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High-Order Isogeometric Methods for Compressible Flows

II: Compressible Euler Equations

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Numerical Methods for Flows

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 132))

Abstract

This work extends the high-resolution isogeometric analysis approach established in chapter “High-Order Isogeometric Methods for Compressible Flows. I: Scalar Conservation Laws” (Jaeschke and Möller: High-order isogeometric methods for compressible flows. I. Scalar conservation Laws. In: Proceedings of the 19th International Conference on Finite Elements in Flow Problems (FEF 2017)) to the equations of gas dynamics. The group finite element formulation is adopted to obtain an efficient assembly procedure for the standard Galerkin approximation, which is stabilized by adding artificial viscosities proportional to the spectral radius of the Roe-averaged flux-Jacobian matrix. Excess stabilization is removed in regions with smooth flow profiles with the aid of algebraic flux correction (Kuzmin et al., Flux-corrected transport, chapter Algebraic flux correction II. Compressible Flow Problems. Springer, Berlin, 2012). The underlying principles are reviewed and it is shown that linearized FCT-type flux limiting (Kuzmin, J Comput Phys 228(7):2517–2534, 2009) originally derived for nodal low-order finite elements ensures positivity-preservation for high-order B-Spline discretizations.

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Acknowledgement

This work has been supported by the European Unions Horizon 2020 research and innovation programme under grant agreement No. 678727.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

    Matthias Möller

  2. Institute of Turbomachinery, Łódź University of Technology, Łódź, Poland

    Andrzej Jaeschke

Authors
  1. Matthias Möller
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  2. Andrzej Jaeschke
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Corresponding author

Correspondence to Matthias Möller .

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Editors and Affiliations

  1. Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, Noord-Brabant, The Netherlands

    Harald van Brummelen

  2. Department of Mechanical and Aerospace Engineering, Sapienza University of Rome, Roma, Italy

    Alessandro Corsini

  3. MOX - Department of Mathematics, Politecnico di Milano, Milano, Italy

    Simona Perotto

  4. SISSA mathLab, Mathematics Area, International School for Advanced Studies, Trieste, Italy

    Gianluigi Rozza

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Möller, M., Jaeschke, A. (2020). High-Order Isogeometric Methods for Compressible Flows. In: van Brummelen, H., Corsini, A., Perotto, S., Rozza, G. (eds) Numerical Methods for Flows. Lecture Notes in Computational Science and Engineering, vol 132. Springer, Cham. https://doi.org/10.1007/978-3-030-30705-9_4

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