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High-Order Embedded WENO Schemes

  • Bart S. van LithEmail author
  • Jan H. M. ten Thije Boonkkamp
  • Wilbert L. IJzerman
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 119)

Abstract

Embedded WENO schemes are a new family of weighted essentially nonoscillatory schemes that always utilise all adjacent smooth substencils. This results in increased control over the convex combination of lower-order interpolations. We show that more conventional WENO schemes, such as WENO-JS and WENO-Z (Borges et al., J. Comput. Phys., 2008; Jiang and Shu, J. Comput. Phys., 1996), do not exhibit this feature and as such do not always provide a desirable linear combination of smooth substencils. In a previous work, we have already developed the theory and machinery needed to construct embedded WENO methods and shown some five-point schemes (van Lith et al., J. Comput. Phys., 2016). Here, we construct a seven-point scheme and show that it too performs well using some numerical examples from the one-dimensional Euler equations.

Notes

Acknowledgements

This work was generously supported by Philips Lighting and the Intelligent Lighting Institute. The authors would especially like to thank Rafael Borges and Wai-Sun Don for the fruitful discussions and the generous sharing of their Matlab code.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Bart S. van Lith
    • 1
    Email author
  • Jan H. M. ten Thije Boonkkamp
    • 1
  • Wilbert L. IJzerman
    • 1
    • 2
  1. 1.CASAEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Philips LightingEindhovenThe Netherlands

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