交互式棱柱网格生成中翘曲现象形成机制及消除算法

在基于径向基函数插值的交互式棱柱网格生成中，当物面网格单元空间法矢变化范围较大或变化剧烈时，棱柱网格生成会发生翘曲问题，降低棱柱网格质量。针对该问题，首先采用DLR-F6机翼外形算例对翘曲现象进行了介绍和初步分析，并结合平板外形棱柱网格生成，通过不同波长推进位移扰动模拟法矢变化对推进位移的影响，研究棱柱网格翘曲现象的形成机制。不同位移扰动下平板棱柱网格生成结果证实边界棱线网格点推进位移不光滑会通过空间插值放大，引起棱柱网格发生翘曲，且网格翘曲的表现形式与推进位移的分布有关。从而间接表明棱柱网格生成中翘曲现象是由法矢变化带来推进位移分布不光滑引起的。然后从翘曲现象的形成机制出发，基于拉普拉斯方法发展了推进位移光顺技术，并通过DLR-F6机翼算例进行了验证。测试结果表明，光顺技术能够完全消除棱柱网格的翘曲，获得光顺的高质量棱柱网格。最后通过DLR-F6翼身组合体外形棱柱网格生成，展示了添加光顺技术的棱柱网格生成算法的应用潜力。

Formation mechanism and elimination algorithm of warping in interactive prismatic grid generation

The prismatic grid warping may appear when the normal vectors of the surface grid element change considerably or fast in the interactive prismatic grid generation based on radial basis function interpolation, consequently reducing the quality of the prismatic grid. To solve this problem, this paper first introduced and analyzed the warping phenomenon through the prismatic grid generation of the DLR-F6 wing configuration. Then the formation mechanism was investigated by adding different wave-length disturbances to advancing displacement to simulate the effect of the normal vector variation in a flat plate prismatic grid generation case. The prismatic grid generation results of the flat plate with different disturbances demonstrate that the roughness of the advancing displacement could be magnified by spatial interpolation, thus causing the prismatic grid warping whose appearance depends on the distribution of the advancing displacement. The results above also show that the prismatic grid warping is induced by the roughness of the advancing displacement caused by the changes of normal vectors. Subsequently, a smoothing technology was developed based on the Laplace method inspired by the formation mechanism of grid warping and verified through the DLR-F6 wing configuration case. The test results show that the smoothing technology can completely eliminate the grid warping and obtain high-quality prismatic grids. Finally, the potentiality of the prismatic grid generation method with the smoothing technology was displayed through the grid generation case of the DLR-F6 wing-body configuration.