An Improved 3rd-Order WENO-Z Type Scheme

WANG Jianling; LI Xiaogang; WANG Wenshuai

doi:10.21656/1000-0887.410203

Volume 42 Issue 4

Apr. 2021

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WANG Jianling, LI Xiaogang, WANG Wenshuai. An Improved 3rd-Order WENO-Z Type Scheme[J]. Applied Mathematics and Mechanics, 2021, 42(4): 394-404. doi: 10.21656/1000-0887.410203

Citation:

WANG Jianling, LI Xiaogang, WANG Wenshuai. An Improved 3rd-Order WENO-Z Type Scheme[J]. Applied Mathematics and Mechanics, 2021, 42(4): 394-404. doi: 10.21656/1000-0887.410203

Citation:

WANG Jianling, LI Xiaogang, WANG Wenshuai. An Improved 3rd-Order WENO-Z Type Scheme[J]. Applied Mathematics and Mechanics, 2021, 42(4): 394-404. doi: 10.21656/1000-0887.410203

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An Improved 3rd-Order WENO-Z Type Scheme

doi: 10.21656/1000-0887.410203

¹China University of Mining and Technology Yinchuan College, Yinchuan 750021, P.R.China
²School of Civil and Hydraulic Engineering, Ningxia University, Yinchuan 750021, P.R.China
³School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P.R.China

Funds: The National Natural Science Foundation of China（42064004）

Received Date: 2020-07-08
Rev Recd Date: 2020-10-28
Publish Date: 2021-04-01

Abstract

Abstract

Based on the high-order global smoothness factor, a low-dissipation and high-resolution 3rd-order WENO difference scheme was obtained under the WENO-Z scheme framework. A parameter was introduced in the nonlinear weight, the parameter range was determined by convergence analysis, and the optimal parameter value was obtained with combined accuracy and non-oscillation. The scheme can maintain expected 3rd-order accuracy at the 1st-order extremum of the function. Finally, the accuracy recovery of the scheme at various extremum points was verified with exact solution examples, and the low-dissipation and high-resolution characteristics of the scheme were tested with the 1D and 2D Euler equations. The results show that, the proposed scheme is a good shock-capturing method.
- WENO scheme,
- low dissipation,
- high resolution,
- global smoothness factor

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References(21)

References

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