固体界面的Allen-Cahn相场模型的一种替代方法--数值效率
An alternative to the Allen-Cahn phase field model for interfaces in solids - numerical efficiency
摘要：
Allen-Cahn和Cahn-Hilliard方程的推导是基于Clausius-Duhem不等式。这不是严格意义上的推导，因为其他相场方程可以满足这个不等式。受尖锐界面问题形式的启发，我们提出了一种替代方程，并比较了弹性方程和Allen-Cahn方程或替代方程组成的固体相界面演化模型的性质。我们发现，数值模拟的相界面与小界面能的替代模型的基础上是更有效的模拟基于Allen-Cahn模型。
英文摘要：
The derivation of the Allen-Cahn and Cahn-Hilliard equations is based on the Clausius-Duhem inequality. This is not a derivation in the strict sense of the word, since other phase field equations can be fomulated satisfying this inequality. Motivated by the form of sharp interface problems, we formulate such an alternative equation and compare the properties of the models for the evolution of phase interfaces in solids, which consist of the elasticity equations and the Allen-Cahn equation or the alternative equation. We find that numerical simulations of phase interfaces with small interface energy based on the alternative model are more effective then simulations based on the Allen-Cahn model.
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