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系統識別號 U0026-2108201911595200
論文名稱(中文) 以修正GLS法與有限差分法分析凝固熱傳問題
論文名稱(英文) Numerical Analysis of Solidification Heat Transfer Problems By Using Modified GLS Scheme and Finite Difference Methods
校院名稱 成功大學
系所名稱(中) 工程科學系
系所名稱(英) Department of Engineering Science
學年度 107
學期 2
出版年 108
研究生(中文) 劉宇岍
研究生(英文) Yu -Chien Liu
學號 N96064361
學位類別 碩士
語文別 中文
論文頁數 102頁
口試委員 指導教授-趙隆山
口試委員-張建宏
口試委員-彭勳章
中文關鍵字 有限差分法  GLS法  可變時間步伐  修正截尾誤差  等效比熱法  等效比熱/熱焓法  史蒂芬問題  紐曼問題 
英文關鍵字 GLS method  effective specific heat method  effective specific heat/enthalpy method  adaptive time step 
學科別分類
中文摘要 在凝固熱傳問題中,相變化的過程中會有潛熱釋放的效應,而潛熱釋放會影響溫度場分布。本文以有限差分法和不同的數值方法與時間步伐方法分析凝固熱傳問題。
本文主要探討的一維暫態性熱傳、一維史蒂芬問題和一維紐曼問題,處理潛熱釋放的數值方法有等效比熱法和等效比熱/熱焓法,時間步伐方法有固定時間步伐、GLS法(ε=1e-3)、修正GLS法(ε<1e-3)和修正截尾誤差(修正LTE)。透過不同的數值方法與時間步伐方法來比較溫度場分布的準確性、潛熱釋放量和CPU運算時間,其中溫度場的準確性以總誤差(Total error)當作比較依據。
從分析的結果發現,在求解一維暫態線性熱傳問題時,GLS法可以有效的節省CPU運算時間和維持一定的精準度;在求解一維史蒂芬問題時,等效比熱法搭配修正GLS法和修正截尾誤差確實能比GLS法求得更精準的數值解,而搭配等效比熱/熱焓法時,一階的Euler法卻比GLS法來的精準;在求解一維紐曼問題時,等效比熱法和等效比熱/熱焓法搭配修正GLS法和修正截尾誤差比GLS法精準。
英文摘要 In the solidification heat transfer problems, the latent heat is released during the phase change process, affecting the distribution of temperature field. In this study, the solidification heat transfer problems are analyzed by using the finite difference methods, different numerical methods and time discretization techniques. Furthermore, the one-dimensional transient heat transfer problem, Stefan problem and Neumann problem will be investigated. The numerical methods for calculating latent heat release are the effective specific heat method and effective specific heat/enthalpy method. As for the time discretization techniques, the uniform time step, GLS methods(ε=〖10〗^(-3)), modified GLS methods(ε<〖10〗^(-3)) and modified local time truncation error scheme are utilized. In order to compare the accuracy of various numerical methods, the temperature field distribution, latent heat release and CPU computation time are important basis. From the analysis results, it is found that the GLS method can effectively save the CPU computation time and maintain precision when solving the one-dimensional transient heat transfer problem. In solving the Stefan problem, the effective specific heat method combined with the modified GLS method and modified local time truncation error scheme can be more accurate than the GLS methods. For the effective specific heat/enthalpy method, the first-order Euler methods is more precise than the GLS methods. However, when solving the Neumann problem, the effective specific heat method and the effective specific heat/enthalpy method combined with the modified GLS method and the modified local time truncation error scheme are more accurate than the GLS methods.
論文目次 摘要 I
Abstract II
致謝 XVII
目錄 XVIII
表目錄 XX
圖目錄 XXI
符號介紹 XXIX
第一章 緒論 1
1-1 前言 1
1-2 文獻回顧 2
1-3 研究方法與目的 4
第二章 相變化熱傳問題與數值方法 5
2-1 暫態線性熱傳問題 5
2-2 史蒂芬問題(Stefan Problem) 6
2-3 紐曼問題(Neumann Problem) 8
2-4 等效比熱法(Effective specific heat method) 11
2-5 等效比熱/熱焓法(Effective specific heat/enthalpy method) 12
2-6 鬆弛法(Relaxation method) 13
第三章 可變時間步伐理論 18
3-1 GLS法 18
3-1-1 簡介與理論 18
3-1-2 截尾誤差與步伐計算 19
3-2 修正GLS法(Modified GLS method, MGLS) 21
3-3 修正截尾誤差(修正LTE) 22
3-3-1 定義Δtext 23
3-3-2 Δtext時間步伐的選擇 24
3-3-3 Δtext初始化 24
3-3-4 Δtext在相變化問題上之調整 25
第四章 結果與討論 26
4-1 一維暫態熱傳問題 27
4-2 史蒂芬問題 28
4-2-1 史蒂芬問題之等效比熱法固定時間步伐 29
4-2-2 史蒂芬問題之等效比熱法可變時間步伐 29
4-2-3 史蒂芬問題之等效比熱/熱焓法固定時間步伐 31
4-2-4 史蒂芬問題之等效比熱/熱焓法可變時間步伐 31
4-3 紐曼問題 33
4-3-1 紐曼問題之等效比熱法固定時間步伐 34
4-3-2 紐曼問題之等效比熱法可變時間步伐 34
4-3-3 紐曼問題之等效比熱/熱焓法固定時間步伐 36
4-3-4 紐曼問題之等效比熱/熱焓法可變時間步伐 36
第五章 結論 98
參考文獻 100

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