有限元素法解對流－擴散問題的探討

陳義麟 ； 陳哲雄

《船舶科技》 6期 (1991/05) Pp. 89-105

https://doi.org/10.30037/MT.199105.0005

摘要

有限元素法是一種能求得許多工程問題近似解的數值分析技巧。雖然最初它是被用來研究複雜航空結構的應力分佈，但迄今已被延伸應用於廣泛的連體力學上。因為這個分析工具具有的多變性與靈活性，所以它受到工業界廣泛的注意。而在熱交換器的計算分析上由於求解穩態及瞬態對流－擴散方程式時，當元素的Peclet值較大時其解會有嚴重的振盪現象產生。因而我們必須瞭解具振盪的原因及其所隱含的意義。在利用遞推關係求解瞬態問題時，我們有兩種方法。即內隱法與外顯法，利用這兩種方法在計算時因其計算效率，準確性及穩定性差異很大，因此我們必須加以比較及探討。

並列摘要

The finite element method is a numerical analysis technique for obtaining approximate solutions to a wide variety of engineering problems. Although originally developed to study the stresses in complex airframe structures, it has since been extended and applied to the broad field of continuum mechanics .Because of its diversity and flexibility as an analysis tool, it is receiving much attention in industry. In analysis of the heat exchanger, because of to solve the convection diffusion problem on the transient stateand stady state, when the peclet number are larger, strong oscillatory variations are present in the numerical solution. Therefor, we must understand the reason of oscillatory and the meaning of it. on appling the recurrence relations to solve the transient state problem there are two methods can use. That is explicit method and implicit method. Basicly the two methods, in conputational efficiency, accuracy, and stability, are quite different. Thus we need to have intensified investigation.