混合动理学通量WENO方法拓展  

An extension of hybrid kinetic WENO method

作　　者：何康 李新亮[1,2] 刘洪伟 HE Kang;LI Xinliang;LIU Hongwei(State Key Laboratory of High Temperature Gas Dynamics,Institute of Mechanics,Chinese Academy of Sciences,Beijing 100190,China;School of Engineering Science,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院力学研究所高温气体动力学国家重点实验室,北京100190 [2]中国科学院大学工程科学学院,北京100049

出　　处：《航空学报》2022年第1期46-62,共17页Acta Aeronautica et Astronautica Sinica

基　　金：国家重点研发计划(2019YFA0405300,2016YFA0401200);国家自然科学基金(91852203,11472278)。

摘　　要：对基于气体动理论的高精度WENO方法进行了拓展研究,将Int.J.Numer.Meth.Fluids 79(6),290-305(2015)中提出的5阶混合动理学通量WENO方法进一步拓展到7阶和9阶;在5阶混合动理学WENO方法框架下,比较了采用不同激波探测技术的计算准确度和效率。在时间方向采用三阶Runge-Kutta方法进行推进,空间离散采用混合动理学通量WENO方法。通过一维和二维算例,验证了构造的7阶和9阶混合动理学方法比传统的矢通量分裂技术具有更高的分辨率和更小的数值耗散,并保持了较好的激波捕捉能力;对比发现Ohwada等提出的激波探测技术具备良好的激波探测能力和计算效率。An extension of the high-order WENO methods based on the gas-kinetic theory is carried out.The hybrid kinetic WENO method proposed in Int.J.Numer.Meth.Fluids 79(6),290-305(2015)is further extended to the 7th-order and the 9th-order cases.Within the framework of the 5th-order hybrid kinetic WENO method,the computational accuracy and efficiency of different shock detection techniques are compared.The TVD Runge-Kutta method is used for temporal integration,and the hybrid kinetic WENO method is employed for spatial discretization.Both one-dimensional and two-dimensional numerical examples are presented to show that the extended hybrid kinetic methods have higher resolution and less numerical dissipation than the traditional flux vector splitting technique,and can also have good shock-capturing ability.It is also found that the shock detection technology proposed by Ohwada et al.has good shock-detection ability and computational efficiency.

关 键 词：WENO重构 气体动理论 高阶方法 数值耗散 激波探测技术 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]