Skip to main content
SpringerLink
Log in
Book cover

European Conference on Numerical Mathematics and Advanced Applications

ENUMATH 2017: Numerical Mathematics and Advanced Applications ENUMATH 2017 pp 899–907Cite as

Third-Order Limiter Functions on Non-equidistant Grids

  • Conference paper
  • First Online:

  • 1581 Accesses

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 126))

Abstract

We have recently developed a third-order limiter function for the reconstruction of cell interface values on equidistant grids (J Sci Comput, 68(2):624–652, 2016). This work now extends the reconstruction technique to non- uniform grids in one space dimension, making it applicable for more elaborate test cases in the context of finite volume schemes.

Numerical examples show that the new limiter function maintains the optimal third-order accuracy on smooth profiles and avoids oscillations in case of discontinuous solutions.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. R. Artebrant, H.J. Schroll, Limiter-free third order logarithmic reconstruction. SIAM J. Sci. Comput. 28(1), 359–381 (2006)

    Article  MathSciNet  Google Scholar 

  2. M. Čada, M. Torrilhon, Compact third order limiter functions for finite volume methods. J. Comput. Phys. 228(11), 4118–4145 (2009)

    Article  MathSciNet  Google Scholar 

  3. S. Gottlieb, C.-W. Shu, E. Tadmor, Strong stability preserving high order time discretization methods. SIAM Rev. 43(1), 89–112 (2001)

    Article  MathSciNet  Google Scholar 

  4. G.-S. Jiang, C.-W. Shu, Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126(1), 202–228 (1996)

    Article  MathSciNet  Google Scholar 

  5. R.J. Le Veque, Numerical Methods for Conservation Laws, 2nd edn. (Birkhäuser, Basel, 1992)

    Google Scholar 

  6. X.-D. Liu, S. Osher, T. Chan, Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115, 200–212 (1994)

    Article  MathSciNet  Google Scholar 

  7. B. Schmidtmann, R. Abgrall, M. Torrilhon, On third-order limiter functions for finite volume methods. Bull. Braz. Math. Soc. 47(2), 753–764 (2016)

    Article  MathSciNet  Google Scholar 

  8. B. Schmidtmann, B. Seibold, M. Torrilhon, Relations between WENO3 and third-order limiting in finite volume methods. J. Sci. Comput. 68(2), 624–652 (2016)

    Article  MathSciNet  Google Scholar 

  9. B. Schmidtmann, P. Buchmller, M. Torrilhon, Third-order limiting for hyperbolic conservation laws applied to adaptive mesh refinement and non-uniform 2d grids (2017, preprint). arXiv:1705.10608

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. MathCCES, RWTH Aachen University, Aachen, Germany

    Birte Schmidtmann & Manuel Torrilhon

Authors
  1. Birte Schmidtmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manuel Torrilhon
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Birte Schmidtmann .

Editor information

Editors and Affiliations

  1. University of Bergen, Bergen, Norway

    Florin Adrian Radu

  2. University of Bergen, Bergen, Norway

    Kundan Kumar

  3. University of Bergen, Bergen, Norway

    Inga Berre

  4. University of Bergen, Bergen, Norway

    Jan Martin Nordbotten

  5. Hasselt University, Diepenbeek, Belgium

    Iuliu Sorin Pop

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Schmidtmann, B., Torrilhon, M. (2019). Third-Order Limiter Functions on Non-equidistant Grids. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_85

Download citation

Publish with us

Policies and ethics

Search

Navigation