Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

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• 作者：Xiaofeng Yang^a ; ^{xfyang@math.sc.edu} ; Daozhi Han^b ; ^djhan@iu.edu
• 关键词：Phase-field crystal ; Second order ; Linear scheme ; Cahn&ndash ; Hilliard ; Unconditional energy stability
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：330
• 期：Complete
• 页码：1116-1134
• 全文大小：5957 K
• 卷排序：330

文摘

In this paper, we develop a series of linear, unconditionally energy stable numerical schemes for solving the classical phase field crystal model. The temporal discretizations are based on the first order Euler method, the second order backward differentiation formulas (BDF2) and the second order Crank–Nicolson method, respectively. The schemes lead to linear elliptic equations to be solved at each time step, and the induced linear systems are symmetric positive definite. We prove that all three schemes are unconditionally energy stable rigorously. Various classical numerical experiments in 2D and 3D are performed to validate the accuracy and efficiency of the proposed schemes.