A conservative Allen–Cahn equation with a space–time dependent Lagrange multiplier
A conservative Allen–Cahn equation with a space–time dependent Lagrange multiplier
复制标题
DOI：
10.1016/j.ijengsci.2014.06.004
复制
发表时间：
2014-11
影响因子：
6.6
通讯作者：
Junseok Kim;Seunggyu Lee;Yongho Choi
中科院分区：
文献类型：
--
作者：
Junseok Kim;Seunggyu Lee;Yongho Choi
本文提出了一种新的数值格式，用于求解带有时空相关的拉格朗日乘子的守恒型Allen-Cahn方程。由于著名的经典Allen-Cahn方程不具有质量守恒性质，Rubinstein和斯滕贝格引入了一个非定域的Allen-Cahn方程，并引入了一个与时间相关的拉格朗日乘子来加强质量守恒。然而，在他们的模型中，很难保持小的特征，因为它们会溶解到体区域中。其中一个原因是，质量守恒是通过使用随时间变化的拉格朗日乘子的全局校正来实现的。为了解决这个问题，我们使用一个时空相关的拉格朗日乘子来保持系统的体积，并提出了一个实际无条件稳定的混合格式来求解模型。数值结果表明，我们提出的数值计算方案，精确计算的界面的几何特征的潜在有用性。
We present a new numerical scheme for solving a conservative Allen–Cahn equation with a space–time dependent Lagrange multiplier. Since the well-known classical Allen–Cahn equation does not have mass conservation property, Rubinstein and Sternberg introduced a nonlocal Allen–Cahn equation with a time dependent Lagrange multiplier to enforce conservation of mass. However, with their model it is difficult to keep small features since they dissolve into the bulk region. One of the reasons for this is that mass conservation is realized by a global correction using the time-dependent Lagrange multiplier. To resolve the problem, we use a space–time dependent Lagrange multiplier to preserve the volume of the system and propose a practically unconditionally stable hybrid scheme to solve the model. The numerical results indicate a potential usefulness of our proposed numerical scheme for accurately calculating geometric features of interfaces.