A spectral collocation method for compressible, non-similar boundary layers

Abstract

An efficient and highly accurate algorithm based on a spectral collocation method is developed for numerical solution of the compressible, two-dimensional and axisymmetric boundary layer equations. The numerical method incorporates a fifth-order, fully implicit marching scheme in the streamwise (timelike) dimension and a spectral collocation method based on Chebyshev polynomial expansions in the wall-normal (spacelike) dimension. The spectral collocation algorithm is used to derive the nonsimilar mean velocity and temperature profiles in the boundary layer of a 'fuselage' (cylinder) in a high-speed (Mach 5) flow parallel to its axis. The stability of the flow is shown to be sensitive to the gradual streamwise evolution of the mean flow and it is concluded that the effects of transverse curvature on stability should not be ignored routinely.