| 徐丽,姜明洋,蔡静静,吴硕.无粘可压缩流动的改进高精度方法[J].计算力学学报,2019,36(6):784~791 |
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| 无粘可压缩流动的改进高精度方法 |
| One improved high accuracy scheme for compressible inviscid flow computation |
| 投稿时间：2018-11-13 修订日期：2018-12-13 |
| DOI：10.7511/jslx20181113003 |
| 中文关键词: 加权本质无振荡 WENO格式 光滑因子 高阶精度 可压缩流动 |
| 英文关键词:weighted essentially non-oscillatory WENO scheme smoothness indicators high order accuracy compressible flows |
| 基金项目:国家自然科学基金（11502141；11701359）资助项目. |
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| 中文摘要: |
| 为更准确捕捉复杂流场的流动细节，通过对WENO格式的光滑因子进行改进，发展了一种新的五阶WENO格式。对三阶ENO格式进行加权可以得到五阶WENO格式，但是不同的加权处理，WENO格式在极值处保持加权基本无振荡的效果不同，本文构造了二阶精度的局部光滑因子，及不含一阶二阶导数的高阶全局光滑因子，从而实现WENO格式在极值处有五阶精度。基于改进五阶WENO格式，对一维对流方程、一维和二维可压缩无粘问题进行算例验证，并与传统WENO-JS格式和WENO-Z格式进行比较。计算结果表明，改进五阶WENO格式有较高的精度和收敛速度，有较低的数值耗散，能有效捕捉间断、激波和涡等复杂流动。 |
| 英文摘要: |
| For more accurately capturing complex flows,a new fifth-order WENO scheme is developed by improving the smoothing factor of WENO scheme. Weighting the third-order ENO scheme can lead to a fifth-order WENO scheme,but with different weighting methods,the WENO scheme will have different effects of maintaining weighted essentially non-oscillatory schemes at extreme values. In this paper,the local smoothing factor of second-order accuracy and the high-order global smoothing factor without first-order or second-order derivative are constructed,so that the WENO scheme has fifth-order accuracy at the extreme values.Based on the improved fifth-order WENO scheme,the classical problems of one-dimensional convection equations,one-dimensional and two-dimensional Euler equations are verified by examples,and compared with the traditional WENO-JS scheme and WENO-Z scheme.The calculation results show that the improved fifth-order WENO scheme has higher accuracy and convergence speed,and can effectively capture complex flows such as discontinuities,shock waves and eddies with low dissipation. |
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