摘要
高精度、高分辨率激波捕捉格式对含激波流场的数值模拟具有重要意义。为了提高三阶WENO-Z格式在极值点处的计算精度,首先通过理论推导给出三阶WENO格式满足收敛精度的充分条件。采用泰勒级数展开的方式,推导确定所构造格式的参数。通过精度测试证明改进格式在光滑流场区域能收敛到三阶精度。选用Sod激波管、Rayleigh-Taylor不稳定性等经典算例证实了提出的改进格式WENO-NN3相较其他格式(WENO-SJ3、WENO-Z3和WENO-N3)具有精度高、耗散低、对流场结构分辨率高的特性。
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.
作者
徐维铮
吴卫国
XU Weizheng;WU Weiguo(Key Laboratory of High Performance Ship Technology of Ministry of Education, Wuhan University of Technology ,Wuhan 430063 ,China;Departments of Naval Architecture,Ocean and Structural Engineering ,School of Transportation , Wuhan University of Technology , Wuhan 430063, China)
出处
《高压物理学报》
EI
CAS
CSCD
北大核心
2018年第3期27-35,共9页
Chinese Journal of High Pressure Physics
基金
装备预研教育部联合基金(青年人才)(6141A020331)
国家自然科学基金(51409202)
中央高校基本科研业务费(2016-YB-016)
关键词
三阶WENO格式
光滑因子
高精度
高分辨率
双曲守恒律
third-order WENO scheme
smoothness indicators
high precision
high resolution
hyperbolic conservation law
