An energy-stable convex splitting for the phase-field crystal equation
An energy-stable convex splitting for the phase-field crystal equation
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DOI：
10.1016/j.compstruc.2015.05.029
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发表时间：
2014-05
影响因子：
4.7
通讯作者：
P. Vignal;Lisandro Dalcin;Donald L. Brown;N. Collier;V. Calo
中科院分区：
文献类型：
--
作者：
P. Vignal;Lisandro Dalcin;Donald L. Brown;N. Collier;V. Calo
相场晶体方程是一个抛物型的六阶非线性偏微分方程，作为解决分子动力学问题的一种可能途径，引起了人们的极大兴趣。尽管如此，求解这个方程并不是一个简单的任务，因为能量耗散和质量守恒需要验证数值解的有效性。这项工作解决了这些问题，并提出了一种新的算法，保证质量守恒，无条件的能量稳定性和二阶精度的时间。数值结果验证我们的证明，并显示了二维和三维模拟涉及晶体生长，突出了该方法的鲁棒性。
The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. Nonetheless, solving this equation is not a trivial task, as energy dissipation and mass conservation need to be verified for the numerical solution to be valid. This work addresses these issues, and proposes a novel algorithm that guarantees mass conservation, unconditional energy stability and second-order accuracy in time. Numerical results validating our proofs are presented, and two and three dimensional simulations involving crystal growth are shown, highlighting the robustness of the method.