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Correction Procedure via Reconstruction Using Summation-by-Parts Operators

  • Philipp Öffner
  • Hendrik RanochaEmail author
  • Thomas Sonar
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 237)

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.

Keywords

High-order methods Summation-by-parts Correction procedure via reconstruction Flux reconstruction Skew-symmetric form 

Mathematics Subject Classification (2010)

65M70 65M60 65M06 65M12 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Philipp Öffner
    • 1
  • Hendrik Ranocha
    • 1
    Email author
  • Thomas Sonar
    • 1
  1. 1.Institute Computational MathematicsTU BraunschweigBraunschweigGermany

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