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

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Abstract

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.

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  1. http://www.morepas.org/software.

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Acknowledgements

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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Authors and Affiliations

  1. Institute for Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Immanuel Martini & Bernard Haasdonk

  2. SISSA MathLab, International School for Advanced Studies, Office A-435, Via Bonomea 265, 34136, Trieste, Italy

    Gianluigi Rozza

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  1. Immanuel Martini
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Martini, I., Haasdonk, B. & Rozza, G. Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models. J Sci Comput 74, 197–219 (2018). https://doi.org/10.1007/s10915-017-0430-y

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