In this research, a new method called elastic surface algorithm is presented for inverse design of 2-D airfoil in a viscous flow regime. In this method as an iterative one, airfoil walls are considered as flexible curved beams. The difference between the target and the current pressure distribution causes the flexible beams to deflect at each shape modification step. In modification shape algorithm, the finite element equations of two-node Timoshenko beam are solved to calculate the deflection of the beams. In order to validate the proposed method, various airfoils in subsonic and transonic regimes are studied, which show the robustness of the method in the viscous flow regime with separation and normal shock. Also, three design examples are presented here, which show the capability of the proposed method.


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