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

Title
Modified Non-linear Weights for Fifth-Order Weighted Essentially Non-oscillatory Schemes
Authors
Kim, Chang HoHa, YoungsooYoon, Jungho
Ewha Authors
윤정호
SCOPUS Author ID
윤정호scopus
Issue Date
2016
Journal Title
JOURNAL OF SCIENTIFIC COMPUTING
ISSN
0885-7474JCR Link1573-7691JCR Link
Citation
vol. 67, no. 1, pp. 299 - 323
Keywords
Hyperbolic conservation lawsEuler equationWENO schemeApproximation orderSmoothness indicator
Publisher
SPRINGER/PLENUM PUBLISHERS
Indexed
SCIE; SCOPUS WOS scopus
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.
DOI
10.1007/s10915-015-0079-3
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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