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

Chang Ho Kim, Youngsoo Ha, Jungho Yoon

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66 Scopus citations


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 (Formula presented.) -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.

Original languageEnglish
Pages (from-to)299-323
Number of pages25
JournalJournal of Scientific Computing
Issue number1
StatePublished - 1 Apr 2016

Bibliographical note

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© 2015, Springer Science+Business Media New York.


  • Approximation order
  • Euler equation
  • Hyperbolic conservation laws
  • Smoothness indicator
  • WENO scheme


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