An analytical solution for supersonic flow over a circular cylinder using an optimized shock shape

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.