Precision Analysis of the 3rd-Order WENO-Z Scheme and Its Improved Scheme

XU Weizheng; WU Weiguo

doi:10.21656/1000-0887.390011

Volume 39 Issue 8

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XU Weizheng, WU Weiguo. Precision Analysis of the 3rd-Order WENO-Z Scheme and Its Improved Scheme[J]. Applied Mathematics and Mechanics, 2018, 39(8): 946-960. doi: 10.21656/1000-0887.390011

Citation:

XU Weizheng, WU Weiguo. Precision Analysis of the 3rd-Order WENO-Z Scheme and Its Improved Scheme[J]. Applied Mathematics and Mechanics, 2018, 39(8): 946-960. doi: 10.21656/1000-0887.390011

Citation:

XU Weizheng, WU Weiguo. Precision Analysis of the 3rd-Order WENO-Z Scheme and Its Improved Scheme[J]. Applied Mathematics and Mechanics, 2018, 39(8): 946-960. doi: 10.21656/1000-0887.390011

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Precision Analysis of the 3rd-Order WENO-Z Scheme and Its Improved Scheme

doi: 10.21656/1000-0887.390011

XU Weizheng^1,2,
WU Weiguo^1,2

¹Key Laboratory of High Performance Ship Technology of Ministry of Education, Wuhan University of Technology, Wuhan 430063, P.R.China;²Department of Naval Architecture, Ocean and Structural Engineering, School of Transportation, Wuhan University of Technology, Wuhan 430063, P.R.China

Funds: The National Natural Science Foundation of China(51409202)

Received Date: 2018-01-03
Rev Recd Date: 2018-01-29
Publish Date: 2018-08-15

Abstract

Abstract

Firstly, the sufficient conditions for the 3rd-order WENO scheme satisfying the convergence precision were deduced. Based on the Taylor series method, the precision of the conventional 3rd-order WENO-Z scheme in the smooth flow field was analyzed. It was found that at the critical points, the 3rd-order WENO-Z scheme fails to achieve the convergence precision. In order to improve the precision near the critical points for the 3rd-order WENO-Z scheme, an improved 3rd-order WENO-Z scheme (WENO-NZ3) was constructed in view of the balance between precision and stability to finally determine the parameters. The improvement of the precision was verified through 2 typical numerical tests. What is more, the Sod shock wave tube, the shock-entropy wave interaction, the Rayleigh-Taylor instability and the 2D Riemann problem were calculated to confirm that the WENO-NZ3 scheme performs better than the conventional WENO schemes like WENO-JS3, WENO-Z3 and WENO-N3.
- 3rd-order WENO scheme,
- smoothness indicator,
- Taylor expansion,
- high precision,
- high resolution,
- hyperbolic conservation law

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References(29)

References

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