本論文說明與討論應用三震波匯流場十次多項式方程式結合斜震波理論計算穩態馬赫反射 (SMR) 或 (局部) 擬似馬赫反射 (PMR) 流場三震波理論多重解的方法。求解 SMR或局部PMR流場多重解較易了解的方法係由入射與反射斜震波極上交點解的移動行為著眼，因為它們分別控制了( 與 ) 及( 與 )的解之行為。我們由十次多項式方程式計算得到馬赫莖壓力比值後代入論文中T1與G1斜震波關係式可求得 與 。隨後應用SMR機械平衡條件多項式方程求解其 ，若該解小於給予SMR題目的 ，則所得到的 與 解為需分別修改成180°- 及- 以成為Inverse MR 解; 否則所得到的 與 解就是正確的MR之 與 解。我們其次應用T1與H1斜震波關係式及分離流的轉折角邊界條件可求得 與 ，隨後應用SMR前後分界條件的多項式方程求解其 ，若該解小於給予SMR題目的 ，則所得的 與 解就是後向反射震波MR正確的答案; 否則所得到該 與 解需分別修改成180°- 及- 以成為前向反射震波MR正確之 與 的解。

Methods of calculating multiply possible theoretical solutions of steady Mach reflections (MR) or (local) pseudo-steady MR using the tenth degree polynomial equation of three-shock confluences combining with oblique shock calculations are discussed and summarized.

1. Multiply possible theoretical solutions of steady MR or (local) pseudo-steady MR can be better understood by moving along the incident oblique shock polar for and , and along the reflected shock polar for and . The intersected solutions move from beneath to , then to forward- and consequently to backward-facing reflected shock solutions, and they finally enter inverse MR solutions, as ’s systematically decrease from beyond forbidden ( < 1) to forbidden then to incident Mach angle conditions. It is impossible for intersected solutions to move into the weak branch of left orienting incident shock polars.
2. First, obtaining the Mach stem pressure ratio from the SMR tenth degree polynomial equation, then using oblique shock relations calculating and , respectively. Secondly, theoretical von Neumann condition polynomial equation is applied to determine its . If the problem given < von Neumann’s , the obtained and are inverse MR solutions with being 180°- and being - . Otherwise, the obtained and are correct solutions of MR.
3. Pressure jump across the reflected shock can be readily determined from the Mach stem pressure ratio. The same oblique shock relations of part 2, the oblique shock relations of pressure ratio and up-/down-stream flow Mach numbers and the slipstream deflection compatibility relations are then used to calculate and . Thirdly, theoretical separating forward-/backward- facing reflected shock polynomial equation is applied to determine its . If the problem’s <separating forward-/backward-facing reflected shock solution’s , the obtained and are correct backward-facing reflected shock solutions. Otherwise, they are forward-facing reflected shock solutions with being 180°- calculated and being –calculated . A better way of determining is by = - with being correctly calculated in the first place.

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