Variable-domain variational finite element solution of inverse problem of 2-D unsteady transonic flow around oscillating airfoils

In this paper, on the basis of the variational principles developed in Ref.[1], the finite element method (FEM) is employed for numerical solution of the inverse problem of 2-D unsteady transonic flow around oscillating airfoils, incorporating the non-reflecting far-field boundary conditions and a new unsteady Kutta condition[7]. All unknown boundary (airfoil contour) and discontinuities(shocks and free trailing vortex sheets) are handled(captured) via the functional variation with variable domain and artificial density concept. For the numerical realization of the variable-domain variation, a special finite element with self-adjusting nodes is also suggested herein. The numerical results show that the present method is effective for the design of unsteady airfoil.