Sixth-order weighted essentially nonoscillatory schemes based on exponential polynomials

Youngsoo Ha, Chang Ho Kim, Hyoseon Yang, Jungho Yoon

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

The aim of this study is to develop a novel sixth-order weighted essentially nonoscillatory (WENO) finite difference scheme. To design new WENO weights, we present two important measurements: a discontinuity detector (at the cell boundary) and a smoothness indi- cator. The interpolation method is implemented by using exponential polynomials with tension parameters such that they can be tuned to the characteristics of the given data, yielding better approximation near steep gradients without spurious oscillations, compared to the WENO schemes based on algebraic polynomials at lower computational cost. A detailed analysis is performed to ver- ify that the proposed scheme provides the required convergence order of accuracy. Some numerical experiments are presented and compared with other sixth-order WENO schemes to demonstrate the new algorithm's ability.

Original languageEnglish
Pages (from-to)A1987-A2017
JournalSIAM Journal on Scientific Computing
Volume38
Issue number4
DOIs
StatePublished - 2016

Keywords

  • Convergence order
  • Euler equation
  • Hyperbolic conservation laws
  • Nonlinear weights
  • Smoothness indicator
  • WENO scheme

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