Monotone nozzle shape by direct method

Two classical gas dynamics axisymmetric problems are considered: the design of a supersonic nozzle with a corner point in the minimum cross section and a uniform exit characteristic and the design of a subsonic nozzle part with a plane sonic line in the minimum cross section. Numerical solving was realized by a direct method by means of minimization of a suitable functional with a minimum corresponding to the optimum nozzle profile. At representation of a nozzle profile were used polynomials, splines and logarithmic functions. In some cases minimization with monotonicity constraits on a nozzle profile is the unique reason of success.