High-order embedded WENO schemes

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

Uittreksel

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-2Engels
TitelSpectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2016
SubtitelSelected Papers from the ICOSAHOM conference, June 27-July 1, 2016, Rio de Janeiro, Brazil
RedacteurenM.L. Bittencourt, N.A. Dumont, J.S. Hesthaven
Plaats van productieDordrecht
UitgeverijSpringer
Pagina's257-268
Aantal pagina's12
ISBN van elektronische versie978-3-319-65870-4
ISBN van geprinte versie978-3-319-65869-8
DOI's
StatusGepubliceerd - 2016
Evenement11th International Conference on Spectral and High-Order Methods (ICOSAHOM 2016) - Rio Othon Palace Copacabana, Rio de Janeiro, Brazilië
Duur: 27 jun 20161 jul 2016
Congresnummer: 11

Publicatie series

NaamLecture Notes in Computational Science and Engineering
Volume119
ISSN van geprinte versie1439-7358

Congres

Congres11th International Conference on Spectral and High-Order Methods (ICOSAHOM 2016)
Verkorte titelICOSAHOM2016
LandBrazilië
StadRio de Janeiro
Periode27/06/161/07/16

Vingerafdruk

WENO Scheme
Euler equations
Machinery
Interpolation
Higher Order
Convex Combination
Euler Equations
Linear Combination
Adjacent
Interpolate
Numerical Examples

Citeer dit

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). Dordrecht: 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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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.",
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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 (redactie), 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. redactie / 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/CongresprocedureConferentiebijdrageAcademicpeer review

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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). https://doi.org/10.1007/978-3-319-65870-4_17