The solution of the parabolized Navier-Stokes equations by a fully implicit method

A fully implicit method of solving the Navier-Stokes equations in parabolic form for supersonic laminar flows has been developed. Full implicitness increases computational efficiency by allowing larger marching steps to be taken over methods which are not fully implicit. The present method utilizes shock fitting at one boundary and no-slip, temperature specified conditions at the other. Special attention was paid to the development of the boundary conditions and boundary point difference scheme in order to assure complete implicitness at the boundaries. The phenomenon of departure solutions is investigated and a theory developed to explain the origin of this behavior. The theoretical argument is supported by numerical results.