High-order embedded WENO schemes

B.S. van Lith; J.H.M. ten Thije Boonkkamp; W.L. IJzerman

doi:10.1007/978-3-319-65870-4_17

High-order embedded WENO schemes

B.S. van Lith, J.H.M. ten Thije Boonkkamp, W.L. IJzerman

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-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 language	English
Title of host publication	Spectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2016
Subtitle of host publication	Selected Papers from the ICOSAHOM conference, June 27-July 1, 2016, Rio de Janeiro, Brazil
Editors	M.L. Bittencourt, N.A. Dumont, J.S. Hesthaven
Place of Publication	Dordrecht
Publisher	Springer
Pages	257-268
Number of pages	12
ISBN (Electronic)	978-3-319-65870-4
ISBN (Print)	978-3-319-65869-8
DOIs	https://doi.org/10.1007/978-3-319-65870-4_17
Publication status	Published - 2016
Event	11th International Conference on Spectral and High-Order Methods (ICOSAHOM 2016) - Rio Othon Palace Copacabana, Rio de Janeiro, Brazil Duration: 27 Jun 2016 → 1 Jul 2016 Conference number: 11

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	119
ISSN (Print)	1439-7358

Conference

Conference	11th International Conference on Spectral and High-Order Methods (ICOSAHOM 2016)
Abbreviated title	ICOSAHOM2016
Country/Territory	Brazil
City	Rio de Janeiro
Period	27/06/16 → 1/07/16

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10.1007/978-3-319-65870-4_17

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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

van Lith, B.S. ; ten Thije Boonkkamp, J.H.M. ; IJzerman, W.L. / High-order embedded WENO schemes. 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. editor / M.L. Bittencourt ; N.A. Dumont ; J.S. Hesthaven. Dordrecht : Springer, 2016. pp. 257-268 (Lecture Notes in Computational Science and Engineering).

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title = "High-order embedded WENO schemes",

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.",

author = "{van Lith}, B.S. and {ten Thije Boonkkamp}, J.H.M. and W.L. IJzerman",

year = "2016",

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van Lith, BS, ten Thije Boonkkamp, JHM & IJzerman, WL 2016, High-order embedded WENO schemes. in ML Bittencourt, NA Dumont & JS 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. Lecture Notes in Computational Science and Engineering, vol. 119, Springer, Dordrecht, pp. 257-268, 11th International Conference on Spectral and High-Order Methods (ICOSAHOM 2016), Rio de Janeiro, Brazil, 27/06/16. https://doi.org/10.1007/978-3-319-65870-4_17

High-order embedded WENO schemes. / van Lith, B.S.; ten Thije Boonkkamp, J.H.M.; IJzerman, W.L.

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. ed. / M.L. Bittencourt; N.A. Dumont; J.S. Hesthaven. Dordrecht : Springer, 2016. p. 257-268 (Lecture Notes in Computational Science and Engineering; Vol. 119).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AB - 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.

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van Lith BS, ten Thije Boonkkamp JHM , IJzerman WL. High-order embedded WENO schemes. In Bittencourt ML, Dumont NA, Hesthaven JS, editors, 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. Dordrecht: Springer. 2016. p. 257-268. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-319-65870-4_17

High-order embedded WENO schemes

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