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afterbody AIAA Journal axial direction blunt forebodies boattail surface Bodies of Revolution body geometry body surface boundary layer effects boundary-layer calculation CALCULATION OF TRANSONIC coefficient functions coefficient in inviscid component in axial computational convergence Damping ratio defined in eqs derivative with respect displacement thickness end of boattail equa extremely sensitive character flow conditions flow is subsonic flow past boattails flow separation free-stream Mach numbers functions at point grid points high subsonic free-stream inviscid analysis inviscid calculation inviscid flow field iteration Jameson ref Lewis Research Center momentum thickness NASA normalized disturbance potential numerical calculations partial derivative Performing Organization point where flow pressure coefficient radial relaxation results obtained Reynolds number shape factor shown in figure Slender Bodies small disturbance theory South and Jameson speed of sound Stagnation point stretching parameter subsonic free-stream Mach Theoretical results tion TRANSONIC BOATTAIL FLOW transonic flow past Turbulent Boundary Layers upstream viscous effects viscous flow viscous layer