High-order embedded WENO schemes

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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.

Original languageEnglish
Title of host publicationSpectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2016
Subtitle of host publicationSelected Papers from the ICOSAHOM conference, June 27-July 1, 2016, Rio de Janeiro, Brazil
EditorsM.L. Bittencourt, N.A. Dumont, J.S. Hesthaven
Place of PublicationDordrecht
PublisherSpringer
Pages257-268
Number of pages12
ISBN (Electronic)978-3-319-65870-4
ISBN (Print)978-3-319-65869-8
DOIs
Publication statusPublished - 2016
Event11th International Conference on Spectral and High-Order Methods (ICOSAHOM 2016) - Rio Othon Palace Copacabana, Rio de Janeiro, Brazil
Duration: 27 Jun 20161 Jul 2016
Conference number: 11

Publication series

NameLecture Notes in Computational Science and Engineering
Volume119
ISSN (Print)1439-7358

Conference

Conference11th International Conference on Spectral and High-Order Methods (ICOSAHOM 2016)
Abbreviated titleICOSAHOM2016
CountryBrazil
CityRio de Janeiro
Period27/06/161/07/16

Fingerprint Dive into the research topics of 'High-order embedded WENO schemes'. Together they form a unique fingerprint.

  • Cite this

    van Lith, B. S., ten Thije Boonkkamp, J. H. M., & IJzerman, W. L. (2016). High-order embedded WENO schemes. In M. L. Bittencourt, N. A. Dumont, & J. S. Hesthaven (Eds.), Spectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2016 : Selected Papers from the ICOSAHOM conference, June 27-July 1, 2016, Rio de Janeiro, Brazil (pp. 257-268). (Lecture Notes in Computational Science and Engineering; Vol. 119). Springer. https://doi.org/10.1007/978-3-319-65870-4_17