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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:
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:国家自然科学基金项目(青年项目)
作者单位E-mail
徐丽 上海电力学院 xulimaths@163.com 
姜明洋 上海电力学院  
蔡静静 上海电力学院  
吴硕 上海电力学院  
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中文摘要:
      为更准确捕捉复杂流场的流动细节,本文通过对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会不同,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 obtain 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, second-order derivative are constructed, so that the WENO scheme has fifth-order accuracy at the extreme value. 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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