本論文首先應用近十年來成大工科所震波管流場實驗室所發表的穩態馬赫反射(SMR)與擬似穩態馬赫反射(PMR)流場之Wuest I/ Wuest II、反射震波前後分界、馮努曼(vN)條件、反射震波強弱分界、反射震波下游音速條件與正常震波反射分離準則，共六項特殊性質解多項式公式，計算、分析與討論這些不同性質理論解方程所得到的多重解，其解於SMR之(M0,Q1)平面上與PMR之(Ms,Qw )平面上所屬之解域。M0，穩態馬赫反射入射震波上游馬赫數；Q1 ，入射震波下游流場轉折角；Ms ，擬似穩態入射震波馬赫數；Qw ，楔形斜平面角。文中應用壓力-轉折角震波極圖解釋高度非線性此種馬赫反射流場中參震波理論解的多樣性。我們說明 之入射震波馬赫波角條件如何區隔SMR流場在(M0,Q1 )解域圖中上述六項特性曲線與 之入射震波馬赫波角條件如何區隔PMR流場在(Ms,Qw )解域圖中之此六項特性曲線，文中並說明這兩種馬赫反射流場之解域圖兩者之間相對應的關係。論文第二部份介紹震波折射流場中所發生的規則震波折射與不規則震波折射現象，在規則震波折射中分別改變入射震波馬赫數及系列變化入射震波波角(由小逐漸變大)以壓力-轉折角震波極圖分析與討論慢-快氣介面與快-慢氣介面可能發生之不同型態的震波折射理論多重解。不規則震波折射部份說明了理論上可能發生的三種不同型態之解。我們以壓力-轉折角震波極圖描述了此三種的不規則震波折射解並依斜震波與膨脹波理論繪出了它們對應的物理流場圖。最後整理出Henderson及其共同作者自1966至1991年間所發表五篇震波折射論文中有錯誤處，並說明我們不同計算與分析的結果。

This thesis calculates, analyzes and discusses multiply possible solutions of six characteristic steady (SMR) and pseudo-steady (PMR) Mach reflections using derived polynomial equations of special conditions of Wuest I, II, reflected backward/forward - facing separating, von Neumann, reflected strong/weak separating, reflected sonic, and regular reflection detachment criterion by Shock Laboratory of Engineering Science of National Cheng Kung University in the past decade. Analyses and discussions are primarily made on the plane for SMR and on the plane for PMR. M0 , incident shock Mach no. of SMR; Q1 , flow deflection downstream of incident shock; Ms, incident shock propagating shock Mach no. of PMR;Qw , reflecting wedge angle. Pressure-deflection shock polar diagrams are applied for illustrating three-shock theoretical solutions multiplicities of highly nonlinear steady and pseudo-steady Mach reflections. Incident shock Mach angle conditions, of SMR and of PMR, separating mathematically and physically different theoretical solution regions on the plane of SMR and plane of PMR are explained. In the second part of this work, regular and irregular shock refractions phenomena are discussed. By systematically varying incident shock Mach number and then, the incident shock angle from small to large, we analyze multiply possible solutions of both Slow-Fast and Fast-Slow regular shock refractions using oblique shock theory based pressure-deflection shock polar diagrams. For irregular shock refractions, three different theoretical solutions patterns discussed by Henderson & Macpherson (1968) are studied and examined. Theoretical oblique shock polar analyses of these three types of irregular shock refractions and their corresponding physical wave and deflection flow configurations are made and graphed, respectively. Finally, mistakes in shock refraction works by Henderson (1966), Henderson (1967), Henderson & Macpherson (1968), Abe-El-Fattah & Henderson (1978), Henderson et al. (1991) are reported and corrected calculations along with analyses and preliminary conclusions are then provided.

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