Vol. 13, no.1, 2021


Mathematical modeling of temperature changes impact on artificial ice islands

Maxim V. Muratov, Vladimir A. Biryukov, Denis S. Konov, Igor B. Petrov

Moscow Institute of Physics and Technology, https://mipt.ru/
Dolgoprudny 141701, Moscow region, Russian Federation
E-mail: max.muratov@gmail.com, biryukov.vova@gmail.com, konov1999@gmail.com, petrov@mipt.ru

Received December 21, 2020, peer-reviewed December 26, 2020, accepted December 29, 2020

Abstract: The article is devoted to the numerical solution of the Stefan problem for thermal effects on an artificial ice island. For modern tasks of the development of the Arctic, associated with the exploration and production of minerals, it is important to create artificial ice islands in the Arctic shelf, due to the speed of their construction, economic feasibility and other factors. The most important task for the exploitation of such islands is their stability, including against melting. This paper discusses the issue of the stability of ice islands to melting. For this, the Stefan problem on the change in the phase state of matter is formulated. An enthalpy solution method is constructed, and the applicability of this method is considered. For the numerical solution, the Peasman-Reckford scheme is used, which is unconditionally spectrally stable in the two-dimensional case, which allows to freely choose the time step. In addition, the developed approach takes into account the flow of water and the flow of melted water, which is important in the task at hand. The developed computational algorithms are parallelized for use on modern multiprocessor computing systems An approach is implemented for modeling thermal processes in the thickness of an arbitrary mass of substances, taking into account arbitrary initial conditions, environmental conditions, tidal currents of water, and solar radiation. This approach was used to calculate the temperature distribution in the thickness of the ice island, as well as to study the impact of seasonal temperature changes on the stability of the island.

Keywords: mathematical modeling, ice island, Stefan problem, enthalpy method, Peasman-Rechford scheme

UDC 004.94

RENSIT, 2021, 13(1):79-86. DOI: 10.17725/rensit.2021.13.079.

Full-text electronic version of this article - web site http://en.rensit.ru/vypuski/article/372/13(1)79-86e.pdf