臺灣博碩士論文加值系統

本研究採用高階自然型式之函數進行局部座標與流場變數之分配，並利用此一分佈函數之變數變換進行格點高階流通量之微分計算，再搭配時間積分來完成穩態或非穩態流場之計算。此方法應用於一維非穩態震波管之模擬上，於次音速下採用低階之分佈函數需要較多之格點數才能與解析解一致，但是在超音速流動下即使使用再多的格點數亦無法以低階方式達成接觸不連續面之解析，必須採用高階方式才可以有效的解決此一問題。其應用在二維無黏性穩態流場之分析上，不論在低馬赫數、次音速、穿音速或是超音速流場上，其模擬結果皆與參考文獻相當接近。至於在二維移動平板黏滯穴流分析上，採用低階之微分量與通量計算也是需要相當多之計算格點才能獲得較佳之解答，若是將速度與溫度梯度採用高階之微分法，則能以較少之網格數達成高精度及低震盪之解答。

High order natural shape functions were used to interpolate the physical coordinates and flow quantities locally. To calculate the high resolution fluxes at a point is based on the chain rule between the computational domain and physical domain. The Runge-Kutta time integration was used to march the solution. For one-dimensional shock tube problem, a higher grid resolution is required for a lower order scheme. When the flow reaches supersonic in the shock tube, it is hard to match the analytical solution by just using grid refinement for a low order scheme. A high order differential operator scheme is proposed. For low Mach number, subsonic, transonic and supersonic flows pass the two-dimensional circular bump, the results of simulations are very similar to reference solutions. For the lid-driven cavity problem, low order scheme provides less accurate solutions. Using high order differential operator to calculate the gradient of velocity and temperature alleviates the problem of oscillation and accuracy.

中文摘要……………………………………………………………I
英文摘要……………………………………………………………II
致謝…………………………………………………………………III
目錄…………………………………………………………………IV
圖目錄………………………………………………………………VI

第一章 緒論
1.1 前言……………………………………………………1
1.2 文獻回顧………………………………………………1
1.3 採用方法………………………………………………2
1.4 文章安排………………………………………………2
第二章 統馭方程式
2.1 Navier-Stokes方程式………………………………… 3
2.2 Shock tube 解析解 ……………………………………4
第三章 數值方法
3.1時間積分 ………………………………………………9
3.2有限元素微分法 ………………………………………9
3.3時間步階計算…………………………………………10
3.4人工黏滯………………………………………………17
3.5邊界條件
3.5-1外流場……………………………………………………19
3.5-2固體壁面…………………………………………………21
第四章 結果與討論
4.1一維震波管問題
4.1-1次音速Sod’s problem……………………………………22
4.1-2超音速Sod’s problem……………………………………26
4.1-3超音速Shu-Osher Shock-Disturbance Interaction………34
4.2二維無黏性可壓縮流分析
4.2-1低馬赫數…………………………………………………36
4.2-2次音速……………………………………………………38
4.2-3穿音速……………………………………………………40
4.2.4超音速……………………………………………………42
4.3二維黏性低馬赫數可壓縮流分析……………………46

第五章 結論與未來工作
5.1結論……………………………………………………51
5.2未來工作………………………………………………52
參考文獻…………………………………………………53

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