Aerodynamic Design of Airfoils Based on Variable-Domain Variational Finite Element Method

Designing airfoils according to given pressure (or velocity) distribution is one kind of free boundary problems. Free boundary condition can be coupled with the flow governing equations by variable-domain variational calculus, which makes it possible to calculate simultaneously the flow field and the free boundary. An accurate deduction of the variable-domain variational principles is taken herein to design airfoils in compressible and incompressible flows. Furthermore, two grid types (H and O) are used in the calculation with better results for the O-type grid. It is shown that convergence is accelerated and good results can be obtained even if the initial guessed airfoil shape is a triangle, demonstrating the strong adaptability of this method.