A method of solving the parabolized Navier–Stokes equations by the global iterations

A numerical method for solving of two-dimensional steady supersonic flow problems over blunt bodies which is based on the parabolized Navier–Stokes equations is proposed. The method is based on carrying out global iterations over marching coordinate, presently coinciding with the length of body circuit. Initial value problem regularity in each global iteration at the presence of large subsonic flow regions near the bluntness and in the vicinity of the body is provided with the approximation of the marching coordinate derivative of pressure, occuring over the pressure values in upstream point, which are calculated from the previous global iteration. Therefore the combined problem is solved by the common algorithm. Application of finite difference scheme of the fourth order of approximation allows to perform calculations following the proposed algorithm, at rather large Reynolds numbers on a grid with moderate number of sites. Comparisons of the results, obtained from the solution of the body flow problems with the experimental data, with the solutions of viscous shock layer equations and that of the Boltzmann's equations for the low Reynolds number flow, are presented.