An implicit finite-difference method for chemical nonequilibrium flow through an axisymmetric supersonic nozzle

A second order accurate, noniterative, implicit procedure is developed for the stiff system of equations of a two dimensional chemical reacting supersonic flow. All equations are solved simultaneously at each grid point by treating the axial derivative terms implicitly, in order to make the scheme stable with respect to the chemical rates. By treating the radial derivative terms explicitly, the scheme becomes simple and has the advantage that only a relatively small computer storage is required. The computational efficiency is compared by investigating the arithmetic operational counts required to solve a linear algebraic equation system constructed in each implicit scheme. It is demonstrated that, although the marching step size of the proposed scheme is restricted due to the explicit treatment of radial derivative terms, the computational efficiency of the proposed scheme is superior to those of other schemes, especially for problems involving a large number of chemically reacting species. The practical computational time of the proposed scheme is also compared with that of an existing explicit implicit method.