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<p>The WENO-S schemes have shown superior performance in various problems due to the incorporation of S-type smoothness indicators. However, the development of three-point S-type smoothness indicators is currently not feasible, which has impeded the expansion of the WENO-S scheme to five- and six-point schemes. A novel six-point WENO scheme, which can be considered as a generalized WENO-S scheme, is developed by introducing a coefficient <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3130_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(q_{i}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>q</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation> into the nonlinear weight formula of a six-point symmetric WENO scheme. This modification results in the same approximated dispersion relation (ADR) as the sixth-order central scheme, indicating excellent dispersion properties and minimal dissipation. In practical applications, the scheme exhibits a moderate level of dissipation which is necessary for numerical simulation. Furthermore, it does not employ any free parameters and can achieve sixth-order of accuracy in continuous regions. Numerical tests validate that this scheme offers favorable resolution in continuous regions and maintains good stability near discontinuities.</p>

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A sixth order extension of WENO-S scheme

  • 期刊论文

  • 发表日期：

    2025年2月15日

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  • Conghai Wu,
  • Yong Luo,
  • Hu Li,
  • Shuaibin Han,
  • Yimin Wang

摘要

The WENO-S schemes have shown superior performance in various problems due to the incorporation of S-type smoothness indicators. However, the development of three-point S-type smoothness indicators is currently not feasible, which has impeded the expansion of the WENO-S scheme to five- and six-point schemes. A novel six-point WENO scheme, which can be considered as a generalized WENO-S scheme, is developed by introducing a coefficient \(q_{i}\) q i into the nonlinear weight formula of a six-point symmetric WENO scheme. This modification results in the same approximated dispersion relation (ADR) as the sixth-order central scheme, indicating excellent dispersion properties and minimal dissipation. In practical applications, the scheme exhibits a moderate level of dissipation which is necessary for numerical simulation. Furthermore, it does not employ any free parameters and can achieve sixth-order of accuracy in continuous regions. Numerical tests validate that this scheme offers favorable resolution in continuous regions and maintains good stability near discontinuities.