Iterative solution of the equations for steady viscous compressible flow, based on similitude

A study was made of an iterative procedure for solving numerically the equations of steady viscous compressible flow. The method, based on a principle of similitude, was tested for the case of laminar two-dimensional hypersonic flow into a compression corner. The first two iterations gave an accurate description of the boundary layer, using less than 1 percent of the computer time required for time-marching integration of the equations for transient two-dimensional flow. However, the equations of the third iteration, in which development of separated flow and recirculation was to have begun, proved unstable. A plausible explanation for the unstable behavior of the third iterate was found. On that basis, alternate equations were developed that may permit stable iteration.