基于简化的晶粒形状，建立了模拟晶粒生长形貌的二维数学物理模型。
On the basis of the simplified grain shape, the physical model and mathematical model for the simplified dendrite shape were established.
根据二维非稳态导热的数学模型和物理模型，编写了可视化软件。
According to the physics and mathematics model of two-dimensional unsteady heat conduction, we wrote the visualization software.
通过变量变换，分离变量等数学手段，将二维数值模型转化为一维数值模型，得出了公式简单实用，物理意义明确的解析解。
Through mathematic means of variant separation and transformation, 2d numerical model was changed into 1d numerical model and acquire the single analytic solution of the equation.
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