A 3rd-Order WENO Scheme for Stencil Smoothness Indicators Based on Mapping

WANG Yahui; GUO Cheng; DU Yulong

doi:10.21656/1000-0887.450150

Volume 46 Issue 3

Mar. 2025

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Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(3): 394-411

WANG Yahui, GUO Cheng, DU Yulong. A 3rd-Order WENO Scheme for Stencil Smoothness Indicators Based on Mapping[J]. Applied Mathematics and Mechanics, 2025, 46(3): 394-411. doi: 10.21656/1000-0887.450150

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A 3rd-Order WENO Scheme for Stencil Smoothness Indicators Based on Mapping

doi: 10.21656/1000-0887.450150

WANG Yahui^{1
,
,},
GUO Cheng^1
,,
DU Yulong^2
,

1.
School of Mathematics and Statistics, Zhengzhou Normal University, Zhengzhou 450044, P.R.China
2.
School of Science, Jiangsu Ocean University, Lianyungang, Jiangsu 222005, P.R.China

Received Date: 2024-05-21
Rev Recd Date: 2024-07-06
Publish Date: 2025-03-01

Abstract

Abstract

The key to whether the WENO scheme can achieve optimal convergence accuracy and maintain essential no-oscillation characteristics near discontinuities lies in the construction of smoothness indicators. The smoothness indicator of the 3rd-order WENO scheme was modified through the construction of a mapping function to correct the smoothness indicators on each candidate stencil with the smoothest indicator. Under the influence of this mapping function, the smoothness indicator of the under-smooth stencil was reduced, thereby the nonlinear weight of the under-smooth stencil was increased. Then the numerical dissipation of the scheme was significantly lowered and its resolution was improved. A series of numerical examples demonstrate that, the new 3rd-order WENO scheme for smoothness indicators based on mapping has higher resolution than the classical WENO-JS3 and WENO-Z3 schemes.
- hyperbolic conservation law,
- WENO,
- mapping,
- smoothness indicator,
- nonlinear weight

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References(27)

References

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