论文标题
相位场模型的差异拉格朗日方案：一种离散的能量变异方法
A Variational Lagrangian Scheme for a Phase Field Model: A Discrete Energetic Variational Approach
论文作者
论文摘要
在本文中，我们为修改的相位模型提出了一个变性拉格朗日方案，该方案可以计算原始Allen-CAHN类型模型的平衡状态。我们的离散化基于根据流量图而言，基于规定的能量消散定律。通过采用离散的能量变化方法，该方案保留了原始能量散发法的变分结构，并且能量稳定。大量的数值测试表明，通过正确选择初始值，我们的方法可以产生所需的平衡，并使用少量网格点捕获薄的弥散界面。
In this paper, we propose a variational Lagrangian scheme for a modified phase-field model, which can compute the equilibrium states for the original Allen-Cahn type model. Our discretization is based on a prescribed energy-dissipation law in terms of the flow map. By employing a discrete energetic variational approach, this scheme preserves the variational structure of the original energy-dissipation law and is energy stable. Plentiful numerical tests show that, by choosing the initial value properly, our methods can produce the desired equilibrium and capture the thin diffuse interface with a small number of mesh points.
