在凝固過程中所涉及的潛熱效應為重要的物理現象，本文以有限元素法利用不同數值方法處理潛熱效應分析相變化凝固熱傳問題的溫度場分佈。
本文主要探討的凝固問題為一維史帝芬問題及一維紐曼問題，將以改變元素幾何、時間步伐、處理比熱的方法來比較溫度場的準確性、潛熱釋放量、計算時間，其中溫度場的準確度以總誤差(total-error)做為比較之數據。而可變時間步伐方法分為GLS法及高斯溫度外插法,則在比熱處理有等效比熱法及等效比熱/熱焓法。
本文末的結論得出在史蒂芬問題GLS法的等效比熱法有減少溫度總誤差;則高斯溫度外插法則分別對潛熱的釋放及溫度總誤差有正向貢獻。紐曼問題使用GLS法及高斯溫度外插法的等效比熱法都有效提升潛熱的釋放量，但兩者時間步伐的計算時間則有所不同。然而藉由本文的方法可選擇較優的時間步伐方法及數值方法，既不會損失太大的潛熱釋放且可減少計算時間多寡。而未來須著重在程式撰寫的精簡性及一致性，例:時間步伐迴圈次數與固定時間步伐相當等等…,讓更多非撰寫程式的人了解結果的差異。

The latent heat effect is an important physical phenomenon during the solidification process. In the research, FROTRAN programs are written to simulate solidification heat transfer problems such as one-dimensional Stefan and Neumann problems with the finite element method and adaptive time step scheme. In this study, a variety of ways are chosen to solve the two problems. Three kinds of element are used, three-node triangular, four-node quadrilateral and nine-node quadrilateral elements. The calculation of latent heat release uses the effective specific heat method and enthalpy/specific heat method. Two Adaptive time step schemes are utilized, which are the Gaussian temperature extrapolation method and the GLS method. The Gaussian method is employed to solve the integrations in the finite element equations based on the different Gaussian points. In order to know which one is good. The accuracy of the temperature distributions are compared by changing element geometry, time step, and the way of handling the release of latent heat. With the effective specific heat method, the GLS scheme in the Stefan problem only reduces total error, while the Gaussian temperature extrapolation method contributes to the completeness of latent heat and the decrease of total error. In the Neumann problem, the GLS method and Gaussian temperature extrapolation scheme are effective to improve the calculation of latent heat release, but the computation time is different. However, we could choose the optimal time step method and numerical method to deal with the problem of solidification, which would not lose too much latent heat released and reduce the computation time. In the future, we should focus on the simplification and consistency of program writing. It is expected that this would help non-program-writers understand the differences of the results by using different solution schemes.

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