A third-order WENO scheme based on exponential polynomials for Hamilton-Jacobi equations

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

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this study, we provide a novel third-order weighted essentially non-oscillatory (WENO) method to solve Hamilton-Jacobi equations. The key idea is to incorporate exponential polynomials to construct numerical fluxes and smoothness indicators. First, the new smoothness indicators are designed by using the finite difference operator annihilating exponential polynomials such that singular regions can be distinguished from smooth regions more efficiently. Moreover, to construct numerical flux, we employ an interpolation method based on exponential polynomials which yields improved results around steep gradients. The proposed scheme retains the optimal order of accuracy (i.e., three) in smooth areas, even near the critical points. To illustrate the ability of the new scheme, some numerical results are provided along with comparisons with other WENO schemes.

Original languageEnglish
Pages (from-to)167-183
Number of pages17
JournalApplied Numerical Mathematics
Volume165
DOIs
StatePublished - Jul 2021

Keywords

  • Approximation order
  • Exponential polynomials
  • Exponential vanishing moment
  • Hamilton-Jacobi equation
  • Smoothness indicators
  • WENO scheme

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