本文目的發展一套MUSCL type之真實黎曼解求解衝壓引擎內部震波捕捉。吾人採用Eulerian-Lagrangian (Unified)整合座標系統之Navier-Stokes方程式進行計算，此座標系統可避免Eulerian 座標系統過度的數值消散以及Lagrangian座標系統的嚴重網格變形，且可維持網格之間角度。數值方面，時間離散與空間離散分別使用Strang-splitting和Godunov通量分離法增加數值精度與穩定性，並且依據1982年，NASA分析衝壓引擎之進氣道外型進行數值模擬並進行比較，計算結果顯示本文所發展於unified座標系統下之MUSCL type之真實黎曼解可準確捕捉到震波以及震波/邊界層相互反應情況，與NASA之研究模擬相符。

In this study, we will develop exact Riemann Solvers of MUSCL type methods to capture shock wave in a scramjet inlet. By using Navier-Stokes equation in coupled Eulerian-Lagrangian coordinate system, we can not only avoid numerical diffusion in Eulerian approach but also avoid severe grid deformation in Lagrangian approach and preserve angle between grids. Numerically time discretion and spatial discretion are using Strang-Splitting method and Godunov flux splitting method, which can increase accuracy and stability. Finally, we take geometry of a scramjet inlet designed by NASA in 1982 and simulate flow-field in inlet to compare NASA’s effects. In our results, the simulation of shock waves and shock/boundary layer interaction are in satisfactory consistency with the computed data and NASA’s simulation results.

中文摘要 i 英文摘要 ii 致謝 iii 目錄 iv 圖與表目錄 vi 符號說明 viii 第一章 緒論 1.1 前言 1 1.2 文獻回顧 4 1.3 內容與組織架構 7 第二章 數值模式 2.1 統御方程式 9 2.2移動網格 13 2.3 邊界條件與架構 16 2.4真實黎曼解 17 2.5解析策略 25 第三章 數值結果 3.1平板流震波之捕捉 30 3.2震波與邊界層交互反應 34 3.3非對稱斜板震波捕捉 40 3.4衝壓引擎之進氣道數值模擬 44 第四章 總結 59 參考文獻 61

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