高精度WCNS格式加权策略改进与数值验证  

Improvement and Numerical Verification of Weighting Strategy for High Precision WCNS Scheme

作　　者：杨强 李伟鹏[1] YANG Qiang;LI Weipeng(School of Aeronautics and Astronautics,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学航空航天学院,上海200240

出　　处：《上海交通大学学报》2023年第6期719-727,共9页Journal of Shanghai Jiaotong University

基　　金：国家自然科学基金(92052101)资助项目。

摘　　要：为了揭示复杂的流动机理,国内外提出了一系列高阶精度格式,其中加权非线性紧致格式(WCNS)具有良好的激波捕捉能力,已广泛用于复杂流动数值模拟,然而在模拟小尺度流动时分辨率不足、耗散偏大.在WCNS的框架下,借鉴基于目标本质无振荡(TENO)格式的加权策略,将间断检测和模板加权的新方法引入WCNS构造中,发展了一种7阶精度的WCNS7-T格式,通过一维激波管问题和二维黎曼问题等开展算例测试,并与传统的WCNS7-Z格式计算结果进行对比来验证新格式的改善性能.数值实验表明,WCNS7-T格式更好地抑制了间断附近的数值振荡,在提高分辨率和激波捕捉能力的同时也进一步降低了耗散.In order to reveal the complex flow mechanism,a series of high-order precision schemes have been proposed at home and abroad,of which,the weighted compact nonlinear scheme(WCNS)has a good shock capture ability and has been widely used in the numerical simulation of complex flows.However,it has insufficient resolution and large dissipation in the simulation of small-scale flows.In the framework of the WCNS,by using the weighting strategy of the targeted essentially non-oscillatory(TENO)scheme for reference,this paper introduces the new methods of discontinuity detection and template weighting into the construction of the WCNS scheme,and develops a WCNS7-T scheme with a 7-order accuracy.Example tests are conducted through one-dimensional shock tube problem and two-dimensional Riemann problem.By comparing with the traditional WCNS7-Z scheme,the improved performance of the new scheme is verified.The numerical experiments show that the WCNS7-T scheme can better suppress the numerical oscillation near the discontinuity,improve the resolution and shock capture ability,and further reduce the dissipation.

关 键 词：可压缩流动 高精度格式 激波间断 非线性加权 

分 类 号：V211[航空宇航科学与技术—航空宇航推进理论与工程] O355[理学—流体力学]