A numerical model based on variational principle for airfoil and wing aerodynamics

Over the last few years, finite element algorithms for solution of the Euler flow equations have gained increased popularity. The objective of the current research is to develop a new method to solve the Euler flow equations numerically using a variational technique for airfoil and wing aerodynamics. A new formulation of Eularian variational principle satisfying the Kutta condition is suggested, and a numerical implementation is presented. The proposed method can obtain improved solution, especially for complicated geometries. A computer code named FLUIDEX was developed to analyze barotropic fluid dynamics. The solution of the flow problem is obtained by using numerical algorithm to find the extremum value of an "Action" i.e. by a variational principle. Predictions of the FLUIDEX numerical model were analyzed for particular cases of potential flow (compressible and incompressible). The results were successfully compared against exact analytical solutions for potential flow test problems. The proposed method obtains fast and stable solutions without the need to integrate the equations in time and space, and thus enables a considerable reduction of the time and cost of the solution.