A novel decoupled and stable scheme for an anisotropic phase-field dendritic crystal growth model
A novel decoupled and stable scheme for an anisotropic phase-field dendritic crystal growth model
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DOI：
10.1016/j.aml.2019.03.029
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发表时间：
2019-09
期刊：
影响因子：
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通讯作者：
Jun Zhang;Chuanjun Chen;Xiaofeng Yang
中科院分区：
文献类型：
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作者：
Jun Zhang;Chuanjun Chen;Xiaofeng Yang
本文考虑了相场枝晶生长模型的数值逼近，该模型是一个耦合各向异性Allen-Cahn型方程和热方程的高度非线性系统。通过将稳定不变能量二次化方法与一种新颖的解耦技术相结合，该方案在每个时间步只需要求解一系列线性椭圆方程，使其成为模型第一个完全解耦、线性、无条件能量稳定的方案。我们进一步严格地证明了无条件能量稳定性，并给出了各种数值模拟来证明其稳定性和准确性。
We consider numerical approximations for a phase-field dendritic crystal growth model, which is a highly nonlinear system that couples the anisotropic Allen–Cahn type equation and the heat equation. By combining the stabilized-Invariant Energy Quadratization method with a novel decoupling technique, the scheme requires solving only a sequence of linear elliptic equations at each time step, making it the first, to the best of the author’s knowledge, totally decoupled, linear, unconditionally energy stable scheme for the model. We further prove the unconditional energy stability rigorously and present various numerical simulations to demonstrate the stability and accuracy.