A generalized variational principle of 2D unsteady compressible flow around oscillating airfoils is established directly from the governing equations and boundary/initial conditions via the semi‐inverse method proposed by He. In this method, an energy integral with an unknown F is used as a trial‐functional. The identification of the unknown F is similar to the identification of the Lagrange multiplier. Based on the variational theory with variable domain, a variational principle for the inverse problem (given as the time‐averaged pressure over the airfoil contour, while the corresponding airfoil shape is unknown) is constructed, and all the boundary/initial conditions are converted into natural ones, leading to well‐posedness and the unique solution of the inverse problems.
He, J. (2000), "Inverse problems of determining the unknown shape of oscillating airfoils in compressible 2D unsteady flow via variational technique", Aircraft Engineering and Aerospace Technology, Vol. 72 No. 1, pp. 18-24. https://doi.org/10.1108/00022660010308633
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