Modeling phase change problems using a new implementation of the numerical manifold method
Modeling phase change problems using a new implementation of the numerical manifold method
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DOI：
10.1016/j.apm.2017.01.022
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发表时间：
2017-08
影响因子：
5
通讯作者：
Y. L. Chen;L. X. Li
中科院分区：
文献类型：
--
作者：
Y. L. Chen;L. X. Li
相变是相界运动时出现的一种典型的不连续问题。根据本研究中描述的新实现，可以使用数值流形方法来模拟这种不连续性。本研究首先解释基本概念，如数学元素、数学覆盖、流形元素和物理覆盖。然后推导了相变问题的公式，并提出了一种通过创建和/或破坏多重元素和物理覆盖来解决移动相界面问题的技术。最后，给出了实例来验证新的实现。研究表明，无论是在规则区域还是在不规则区域，数值流形方法都能用规则网格平滑地捕捉到相变过程中的相界面，给出了令人满意的数值结果。
A phase change is a typical discontinuous problem that occurs when phase interfaces move. This discontinuity can be modeled using the numerical manifold method according to the new implementation described in this study. This study begins by explaining basic concepts, such as a mathematical element, mathematical cover, manifold element, and physical cover. Formulations are then derived for the phase change problem and a technique is also proposed for tackling the problem of moving phase interfaces via the creation and/or destruction of manifold elements and physical covers. Finally, practical examples are given to validate the new implementation. The present study shows that when solving phase change problems in either a regular domain or irregular domain, the numerical manifold method can smoothly capture the phase interfaces during the phase change process with a regular mesh to give highly satisfactory numerical results.