Embedded WENO: A design strategy to improve existing WENO schemes

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Abstract

Embedded WENO methods utilise all adjacent smooth substencils to construct a desirable interpolation. Conventional WENO schemes under-use this possibility close to large gradients or discontinuities. We develop a general approach for constructing embedded versions of existing WENO schemes. Embedded methods based on the WENO schemes of Jiang and Shu [1] and on the WENO-Z scheme of Borges et al. [2] are explicitly constructed. Several possible choices are presented that result in either better spectral properties or a higher order of convergence for sufficiently smooth solutions. However, these improvements carry over to discontinuous solutions. The embedded methods are demonstrated to be indeed improvements over their standard counterparts by several numerical examples. All the embedded methods presented have no added computational effort compared to their standard counterparts.

Original languageEnglish
Pages (from-to)529-549
Number of pages21
JournalJournal of Computational Physics
Volume330
DOIs
Publication statusPublished - 1 Feb 2017

Keywords

  • Essentially non-oscillatory
  • High-resolution scheme
  • Hyperbolic conservation laws
  • Nonlinear interpolation
  • Spectral analysis
  • WENO

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