三阶WENO-Z格式精度分析及其改进格式  

Precision Analysis of the 3rd-Order WENO-Z Scheme and Its Improved Scheme

作　　者：徐维铮[1,2] 吴卫国[1,2] XU Weizheng;WU Weiguo(Laboratory of High Performance Ship Technology of Ministry of Education,Wuhan University of Technology,Wuhan 430063,P.R.China;Department of Naval Architecture,Ocean and Structural Engineering,School of Transportation,Wuhan University of Technology,Wuhan 430063,P.R.China)

机构地区：[1]武汉理工大学高性能舰船技术教育部重点实验室,武汉430063 [2]武汉理工大学交通学院船舶海洋与结构工程系,武汉430063

出　　处：《应用数学和力学》2018年第8期946-960,共15页Applied Mathematics and Mechanics

基　　金：国防基础研究项目(B1420133057);国家自然科学基金(51409202);中央高校基本科研业务费(2016-YB-016)~~

摘　　要：首先通过理论推导给出了三阶WENO格式(WENO-JS3格式)满足收敛精度的充分条件.采用Taylor(泰勒)级数展开的方法,分析发现传统的三阶WENO-Z格式(WENO-Z3格式)在光滑流场极值点处精度降低.为了提高WENO-Z3格式在极值点处的计算精度,根据收敛精度的充分条件构造一种改进的三阶WENO-Z格式(WENO-NZ3格式),并综合权衡计算精度和计算稳定性确定所构造格式的参数.通过两个典型的精度测试,验证了WENO-NZ3格式在光滑流场极值点区域逼近三阶精度.选用Sod激波管、激波与熵波相互作用、Rayleigh-Taylor不稳定性、二维Riemann(黎曼)问题经典算例,进一步证实了本文提出的WENO-NZ3格式相较其他格式(WENO-JS3、WENOZ3、WENO-N3),不仅提高了计算精度,而且提高了对复杂流场结构的分辨率.Firstly,the sufficient conditions for the 3 rd-order WENO scheme satisfying the convergence precision were deduced. Based on the Taylor series method,the precision of the conventional 3 rd-order WENO-Z scheme in the smooth flow field was analyzed. It was found that at the critical points,the 3 rd-order WENO-Z scheme fails to achieve the convergence precision. In order to improve the precision near the critical points for the 3 rd-order WENO-Z scheme,an improved 3 rd-order WENO-Z scheme（ WENONZ3） was constructed in view of the balance between precision and stability to finally determine the parameters. The improvement of the precision was verified through 2 typical numerical tests. What is more,the Sod shock wave tube,the shock-entropy wave interaction,the Rayleigh-Taylor instability and the 2 D Riemann problem were calculated to confirm that the WENO-NZ3 scheme performs better than the conventional WENO schemes like WENO-JS3,WENO-Z3 and WENO-N3.

关 键 词：三阶WENO格式 光滑因子 TAYLOR展开 高精度 高分辨率 双曲守恒律 

分 类 号：O357.1[理学—流体力学]