基于变域变分有限元的翼型反设计

反问题作为一种自由(未知)边界问题近年来得到了广泛的研究。变域变分通过把自由边界结合在变分泛函中，使其与求解流场的控制方程结合起来，从而自由边界求解和流场分析可以完全耦合进行。本文采用变域变分和可变形有限元来设计可压缩和不可压缩翼型，计算显示即使在初始翼型的一侧为三角形时仍能得到满意的结果。文中还采用了两种计算网格(H型和O型)来设计翼型，比较了它们的精度，计算表明本方法完全能用于翼型的反设计。

Inverse design of airfoil based on variable-domain variational FEM

Inverse problems are widely discussed nowadays. Variable-domain variational principles can couple the variable domain into functional, which makes it possible to calculate the flow field with the variable-domain simultaneously. The variable-domain variational principle and variable finite element method are used hereinafter to design compressible and incompressible foils. The results show that even if the initial foil type is a triangle, it can still lead to good results. Furthermore, two grid types (H and O) are used in the calculation, which shows that the O-type grid can get better results. It can be seen from all the results that the present method is correct and highly applicable.