On the choice of approximations in direct problems of nozzle design

Two problems are considered: the design of a supersonic nozzle with a uniform exit characteristic and the design of a subsonic nozzle part with a plane (straight) sonic line in the minimum cross section. It is shown how the choice of a nozzle profile approximation affects the direct solutions to variational gas dynamics problems. The nozzle profile is described by polynomials or splines (quadratic, cubic, rational). The varied variables are the profile's expansion coefficients in terms of basis functions or the parameters to be interpolated. It is shown that a priori information on the monotonicity of the desired profile improves the efficiency of the solution.