Multipoint inverse shape design of airfoils based on variable‐domain variational principle

As a kind of free (unknown) boundary problem, inverse shape design of airfoils has attracted extensive attention in recent years. By variable‐domain variational theory, free boundary condition can be coupled with the governing equations for flow field, which makes it possible to calculate the flow field with the free boundary simultaneously. In this paper, the variational principle (VP) of 2D airfoil shape design problem is obtained from the basic dimensionless velocity potential equations for 2D compressible flow by using a systematic approach and variable‐domain variational formula. The deformable finite element method based on the VP is used to segmentally design airfoil at two design points (angles of attack) and four design points, respectively. The results show that the present method is highly effective and accurate for solving multipoint inverse problem of airfoils.