潛熱釋放在凝固過程中的相變化是極為重要的物理現象，本文以有限元素法搭配等效比熱法、等效比熱/熱焓法、可變時間步伐之等效比熱法及可變時間步伐之等效比熱/熱焓法來處理潛熱效應，比較上述四種方法之所需計算時間、潛熱釋放多寡及溫度分佈準確度，並探討一維史帝芬問題、一維紐曼問題及二維瑞特延問題。其中利用溫度分佈之數值解與正解的總誤差(total-error)來比較各數值方法及節點的準確度。為使溫度分佈更精準，本研究藉由變換所採用之數值方法及調整參數來達到此目的，例如：縮小時間步伐、針對單位元素增加節點數、以不同形狀之元素組成求解區域及增加求解區域之節點數等等。
研究結果發現史帝芬問題加上可變時間步伐的等效比熱法溫度分佈及潛熱釋放的計算皆較準確，且電腦運算時間皆有減少，而等效比熱/熱焓法本身就很精準，因此加上可變時間步伐無法再提升溫度計算準確度，但可有效地減少運算時間；紐曼問題加上可變時間步伐亦不能增加準確度，但可提升計算效率；瑞特延問題使用三種元素節點所得液固界面皆很接近數值解，其中以四邊形元素平均誤差較小。

The phase change involving latent heat effect in a solidification process is an important physical phenomenon because it would affect the accuracy of the temperature distribution. In the thesis, FORTRAN programs of finite element method and adaptive time stepping scheme are written to simulate the heat transfer problems with phase change including one-dimensional Stefan and Neumann problems and two-dimensional Rathjen problem. The effective specific heat and the enthalpy/specific heat methods are applied to the calculation of the latent heat released during the phase change, which is related to the adaptive or uniform time step scheme and the node number and the geometry of the element, such as four-node quadrilateral and nine-node quadrilateral elements and three-node triangular element. Gaussian method is employed to solve the integral in the element equations. To compare the numerical methods, the accuracy of temperature, the release of latent heat, and the CPU time are utilized as the comparison base. From the analysis results, the quadrilateral element has the better accuracy of temperature than the triangular one. The adaptive time step of effect specific heat method could obtain greater accuracy of temperature and calculation efficiency than the uniform time step scheme. However, since the high accuracy is inherent in enthalpy/specific heat method, the adaptive time step is not more accurate than the uniform one. The calculated results of Neumann problem is similar to those of Stefan problem with the effective specific heat method. Whereas, the adaptive time step effective specific heat method could only reduce the calculation time but not improve the accuracy of temperature. For Rathjen problem, using triangular element brings out higher average error than applying quadrilateral element.

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