Abstract: In order to research the effects of different principle direction defined methods based on the multidimensional inviscid flux reconstruction on the stability of shock wave and pressure field， the analysis for the results in which the principle direction defined method based on Cartesian directions， density gradient and pressure gradient indicates that the non-physical ‘zigzag’ pressure contour occurs in the flowfield when the principle direction only relying on the gradient of physical quantities. In order to avoid this nonphysical phenomena， a new hybrid method based on pressure function is employed to define the principle direction. The simulation results for cylinder with single cell and ten rows of spanwise cells show that the hybrid method has better performance than other methods. The developed hybrid method not only eliminates the carbuncle phenomenon which occurs in the result solved by the principle direction based on Cartesian directions， but also removes the pressure contour ‘zigzag’ phenomenon which occurs in the result solved by the principle direction based on the gradient of density or pressure. The relative error of heat flux at stagnation point is 29.2% for the grid-align scheme by comparing with the result of structured grid solver， while this data is 4.0% for the multidimensional scheme by hybrid principle defined method. Therefore， it shows that the surface heat flux evaluated by the hybrid defined method for principle direction is reasonable.

Key words: Multidimensional inviscid flux reconstruction；Unstructured grid；Aero-heating；Principle direction

摘要： 为了研究多维对流通量重构格式中不同形式主方向对激波稳定性、压力场计算方面的影响，分别采用以笛卡尔方向、密度梯度及压力梯度作为主方向进行计算，对结果分析后发现，单纯依赖物理量梯度的主方向会造成压力等值线曲折的非物理解。为了消除这种非物理现象，采用一种基于压力函数的混合方式来确定主方向。单层及展向多层高超声速圆柱绕流问题模拟分析的结果表明:混合方式所确定的主方向不仅可以消除笛卡尔坐标系确定的主方向计算带来的红玉现象，同时还可以消除单纯的密度或压力梯度作为主方向所带来的压力场“zigzag”的非物理现象；通过与结构网格结果的比较表明:网格相关格式驻点处热流的相对误差为29.2%，而混合主方向确定方法所计算驻点热流相对误差只为4%，表明此改进方法计算得到的壁面热流是合理的。

关键词: 多维对流通量重构；非结构网格；气动热；主方向