Numerical experiments on an ill-posed inverse problem for a given velocity around a hydrofoil by iterative and noniterative regularizations

For a given velocity distribution around a hydrofoil, the inverse problem of the hydrofoil is studied. The inverse problem is formulated by representing the hydrofoil in terms of vortices within the framework of linear potential theory. From the mathematical formulation, it is known that the inverse problem turns out to be ill-posed in the usual topology. In this paper, iterative and noniterative regularizations are applied to solve the problem and to find their suitability for the two-dimensional inverse hydrofoil problem. Numerical experiments demonstrate that the regularization methods are accurate and suitable for the inverse mathematical formulation for a given velocity distribution around a hydrofoil. Received: June 6, 2000 / Accepted: December 8, 2000