An Improved Third-Order WENO-Z Scheme for Achieving Optimal Order near Critical Points and Its Application

XU Weizheng; WU Weiguo

doi:10.11858/gywlxb.20170696

Volume 32 Issue 3

Apr 2018

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Chinese Journal of High Pressure Physics > 2018 > 32(3): 032302.

XU Weizheng, WU Weiguo. An Improved Third-Order WENO-Z Scheme for Achieving Optimal Order near Critical Points and Its Application[J]. Chinese Journal of High Pressure Physics, 2018, 32(3): 032302. doi: 10.11858/gywlxb.20170696

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XU Weizheng, WU Weiguo. An Improved Third-Order WENO-Z Scheme for Achieving Optimal Order near Critical Points and Its Application[J]. Chinese Journal of High Pressure Physics, 2018, 32(3): 032302. doi: 10.11858/gywlxb.20170696

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An Improved Third-Order WENO-Z Scheme for Achieving Optimal Order near Critical Points and Its Application

doi: 10.11858/gywlxb.20170696

XU Weizheng^{1, 2
,},
WU Weiguo^{1, 2,*
,
,}

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

Received Date: 29 Dec 2017
Rev Recd Date: 11 Feb 2018

Abstract

Abstract

A high-precision and resolution shock capturing scheme is of great significance for numerical simulation of the complex flow field containing shock waves.In this study, to improve the convergence accuracy of the conventional third-order WENO-Z scheme at the critical points, we firstly derived the sufficient conditions for satisfying the convergence precision of the third-order WENO scheme from the theoretical derivation, then determined the parameters of the constructed scheme using the Taylor series expansion for satisfying the sufficient conditions, and proved using the accuracy test that the proposed scheme converges to the third order precision in smooth flow field including the critical points.Furthermore, we selected the Sod shock tube, the Rayleigh-Taylor instability and some other classic examples, verifying that the improved scheme WENO-NN3 was capable of giving more precision and high resolution results of the complex flow field structures compared with other WENO schemes such as the WENO-JS3, WENO-Z3, and WENO-N3.
- third-order WENO scheme,
- smoothness indicators,
- high precision,
- high resolution,
- hyperbolic conservation law

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References

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An Improved Third-Order WENO-Z Scheme for Achieving Optimal Order near Critical Points and Its Application

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