Efficient and accurate numerical scheme for a magnetic-coupled phase-field-crystal model for ferromagnetic solid materials
Efficient and accurate numerical scheme for a magnetic-coupled phase-field-crystal model for ferromagnetic solid materials
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DOI：
10.1016/j.cma.2020.113310
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发表时间：
2020-11
影响因子：
7.2
通讯作者：
Jun Zhang;Xiaofeng Yang
中科院分区：
文献类型：
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作者：
Jun Zhang;Xiaofeng Yang
本文考虑铁磁固体材料磁耦合相场-晶体模型的数值逼近。控制PDE系统由两个耦合的、高度非线性的方程组成，其中一个是原子密度的Cahn-Hilliard方程，另一个是磁化场的Allen-Cahn方程。为了解决这个问题，我们在最近发展的稳定化SAV方法的基础上构造了一个具有时间二阶精度的无条件能量稳定格式。证明了格式的能量稳定性，并通过二维和三维数值算例验证了格式的稳定性和精度，包括无磁和磁耦合两种情况下的晶体生长和相分离。
In this paper, we consider numerical approximations for the magnetic-coupled phase-field-crystal model for ferromagnetic solid materials. The governing PDE system consists of two coupled and highly nonlinear equations in which one is the Cahn–Hilliard equation for the density of atoms, and the other is the Allen–Cahn equation for the magnetization field. To solve it, we construct an unconditionally energy stable scheme with the second-order accuracy in time based on the recently developed stabilized-SAV approach. The energy stability of the scheme is proved, and the stability and accuracy are then demonstrated numerically by implementing various numerical examples in 2D and 3D, including the crystal growth and phase separations for both of the magnetic-free and magnetic-coupled cases.