This paper deals with the mathematical and numerical analysis of a
simplified two-dimensional model for the interaction between the wind
and a sail. The wind is modeled as a steady irrotational plane flow past
the sail, satisfying the Kutta-Joukowski condition. This condition
guarantees that the flow is not singular at the trailing edge of the
sail. Although for the present analysis the position of the sail is
taken as data, the final aim of this research is to develop tools to
compute the sail shape under the aerodynamic pressure exerted by the
wind. This is the reason why we propose a fictitious domain formulation
of the problem, involving the wind velocity stream function and a
Lagrange multiplier; the latter allows computing the force density
exerted by the wind on the sail. The Kutta-Joukowski condition is
imposed in integral form as an additional constraint. The resulting
problem is proved to be well posed under mild assumptions. For the
numerical solution, we propose a finite element method based on
piecewise linear continuous elements to approximate the stream function
and piecewise constant ones for the Lagrange multiplier. Error estimates
are proved for both quantities and a couple of numerical tests
confirming the theoretical results are reported. Finally the method is
used to determine the sail shape under the action of the wind.