高精度IPDG湍流模拟及通量格式数值特性  

High-precision IPDG based turbulence simulation and the numerical characteristics of flux schemes

作　　者：郝世熙 丁秋实 魏桐 刘正先[1] 刘伟[2] 李孝检 赵明[1] HAO Shixi;DING Qiushi;WEI Tong;LIU Zhengxian;LIU Wei;LI Xiaojian;ZHAO Ming(Department of Mechanics,School of Mechanical Engineering,Tianjin University,Tianjin 300350,China;School of Computer Science and Engineering,University of Electronic Science and Technology of China,Chengdu 611731,China)

机构地区：[1]天津大学机械工程学院,天津300350 [2]电子科技大学计算机科学与工程学院,成都611731

出　　处：《空气动力学学报》2023年第11期94-102,I0002,共10页Acta Aerodynamica Sinica

基　　金：国家自然科学基金(11972250,12102298);天津市自然科学基金(20JCQNJC01950)。

摘　　要：为更高精度数值求解复杂湍流问题,在内罚间断伽辽金(internal penalty discontinuous Galerkin,IPDG)方法框架内发展了基于SST k-ω模型的湍流模拟方法,通过对亚/跨/超声速工况下流场的数值计算与湍流特征捕捉,验证了方法的适用性,进而系统分析了AUSM、Lax-F、HLL和Roe 4种通量格式在IPDG湍流模拟中的数值特性。结果表明:AUSM格式在超声速工况下脱体激波面“褶皱”现象明显;Lax-F格式和HLL格式数值耗散大,在激波解析方面精度较低,且Lax-F格式在激波脚后诱导产生流动分离;Roe格式具备宽速域适用性,计算精度较高且能精确解析激波结构。In this study,the SST k-ωturbulence model is applied within the framework of the internal penalty discontinuous Galerkin(IPDG)method.The applicability of the method is verified by numerical simulations of the flow fields and the turbulence characteristics under subsonic,transonic and supersonic conditions.Based on the present method,the numerical characteristics of four different flux schemes(AUSM,Lax F,HLL and Roe)for the convection term in the weak form of the RANS equations with IPDG are systematically analyzed.The results show that,the AUSM scheme presents an obvious folding phenomenon on the detached shock surface under supersonic condition.The Lax-F and HLL schemes have large numerical dissipation and perform poorly in the shock wave analysis.Moreover,flow separation is induced after the shock surface in the Lax-F scheme.The Roe scheme has the applicability for a wide range of velocity,and presents a high calculation accuracy that can precisely resolve the shock structure.

关 键 词：间断伽辽金 内罚方法 通量格式 SST k-ω湍流模型 

分 类 号：O354[理学—流体力学]