Four different finite element level-set (FE-LS) formulations are compared for the modeling of grain growth in the context of polycrystalline structures and, moreover, two of them are presented for the first time using anisotropic grain boundary (GB) energy and mobility. Mean values and distributions are compared using the four formulations. First, we present the strong and weak formulations for the different models and the crystallographic parameters used at the mesoscopic scale. Second, some Grim Reaper analytical cases are presented and compared with the simulation results, here the evolutions of individual multiple junctions are followed. Additionally, large scale simulations are presented. Anisotropic GB energy and mobility are respectively defined as functions of the misorientation/inclination and disorientation. The evolution of the disorientation distribution function (DDF) is computed and its evolution is in accordance with prior works. We found that the formulation called "Anisotropic" is the more physical one but it could be replaced at the mesoscopic scale by an Isotropic formulation for simple microstructures presenting an initial Mackenzie-type DDF.

中文翻译：

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用于模拟各向异性晶粒生长的不同水平集公式的比较研究和限制

比较了四种不同的有限元水平集 (FE-LS) 公式，用于多晶结构背景下的晶粒生长建模，此外，首次使用各向异性晶界 (GB) 能量和迁移率展示了其中的两种公式. 使用四种公式比较平均值和分布。首先，我们介绍了不同模型的强弱公式以及在介观尺度上使用的晶体学参数。其次，介绍了一些死神分析案例并与模拟结果进行了比较，这里跟踪了单个多个连接点的演变。此外，还提供了大规模模拟。各向异性 GB 能量和迁移率分别定义为定向错误/倾斜和定向障碍的函数。计算了迷失方向分布函数 (DDF) 的演变，其演变与先前的工作一致。我们发现称为“各向异性”的公式是更具物理意义的公式，但它可以在介观尺度上被简单微观结构的各向同性公式取代，呈现初始 Mackenzie 型 DDF。