界面耦合法在移動界面問題上的應用

Solving Some Moving Interface Problems by the Coupling Interface Method

劉思瀚(Ssu-Han Liu)

指導教授 ： 陳宜良

國立臺灣大學/理學院/數學研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.02098

摘要

由陳宜良教授以及舒宇宸教授所提出的界面耦合法目的在笛卡兒網格下解橢圓介面問題，此方法已被證明是處理界面問題中非常有競爭力的方法。在這篇論文,我們把界面耦合法應用在不同問題上,例如:一維移動界面問題、二維固定界面的熱傳導問題以及二維的融化問題等,我們也提供數值例子來驗證方法的收斂性。

關鍵字

界面耦合法 ； 移動界面問題 ； 交替方向隱式法 ； 克蘭克－尼科爾森方法 ； 融化問題 ； 界面追蹤法

並列摘要

The coupling interface method (CIM) proposed by Chern and Shu aims for solving elliptic complex interface problems in arbitrary dimensions under Cartesian grid. It has been proven that the method is very competitive in dealing with interface problems. In this thesis, we apply the CIM to various problems, including one dimensional moving interface problems, two dimensional diffusion equations with fixed interface, two dimensional melting problems, etc. Numerical examples are presented to test the accuracy of the method in these applications.

並列關鍵字

coupling interface method ； moving interface problems ； ADI method ； Crank-Nicolson scheme ； melting problems ； front tracking method

參考文獻

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