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Mathematical model and numerical simulation of faceted crystal growth

机译：多面晶体生长的数学模型和数值模拟

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A new mathematical macroscopic model is proposed to describe the nonstationary process of faceted crystal growth by the methods of directional crystallization with a slow change in external thermal conditions and low pulling rate of a cell through the growth system. The facet-growth rate is determined by the Stefan condition, integral over the face. Two boundary conditions are set for temperature: the continuity condition and the relation between the heat-flux jump and the supercooling at the facet points. The supercooling is determined by solving the entire heat problem. A facet is selected as a planar part of the phase boundary. The kinetic coefficient at the facet may depend on the supercooling. The energy conservation law is valid within the model developed. Examples of calculations of some model problems are presented. (C) 2005 Pleiades Publishing, Inc.
机译：提出了一种新的数学宏观模型，通过定向结晶的方法描述刻面晶体生长的非平稳过程，该方法具有外部热条件缓慢变化且细胞通过生长系统的提速低的特点。刻面增长速率由Stefan条件确定，该条件在脸上是不可或缺的。为温度设置了两个边界条件：连续性条件以及热流跳跃和刻面过冷之间的关系。过冷是通过解决整个热量问题来确定的。选择小平面作为相位边界的平面部分。小平面上的动力学系数可能取决于过冷度。节能规律在开发的模型内有效。给出了一些模型问题的计算示例。 （C）2005年Pleiades Publishing，Inc.

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