A new adaptive weighted essentially non-oscillatory WENO-θ scheme for hyperbolic conservation laws

Chang Yeol Jung, Thien Binh Nguyen

Research output: Contribution to journalArticleResearchpeer-review

Abstract

A new adaptive weighted essentially non-oscillatory WENO-θ scheme in the context of finite difference is proposed. Depending on the smoothness of the large stencil used in the reconstruction of the numerical flux, a parameter θ is set adaptively to switch the scheme between a 5th-order upwind and 6th-order central discretization. A new indicator τθ measuring the smoothness of the large stencil is chosen among two candidates which are devised based on the possible highest-order variations of the reconstruction polynomials in L2 sense. In addition, a new set of smoothness indicators β̃k of the substencils is introduced. These are constructed in a central sense with respect to the Taylor expansions around the point xj. Numerical results show that the new scheme outperforms other comparing 6th-order WENO schemes in terms of improving the resolution at critical regions of nonsmooth problems as well as maintaining symmetry in the solutions.

Original languageEnglish
Pages (from-to)314-339
Number of pages26
JournalJournal of Computational and Applied Mathematics
Volume328
DOIs
Publication statusPublished - 15 Jan 2018

Keywords

  • Adaptive upwind-central schemes
  • Euler equations
  • Hyperbolic conservation laws
  • Shock-capturing methods
  • Smoothness indicators
  • Weighted essentially non-oscillatory (WENO) schemes

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