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| A third-order WENO-Z scheme for improving the convergence order near the critical points |
| Received:January 01, 2018 Revised:April 27, 2018 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20180101001 |
| KeyWord:third-order WENO scheme smoothness indicators high precision high resolution hyperbolic conservation law |
| Author | Institution |
| 徐维铮 |
武汉理工大学 高性能舰船技术教育部重点实验室, 武汉 ;武汉理工大学 交通学院 船舶、海洋与结构工程系, 武汉 |
| 吴卫国 |
武汉理工大学 高性能舰船技术教育部重点实验室, 武汉 ;武汉理工大学 交通学院 船舶、海洋与结构工程系, 武汉 |
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| Abstract: |
| In order to improve the convergence of the conventional third-order WENO-Z scheme at the critical points,the sufficient conditions for satisfying the convergence of the third-order WENO scheme are firstly derived.The expressions of the non-linear weights are derived from a Taylor series expansion.Then the parameters of the constructed scheme are finally determined considering the balance between the convergence precision and the computational stability.The accuracy tests prove that the proposed scheme almost converges to the third-order precision in a smooth flow field near the critical points.Shock-entropy wave test,Richtmyer-Meshkov instability and some other classic examples are computed to verify that the improved scheme WENO-PZ3 can give more accurate and higher-resolution results of the complex flow field structures compared with other WENO schemes like the WENO-JS3,and WENO-Z3. |