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Journal of Scientific Computing

Erschienen in:

08.08.2015

Modified Non-linear Weights for Fifth-Order Weighted Essentially Non-oscillatory Schemes

verfasst von: Chang Ho Kim, Youngsoo Ha, Jungho Yoon

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2016

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Abstract

This paper is concerned with fifth-order weighted essentially non-oscillatory (WENO) scheme with a new smoothness indicator. As the so-called WENO-JS scheme (Jiang and Shu in J Comput Phys 126:202–228, 1996) provides the third-order accuracy at critical points where the first and third order derivatives do not becomes zero simultaneously, several fifth-order WENO scheme have been developed through modifying the known smoothness indicators of WENO-JS. Recently a smoothness indicator based on \(L^1\)-norm has been proposed by Ha et al. (J Comput Phys 232:68–86, 2013) (denoted by WENO-NS). The aim of this paper is twofold. Firstly, we further improve the smoothness indicator of WENO-NS and secondly, using this measurement, we suggest new nonlinear weights by simplifying WENO-NS weights. The proposed WENO scheme provides the fifth-order accuracy, even at critical points. Some numerical experiments are provided to demonstrate that the present scheme performs better than other WENO schemes of the same order.

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Titel: Modified Non-linear Weights for Fifth-Order Weighted Essentially Non-oscillatory Schemes
verfasst von: Chang Ho Kim
Youngsoo Ha
Jungho Yoon
Publikationsdatum: 08.08.2015
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-015-0079-3

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