An analytical solution for high supersonic flow over a circular cylinder based on Schneider's inverse method has been presented. In the inverse method, a shock shape is assumed and the corresponding flow field and the shape of the body producing the shock are found by integrating the equations of motion using the stream function. A shock shape theorised by Moeckel has been assumed and it is optimized by minimising the error between the shape of the body obtained using Schneider's method and the actual shape of the body. A further improvement in the shock shape is also found by using the Moeckel's shock shape in a small series expansion. With this shock shape, the whole flow field in the shock layer has been calculated using Schneider's method by integrating the equations of motion. This solution is compared against a fifth order accurate numerical solution using the discontinuous Galerkin method (DGM) and the maximum error in density is found to be of the order of 0.001 which demonstrates the accuracy of the method used for both plane and axisymmetric flows.

翻译：本文基于Schneider逆方法，提出了高超声速圆柱绕流的解析解。逆方法中，先假定激波形态，再通过流函数积分运动方程，求解产生该激波的对应流场及物面形状。采用Moeckel假定的激波形态，并通过最小化Schneider方法所得物面形状与实际物面形状的误差进行优化。进一步利用Moeckel激波形态的小量级数展开，改进激波形态。基于该激波形态，采用Schneider方法积分运动方程，计算了整个激波层流场。将该解与采用间断伽辽金法（DGM）的五阶精度数值解进行比较，发现密度最大误差量级为0.001，验证了该方法在平面和轴对称流动中的精度。