一种提高极值点处收敛精度的三阶WENO-Z格式  

A third-order WENO-Z scheme for improving the convergence order near the critical points

作　　者：徐维铮[1,2] 吴卫国[1,2] XU Wei-zheng;WU Wei-guo(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)

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：《计算力学学报》2019年第2期261-266,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(51409202;51509196);中央高校基本科研业务费(2016-YB-016)资助项目

摘　　要：为了提高三阶WENO-Z格式在极值点处的计算精度,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,推导给出所构造格式非线性权重的计算公式,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,验证了改进格式在光滑流场极值点区域逼近三阶精度。进一步选用激波与熵波相互作用和Richtmyer-Meshkov不稳定性等经典算例,证实了本文提出的改进格式WENO-PZ3相较其他格式(WENO-JS3和WENO-Z3)不仅具有较高的精度,而且降低了格式的耗散,提高了对流场结构的分辨率。In order to improve the convergence of the conventional third-order WENO-Z scheme at the critical points,the sufficient conditions for satisfying the convergence of the third-order WENO scheme are firstly derived.The expressions of the non-linear weights are derived from a Taylor series expansion.Then the parameters of the constructed scheme are finally determined considering the balance between the convergence precision and the computational stability.The accuracy tests prove that the proposed scheme almost converges to the third-order precision in a smooth flow field near the critical points.Shock-entropy wave test,Richtmyer-Meshkov instability and some other classic examples are computed to verify that the improved scheme WENO-PZ3 can give more accurate and higher-resolution results of the complex flow field structures compared with other WENO schemes like the WENO-JS3,and WENO-Z3.

关 键 词：三阶WENO格式 光滑因子 高精度 高分辨率 双曲守恒律 

分 类 号：O357.1[理学—流体力学]