非结构网格上的TV-van Leer混合迎风格式  

Hybrid TV-van Leer upwind scheme on unstructured grids

作　　者：张帆[1] 张力丹[1] 刘君[1] 陈飙松[1] ZHANG Fan;ZHANG Lidan;LIU Jun;CHEN Biaosong(State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室

出　　处：《空气动力学学报》2019年第5期855-863,共9页Acta Aerodynamica Sinica

基　　金：国家重点研发计划项目（2016YFB0200702）;国家自然科学基金（11872144）

摘　　要：为了改进迎风型对流通量格式的激波捕捉计算稳定性,对迎风格式产生数值激波不稳定现象的原因进行分析,并且在分析结果基础上构造新型迎风型格式。为此,首先设计了数值算例,分析非结构网格上迎风格式出现数值激波不稳定现象的主要影响因素。结果表明,在一定条件下,网格和流动状态共同作用导致产生不合理的数值结果,并影响计算的稳定。其中,网格间的动量通量对数值激波不稳定现象影响显著。因此,基于TV格式构造了一种自适应调节动量通量耗散项的混合格式,从而在激波附近引入耗散,抑制扰动的产生和传播。数值计算结果显示新型混合格式在非结构网格离散条件下能够稳定地捕捉激波,同时混合格式保持了TV格式原有的黏性流动计算分辨率。In order to improve their numerical stability in shock-capturing computations,upwind flux schemes are analyzed to figure out the reason causing numerical shock instability,and a new hybrid upwind flux scheme is designed based on the analyses. Numerical test cases are specifically designed,for investigating the major factors which cause numerical shock instability of upwind schemes on unstructured grids. The test cases show that,in certain circumstance,inappropriate numerical results can be produced by the coeffect of grid discretization and flow condition,affecting the stability of computation. The numerical flux of momentum equations presents significant impact on numerical shock stability. Therefore,a hybrid scheme with adaptive dissipation term of momentum fluxes is designed based on TV scheme,and extra numerical dissipation can be introduced near shock wave,suppressing numerical perturbation. Numerical results show that,the new hybrid scheme is capable to stably capture shock wave on unstructured grids and remains the numerical resolution of the original TV scheme in simulating viscous flows.

关 键 词：迎风格式 激波捕捉 非结构网格 稳定性 混合格式 

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]