Construction of Third-Order WNND Scheme and Its Application in Complex Flow
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摘要: 引入Liu的加权(weight)思想，在NND格式的二阶模板基础上，构造了空间三阶精度的WNND格式．通过对线性波动方程、一维Euler方程和三维Navier-Stokes方程的数值模拟表明：WNND格式在不增加模板插值点的前提下,在对各种间断的分辨率和收敛特性等方面均优于NND格式．采用WNND格式对升力体外形高超声速流场数值模拟表明：升力体外形三维流场结构十分复杂，攻角从0°～50°变化时，背风面表面极限流线依次由不分离、开式分离向起始于鞍、结点组合的高阶奇点的分离方式转化，翼面横向分离亦随攻角增大而增大；垂直于体轴的横截面流动拓扑结构与张涵信给出的理论分析一致，大于20°攻角后，在部分横截面背风对称线上出现结构不稳定的鞍点相连现象．Abstract: According to the Liu's weighted idea,a space third-order WNND scheme was constructed based on the stencils of second-order NND scheme.It was applied in solving linear-wave equation,1D Euler equations and 3D Navier-Stokes equations.The numerical results indicate that the WNND scheme which doesn't increase interpolated point(compared to NND scheme) has more advantages in simulating discontinues and convergence than NND scheme.Appling WNND scheme to simulating the hypersonic flow around lift-body shows:With the AoA(angle of attack) increasing from 0° to 50°,the structure of limiting streamline of leeward surface changes from unseparating,open-separating to separating,which occurs from the combined-point(which consists of saddle and node points).The separating area of upper wing surface is increasing with the AoA's increasing.The topological structures of hypersonic flowfield based on the sectional flow patterns perpendicular to the body axis agree well with ZHANG Han-xin's theory.Additionally,the unstable-structure phenomenon which is showed by two saddles connection along leeward symmetry line occurs at some sections when the AoA is bigger than 20°.
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