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| Precision analysis and improvement of third-order WENO scheme |
| Received:October 24, 2016 Revised:February 05, 2017 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20161024001 |
| KeyWord:third-order WENO scheme precision analysis high resolution low dissipation |
| 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 |
| 孔祥韶 |
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 |
| 郑成 |
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: |
| High resolution shock capturing schemes are of great significance for numerical simulation of flow fields containing shock waves.Precision of both WENO-JS3 scheme and WENO-Z3 scheme are firstly analyzed theoretically.It is indicated that the two schemes share the same accuracy in the smooth flow field including critical points and actually fail to achieve designed third-order convergence.However,WENO-Z3 scheme is better than WENO-JS3 scheme because of larger weight assignment to the discontinuous stencils.WENO-Z+3 scheme and its improved high-resolution schemes (WENO-Z+3P1,WENO-Z+3P32) are then proposed in present paper.And it is proved that the improved schemes can recover the designed-order convergence at critical points as well as other smooth flow fields theoretically.Several classical one-dimensional Riemann problems and double Mach reflection case are simulated based on the schemes discussed in this paper.The proposed WENO-Z+3 scheme and its improved schemes are proved to have better characteristics with low numerical dissipation and high resolution to the flow features. |
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