Toward to usage of regularized Stefan problem solution in icing modeling

In 2019 Tong Liu and coauthors proposed the development of the Messinger-Myers models for modeling the icing of aircraft. Their proposal consists in replacing the quasi-stationary heat equation for the ice region with a non-stationary heat equation. In our work, we propose to consider the same replacement for the water film region also. Then in the region of ice and water film, the temperature is described by a unified equation of thermal conductivity with discontinuous coefficients at the interface is known as Stefan problem. Stefan problem is a fundamental problem describing phenomena in phase transitions of substance. It was investigated as analytically and numerical both by various authors. Due to complexity of the considering problem the analytics is available only in simple cases. The main complexity of this problem relates with the internal boundary moving. The numerical solution of this incorrect problem is not simple. To date, a few of regularization methods proposed for the solution of Stefan problems by various authors. The main goal of this paper is investigate regularization of considering problem by omitting of classic Stefan condition at interface boundary. For solving of regularized problem we apply two different finite difference schemes of the second order approximation. The first is a second order hybrid finite difference scheme in and the second is a uniform second order finite difference scheme. Computations in Open Source Octave environment were provided and numerical results obtained by different schemes compared together, and with analytical solution. Computations of ice accretion on the NACA 0012 airfoil computed by iceFoam solver and Messenger-Mayer model are presented.