Efficient second order unconditionally stable time marching numerical scheme for a modified phase-field crystal model with a strong nonlinear vacancy potential
Efficient second order unconditionally stable time marching numerical scheme for a modified phase-field crystal model with a strong nonlinear vacancy potential
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DOI：
10.1016/j.cpc.2019.106860
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发表时间：
2019-12
期刊：
影响因子：
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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
在本文中，我们考虑数值近似求解一个修改的相位场晶体模型与强非线性空位势。我们开发了一种有效的时间推进数值格式，它结合了新开发的SAV方法与传统的稳定技术，其中一个新的辅助变量被引入到重新制定的模型和一个关键的线性稳定项被添加到稳定的计划，并保持所需的精度，同时使用大的时间步长。我们证明了无条件的能量稳定性的发展计划严格，并进行了大量的基准数值例子在二维和三维。通过与非稳定SAV格式的数值比较，证明了该格式的稳定性和精度。
In this paper, we consider numerical approximations for solving a modified phase-field crystal model with a strong nonlinear vacancy potential. We develop an efficient time marching numerical scheme which combines the newly developed SAV approach with the traditional stabilization technique, where a new auxiliary variable is introduced to reformulate the model and a crucial linear stabilization term is added to stabilize the scheme and keep the required accuracy while using large time steps. We prove the unconditional energy stability of the developed scheme rigorously and perform numerous benchmark numerical examples in 2D and 3D. Through the comparisons with the non-stabilized SAV scheme, the stability and accuracy of the proposed scheme are demonstrated numerically.