Embedded WENO: A design strategy to improve existing WENO schemes

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Embedded WENO methods utilise all adjacent smooth substencils to construct a desirable interpolation. Conventional WENO schemes under-use this possibility close to large gradients or discontinuities. We develop a general approach for constructing embedded versions of existing WENO schemes. Embedded methods based on the WENO schemes of Jiang and Shu [1] and on the WENO-Z scheme of Borges et al. [2] are explicitly constructed. Several possible choices are presented that result in either better spectral properties or a higher order of convergence for sufficiently smooth solutions. However, these improvements carry over to discontinuous solutions. The embedded methods are demonstrated to be indeed improvements over their standard counterparts by several numerical examples. All the embedded methods presented have no added computational effort compared to their standard counterparts.

Originele taal-2Engels
Pagina's (van-tot)529-549
Aantal pagina's21
TijdschriftJournal of Computational Physics
Volume330
DOI's
StatusGepubliceerd - 1 feb 2017

Vingerafdruk

WENO Scheme
interpolation
Interpolation
discontinuity
gradients
Discontinuous Solutions
Order of Convergence
Smooth Solution
Spectral Properties
Discontinuity
Adjacent
Interpolate
Design
Strategy
Higher Order
Gradient
Numerical Examples

Citeer dit

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title = "Embedded WENO: A design strategy to improve existing WENO schemes",
abstract = "Embedded WENO methods utilise all adjacent smooth substencils to construct a desirable interpolation. Conventional WENO schemes under-use this possibility close to large gradients or discontinuities. We develop a general approach for constructing embedded versions of existing WENO schemes. Embedded methods based on the WENO schemes of Jiang and Shu [1] and on the WENO-Z scheme of Borges et al. [2] are explicitly constructed. Several possible choices are presented that result in either better spectral properties or a higher order of convergence for sufficiently smooth solutions. However, these improvements carry over to discontinuous solutions. The embedded methods are demonstrated to be indeed improvements over their standard counterparts by several numerical examples. All the embedded methods presented have no added computational effort compared to their standard counterparts.",
keywords = "Essentially non-oscillatory, High-resolution scheme, Hyperbolic conservation laws, Nonlinear interpolation, Spectral analysis, WENO",
author = "{van Lith}, B.S. and {ten Thije Boonkkamp}, J.H.M. and W.L. IJzerman",
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Embedded WENO : A design strategy to improve existing WENO schemes. / van Lith, B.S.; ten Thije Boonkkamp, J.H.M.; IJzerman, W.L.

In: Journal of Computational Physics, Vol. 330, 01.02.2017, blz. 529-549.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

TY - JOUR

T1 - Embedded WENO

T2 - A design strategy to improve existing WENO schemes

AU - van Lith, B.S.

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AU - IJzerman, W.L.

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AB - Embedded WENO methods utilise all adjacent smooth substencils to construct a desirable interpolation. Conventional WENO schemes under-use this possibility close to large gradients or discontinuities. We develop a general approach for constructing embedded versions of existing WENO schemes. Embedded methods based on the WENO schemes of Jiang and Shu [1] and on the WENO-Z scheme of Borges et al. [2] are explicitly constructed. Several possible choices are presented that result in either better spectral properties or a higher order of convergence for sufficiently smooth solutions. However, these improvements carry over to discontinuous solutions. The embedded methods are demonstrated to be indeed improvements over their standard counterparts by several numerical examples. All the embedded methods presented have no added computational effort compared to their standard counterparts.

KW - Essentially non-oscillatory

KW - High-resolution scheme

KW - Hyperbolic conservation laws

KW - Nonlinear interpolation

KW - Spectral analysis

KW - WENO

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