Convexity splitting in a phase field model for surface diffusion
Convexity splitting in a phase field model for surface diffusion
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发表时间：
2017-10
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通讯作者：
R. Backofen;S. Wise;M. Salvalaglio;A. Voigt
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作者：
R. Backofen;S. Wise;M. Salvalaglio;A. Voigt
针对表面扩散相场模型，提出了精度较高的类凸分裂格式。这些方案是为了能够在三个空间维度上进行大规模模拟，描述实验观察到的固体脱湿现象。我们引入了一阶和二阶无条件能量稳定格式，并详细阐述了这种格式中与大时间步长相关的精度损失。然后给出了一类Rosenbrock凸分裂格式。我们证明了最大数值时间步长的存在性，并使用Rosenbrock方法证明了这个最大数值时间步长的增加至少一个数量级。该方案用于研究接触角对固体脱湿现象的影响。
Convexity splitting like schemes with improved accuracy are proposed for a phase field model for surface diffusion. The schemes are developed to enable large scale simulations in three spatial dimensions describing experimentally observed solid state dewetting phenomena. We introduce a first and a second order unconditionally energy stable scheme and carefully elaborate the loss in accuracy associated with large time steps in such schemes. We then present a family of Rosenbrock convex splitting schemes. We show the existence of a maximal numerical timestep and demonstrate the increase of this maximal numerical time step by at least one order of magnitude using a Rosenbrock method. This scheme is used to study the effect of contact angle on solid state dewetting phenomena.