Grain growth in polycrystals is one of the principal mechanisms that take place during heat treatment of metallic components. This work treats an aspect of the anisotropic grain growth problem. By applying the first principles of thermodynamics and mechanics, an expression for the velocity field of a migrating grain boundary with an inclination dependent energy density is expressed. This result is used to generate the first, to the authors' knowledge, analytical solution (for both the form and kinetics) to an anisotropic boundary configuration. This new benchmark is simulated in order to explore the convergence properties of the proposed level set finite element numerical model in an anisotropic setting. Convergence of the method being determined, another configuration, using a more general grain boundary energy density, is investigated in order to show the added value of the new formulation.

中文翻译：

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用于各向异性晶界迁移的新水平集有限元公式

多晶中的晶粒生长是金属部件热处理过程中发生的主要机制之一。这项工作处理各向异性晶粒生长问题的一个方面。通过应用热力学和力学的第一原理，表达了具有倾斜相关能量密度的迁移晶界的速度场的表达式。据作者所知，该结果用于生成各向异性边界配置的第一个解析解（对于形式和动力学）。模拟这个新的基准是为了探索所提出的水平集有限元数值模型在各向异性设置中的收敛特性。正在确定的方法的收敛性，另一种配置，使用更一般的晶界能量密度，