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.

中文翻译：

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在 TPM 框架内模拟浮冰冻结过程

海冰是由地球两极地区，即北极和南极的海水冻结形成的浮冰。因此，可以形成由这些冰结构组成的封闭的光滑冰面。近年来，海冰演化的模拟，尤其是在气候模型中的使用，变得更加重要，例如，参见 Danilov 等人。（Geosci Model Dev 8:1747–1761, 2015）及其中的参考资料。在本文中，针对在平静海面和天气条件下由于冻结引起的浮冰合并的有限元模拟，引入了基于多孔介质理论的耦合宏观模型。注意温度发展的描述，能量的测定，焓，水和冰之间的比热和质量交换以及由于冻结过程中冰形成而导致的体积变形。主要思想是基于理论驱动的冰水相变演化方程，这保证了热力学的一致性。数值例子表明，简化模型确实能够模拟相变过程中的温度发展和能量效应。