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

  • Joan Baiges
  • Ramon Codina
  • Sergio R. Idelsohn
Chapter
Part of the Computational Methods in Applied Sciences book series (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.

Keywords

Proper Orthogonal Decomposition Domain Decomposition Finite Element Mesh Proper Orthogonal Decomposition Base Local Basis Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Joan Baiges
    • 1
    • 2
  • Ramon Codina
    • 1
    • 2
  • Sergio R. Idelsohn
    • 1
    • 3
  1. 1.Centre Internacional de Mètodes Numèrics a l’Enginyeria (CIMNE)BarcelonaSpain
  2. 2.Universitat Politècnica de CatalunyaBarcelonaSpain
  3. 3.Instituciò Catalana de Recerca i Estudis Avançats (ICREA)BarcelonaSpain

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