Modeling of freezing processes of ice floes within the framework of the TPM

Sea ice is floating ice which is formed by the freezing of ocean water in the polar regions of the Earth, i.e., the Arctic and the Antarctic. Thus, a closed smooth ice surface can be formed consisting of these ice configurations. In recent years, the simulation of sea ice evolution, especially for the use in climate models, became more important, see, for instance, Danilov et al. (Geosci Model Dev 8:1747–1761, 2015) and the references therein. In the present paper, a coupled macroscopic model based on the Theory of Porous Media is introduced in view of the finite element simulation of the coalescence of ice floes due to freezing in calm sea and weather conditions. Attention is paid to the description of the temperature development, the determination of energy, enthalpy, specific heat and mass exchange between water and ice as well as volume deformations due to ice formation during freezing. The main idea is based on a theoretically motivated evolution equation for the phase transition of ice and water, which guarantees the thermodynamical consistency. Numerical examples show that the simplified model is indeed capable of simulating the temperature development and energetic effects during phase change.