Linear second order energy stable schemes for phase field crystal growth models with nonlocal constraints
Linear second order energy stable schemes for phase field crystal growth models with nonlocal constraints
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DOI：
10.1016/j.camwa.2019.07.030
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发表时间：
2020-02
期刊：
影响因子：
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通讯作者：
Xiaobo Jing;Qi Wang
中科院分区：
文献类型：
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作者：
Xiaobo Jing;Qi Wang
我们提出了一套线性，二阶，无条件能量稳定的计划与非局部约束的晶体生长，保持每个阶段的质量的艾伦-卡恩模型。建立了由该方案得到的线性方程组的可解性条件。收敛速度进行了数值验证。使用Allen-Cahn模型与非局部约束的动力学进行了比较，得到一个使用经典的Allen-Cahn模型以及Cahn-Hilliard模型，分别表现出慢的动态比Allen-Cahn模型，但更快的动态比Cahn-Hilliard模型。因此，具有非局部约束的Allen-Cahn模型可以作为Cahn-Hilliard模型的替代模型来模拟晶体生长，同时保持每个相的质量。给出了两个Benchmark示例来对比四种模型的预测，强调了具有非局部约束的Allen-Cahn模型的准确性和有效性。
We present a set of linear, second order, unconditionally energy stable schemes for the Allen–Cahn model with nonlocal constraints for crystal growth that conserves the mass of each phase. Solvability conditions are established for the linear systems resulting from the schemes. Convergence rates are verified numerically. Dynamics obtained using the Allen–Cahn model with nonlocal constraints are compared with the one obtained using the classic Allen–Cahn model as well as the Cahn–Hilliard model, respectively, demonstrating slower dynamics than that of the Allen–Cahn model but faster dynamics than that of the Cahn–Hilliard model. Thus, the Allen–Cahn model with nonlocal constraints can serve as an alternative to the Cahn–Hilliard model in simulating crystal growth while conserving the mass of each phase. Two Benchmark examples are presented to contrast the predictions made with the four models, highlighting the accuracy and effectiveness of the Allen–Cahn model with nonlocal constraints.