfill an incompressibility constraint weakly. This allows a hyper-reduction approach in which only the right-hand-side vector needs to be reconstructed. In the second part of the chapter we present a domain decomposition approach for reduced-order models. The method consists in restricting the reduced-order basis functions to the nodes belonging to each of the subdomains. The method is extended to the particular case in which one of the subdomains is solved by using the high-fidelity, full-order model, while the other ones are solved by using the low-cost, reduced-order equations.

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Authors and Affiliations

  1. Centre Internacional de Mètodes Numèrics a l’Enginyeria (CIMNE), Edifici C1, Campus Nord UPC C/ Gran Capità S/N, 08034, Barcelona, Spain

    Joan Baiges, Ramon Codina & Sergio R. Idelsohn

  2. Universitat Politècnica de Catalunya, Jordi Girona 1-3, Edifici C1, 08034, Barcelona, Spain

    Joan Baiges & Ramon Codina

  3. Instituciò Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain

    Sergio R. Idelsohn

Authors
  1. Joan Baiges
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  2. Ramon Codina
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  3. Sergio R. Idelsohn
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Correspondence to Joan Baiges .

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  1. Centre Internacional de Mètodes Numerics en l'Enginyeria (CIMNE), Catalan Institution for Research and Advanced Studies (ICREA), and International Center for Numercial Methods in Engineering (CIMNE), Barcelona, Spain

    Sergio R. Idelsohn

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Baiges, J., Codina, R., Idelsohn, S.R. (2014). Reduced-Order Modelling Strategies for the Finite Element Approximation of the Incompressible Navier-Stokes Equations. In: Idelsohn, S. (eds) Numerical Simulations of Coupled Problems in Engineering. Computational Methods in Applied Sciences, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-319-06136-8_9

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  • DOI: https://doi.org/10.1007/978-3-319-06136-8_9

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