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Correction Procedure via Reconstruction Using Summation-by-Parts Operators

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Theory, Numerics and Applications of Hyperbolic Problems II (HYP 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 237))

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Abstract

The correction procedure via reconstruction (CPR, also known as flux reconstruction), is a high-order numerical scheme for conservation laws introduced by Huynh (2007), unifying some discontinuous Galerkin, spectral difference and spectral volume methods. A general framework of summation-by-parts (SBP) operators with simultaneous approximation terms (SATs) is presented, allowing semidiscrete stability for Burgers’ equation using nodal bases without boundary nodes or modal bases. The linearly stable schemes of Vincent et al. (2011, 2015) are embedded within this general kind of semidiscretisation. The contributed talk Artificial Viscosity for Correction Procedure via Reconstruction Using Summation-by-Parts Operators given by Philipp Öffner extends these results.

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Authors and Affiliations

  1. Institute Computational Mathematics, TU Braunschweig, Pockelsstraße 14, 38106, Braunschweig, Germany

    Philipp Öffner, Hendrik Ranocha & Thomas Sonar

Authors
  1. Philipp Öffner
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  2. Hendrik Ranocha
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  3. Thomas Sonar
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Corresponding author

Correspondence to Hendrik Ranocha .

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Editors and Affiliations

  1. Department of Mathematics, Würzburg University, Würzburg, Germany

    Christian Klingenberg

  2. Department of Mathematics, RWTH Aachen University, Aachen, Germany

    Michael Westdickenberg

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Öffner, P., Ranocha, H., Sonar, T. (2018). Correction Procedure via Reconstruction Using Summation-by-Parts Operators. In: Klingenberg, C., Westdickenberg, M. (eds) Theory, Numerics and Applications of Hyperbolic Problems II. HYP 2016. Springer Proceedings in Mathematics & Statistics, vol 237. Springer, Cham. https://doi.org/10.1007/978-3-319-91548-7_37

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