晶界迁移数值处理的进展：与质量输运和力学的耦合
Advances in the numerical treatment of grain-boundary migration: Coupling with mass transport and mechanics
摘要：
这项工作是基于一个耦合，晶格为基础的连续制剂，以前被应用到力学和质量传输之间的强耦合的问题，例如扩散蠕变和电迁移。在这里，我们讨论了这个配方的增强考虑迁移晶界。水平集方法是用来模拟晶界迁移的欧拉框架中的晶界表示为一个不断发展的高维函数的零水平集。这种方法可以很容易地推广到模型涉及迁移界面的其他问题，例如空洞的演变和自由表面形态的演变。水平集方程是重铸在一个非常简单的形式，避免了空间稳定技术的需要。这种简化的水平集公式利用速度扩展和场重新初始化技术。此外，一个最小二乘平滑技术被用来计算的局部曲率的晶界直接从水平集场，而不诉诸高阶插值。一个显着的特点是，质量传输，力学和晶界迁移之间的耦合是充分考虑。与此耦合的复杂性突出和运营商分裂算法用于解决耦合方程的描述。
英文摘要：
This work is based upon a coupled, lattice-based continuum formulation that was previously applied to problems involving strong coupling between mechanics and mass transport; e.g. diffusional creep and electromigration. Here we discuss an enhancement of this formulation to account for migrating grain boundaries. The level set method is used to model grain-boundary migration in an Eulerian framework where a grain boundary is represented as the zero level set of an evolving higher-dimensional function. This approach can easily be generalized to model other problems involving migrating interfaces; e.g. void evolution and free-surface morphology evolution. The level-set equation is recast in a remarkably simple form which obviates the need for spatial stabilization techniques. This simplified level-set formulation makes use of velocity extension and field re-initialization techniques. In addition, a least-squares smoothing technique is used to compute the local curvature of a grain boundary directly from the level-set field without resorting to higher-order interpolation. A notable feature is that the coupling between mass transport, mechanics and grain-boundary migration is fully accounted for. The complexities associated with this coupling are highlighted and the operator-split algorithm used to solve the coupled equations is described.
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