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

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

Samenvatting

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.

Originele taal-2	Engels
Titel	Spectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2016
Subtitel	Selected Papers from the ICOSAHOM conference, June 27-July 1, 2016, Rio de Janeiro, Brazil
Redacteuren	M.L. Bittencourt, N.A. Dumont, J.S. Hesthaven
Plaats van productie	Dordrecht
Uitgeverij	Springer
Pagina's	257-268
Aantal pagina's	12
ISBN van elektronische versie	978-3-319-65870-4
ISBN van geprinte versie	978-3-319-65869-8
DOI's	https://doi.org/10.1007/978-3-319-65870-4_17
Status	Gepubliceerd - 2016
Evenement	11th International Conference on Spectral and High-Order Methods (ICOSAHOM 2016) - Rio Othon Palace Copacabana, Rio de Janeiro, Brazilië Duur: 27 jun. 2016 → 1 jul. 2016 Congresnummer: 11

Publicatie series

Naam	Lecture Notes in Computational Science and Engineering
Volume	119
ISSN van geprinte versie	1439-7358

Congres

Congres	11th International Conference on Spectral and High-Order Methods (ICOSAHOM 2016)
Verkorte titel	ICOSAHOM2016
Land/Regio	Brazilië
Stad	Rio de Janeiro
Periode	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 (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 (blz. 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. redacteur / M.L. Bittencourt ; N.A. Dumont ; J.S. Hesthaven. Dordrecht : Springer, 2016. blz. 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",

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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 (uitgave), 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, blz. 257-268, 11th International Conference on Spectral and High-Order Methods (ICOSAHOM 2016), Rio de Janeiro, Brazilië, 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. uitgave / M.L. Bittencourt; N.A. Dumont; J.S. Hesthaven. Dordrecht: Springer, 2016. blz. 257-268 (Lecture Notes in Computational Science and Engineering; Vol. 119).

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › 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, redacteurs, 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. blz. 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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