Journal of Scientific Computing

, Volume 74, Issue 1, pp 197–219 | Cite as

Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models

  • Immanuel MartiniEmail author
  • Bernard Haasdonk
  • Gianluigi Rozza


We present a model order reduction approach for parametrized laminar flow problems including viscous boundary layers. The viscous effects are captured by the incompressible Navier–Stokes equations in the vicinity of the boundary layer, whereas a potential flow model is used in the outer region. By this, we provide an accurate model that avoids imposing the Kutta condition for potential flows as well as an expensive numerical solution of a global viscous model. To account for the parametrized nature of the problem, we apply the reduced basis method. The accuracy of the reduced order model is ensured by rapidly computable a posteriori error estimates. The main contributions of this paper are the combination of an offline-online splitting with the domain decomposition approach, reducing both offline and online computational loads and a new kernel interpolation method for the approximation of the stability factor in the online evaluation of the error estimate. The viability of our approach is demonstrated by numerical experiments for the section of a NACA airfoil.


Reduced basis method Coupled problems Error estimation Navier–Stokes equations 

Mathematics Subject Classification

65N55 76D09 76G25 



The authors would like to thank the Trans-Domain COST Action TD1307 “European Model Reduction Network” (EU-MORNET) for the grant of a Short Term Scientific Mission (STSM), allowing I. Martini to spend a visiting period at SISSA. We also acknowledge financial support by the German Research Foundation (DFG) within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart and by the Baden-Württemberg Stiftung gGmbH. G. Rozza acknowledges the NOFYSAS program: New Opportunities for Young Scientists at SISSA, Trieste, Italy and the INDAM-GNCS projects 2015–2016.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Immanuel Martini
    • 1
    Email author
  • Bernard Haasdonk
    • 1
  • Gianluigi Rozza
    • 2
  1. 1.Institute for Applied Analysis and Numerical SimulationUniversity of StuttgartStuttgartGermany
  2. 2.SISSA MathLabInternational School for Advanced StudiesTriesteItaly

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