Numerical-Stochastic Method of Modeling the Aircraft Wing Icing in Flight

The paper proposes a numerical-stochastic method for determining the thermal state of an aircraft wing during flight under icing conditions. The method is based on the probabilistic representation of the boundary value problem for a parabolic equation and the numerical solution of stochastic differential equations. Navier–Stokes equations averaged by the Reynolds criterion are used. It is proposed to model the ice growths using a triangular grid in icing areas. A one-to-one transformation is introduced, which maps any movable triangle to a fixed isosceles right triangle, the legs of which are directed along the positive directions of the coordinate axes of the two-dimensional right-angle coordinate system. The results of the work make it possible to determine the probability of ice formation on a wing made of a certain material and having a selected profile under various flight modes and meteorological conditions.