"Transferring the boundary conditions to the middle surface for the numerical solution of a boundary value problem in the linear wing theory"
Pisarev I.V. and Setukha A.V.

A three-dimensional boundary value problem is considered for the Laplace equation in the framework of an ideal incompressible fluid model in the linear theory of finite span wings. For the numerical solution of this problem, an approach based on the method of potentials and boundary integral equations is used. The thickness of the wing is taken into account in the formulation of the boundary value problem at the middle surface with transferring the boundary conditions to this surface. As a result, the problem is reduced to a system of two-dimensional singular integro-differential equations. A numerical method is proposed for solving these equations on the basis of the vortex-frame method. The efficiency of the proposed method is illustrated by the example of determining the pressure distribution along the surface of the wing.

Keywords: numerical methods, boundary value problems, Laplace equation, integral equations, vortex methods, theory of finite span wings.

  • Pisarev I.V. – Orlov State University, Faculty of Physics and Mathematics; ulitsa Komsomol’skaya 95, Orel, 302026, Russia;; Graduate Student, e-mail: demoruss@inbox.ru
  • Setukha A.V. – Research Computing Center, Lomonosov Moscow State University; Leninskie Gory, Moscow, 119992, Russia; Ph.D., Leading Scientist, e-mail: setuhaav@rambler.ru