An improved weighted essentially non-oscillatory scheme with a new smoothness indicator

Youngsoo Ha, Chang Ho Kim, Yeon Ju Lee, Jungho Yoon

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In this paper, we present a new smoothness indicator that evaluates the local smoothness of a function inside of a stencil. The corresponding weighted essentially non-oscillatory (WENO) finite difference scheme can provide the fifth convergence order in smooth regions, especially at critical points where the first derivative vanishes (but the second derivatives are non-zero). We provide a detailed analysis to verify the fifth-order accuracy. Some numerical experiments are presented to demonstrate the performance of the proposed scheme. We see that the proposed WENO scheme provides at least the same or improved behavior over the fifth-order WENO-JS scheme [10] and other fifth-order WENO schemes called as WENO-M [9] and WENO-Z [2], but its advantage seems more salient in two dimensional problems.

Original languageEnglish
Pages (from-to)68-86
Number of pages19
JournalJournal of Computational Physics
Issue number1
StatePublished - 1 Jan 2013

Bibliographical note

Funding Information:
The authors are very grateful to the anonymous referee for the valuable suggestion on this paper. This work was supported by Basic Science Research Program 2010–0011689 (Y. Lee) and Priority Research Centers Program 2011–0022979 (Y. Lee, J. Yoon), through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology .


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


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