  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.
