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Shape transformation using the modified Allen–Cahn equation
Applied Mathematics Letters ( IF 3.7 ) Pub Date : 2020-05-17 , DOI: 10.1016/j.aml.2020.106487
Hyundong Kim , Sungha Yoon , Jian Wang , Chaeyoung Lee , Sangkwon Kim , Jintae Park , Junseok Kim

In this paper, we propose a phase-field model for the shape transformation and its simple numerical method. The proposed phase-field model is based on the Allen–Cahn equation, which is a second-order nonlinear parabolic partial differential equation and originally arises from modeling phase separation in alloys. The numerical scheme is a hybrid method using the operator splitting method. To validate the proposed phase-field model for the shape transformation, we perform two- and three-dimensional shape metamorphosis. The proposed phase-field model is also compared with the linear interpolation. The computational results demonstrate that the proposed mathematical model satisfactorily and naturally simulate the shape transformation.



中文翻译:

使用修正的Allen–Cahn方程进行形状变换

在本文中,我们提出了一种用于相变的相场模型及其简单的数值方法。提出的相场模型基于Allen-Cahn方程,该方程是二阶非线性抛物线偏微分方程,最初是通过对合金中的相分离建模而产生的。数值方案是使用算子拆分方法的混合方法。为了验证所提出的用于相变的相场模型,我们执行了二维和三维形状变形。所提出的相场模型也与线性插值进行了比较。计算结果表明,所提出的数学模型令人满意且自然地模拟了形状变换。

更新日期:2020-05-17
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