Solving heat transfer problems of bodies with moving boundaries using the statistical modeling method

A numerical and statistical method for solving heat exchange problems of bodies with moving boundaries is offered in the paper. It is assumed that heat transfer in a problem of this type is described quit well by a boundary value problem for 2D heat equation with moving boundary. The offered method is based on the probabilistic representation of the solution of the boundary value problem in the form of mathematical expectation of a functional of a random process of the diffusion type. Calculation of the approximate solution of the problem is reduced to the numerical modeling of a large number trajectories of the random process. As result, we have a statistical evaluation of its solution. The method uses a piecewise linear approximation of the moving boundary. In the process of modeling the trajectories at each time step, the spatial variables are transformed in such a way that the trajectories are calculated in a domain with a fixed boundary. The paper considers the application of the proposed method to the problems of melting the ice plate and icing of the aircraft wing.