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A finite difference method for solving the quasi one‐dimensional non‐equilibrium hypersonic flow equations in a diverging nozzle is presented and discussed. In chemically reacting flows the system of equations to be solved is very stiff. Some reactions may be several orders of magnitude faster than others and generally, they are much faster than the convective process except for very high Ma numbers. For this reason the development of a numerical scheme whose stability is independent of the chemical reaction rates is of importance. The main advantage of this scheme is the conservation of each chemical component, the positivity of densities and vibrational energies, as well as its relative simplicity, which results in a fast computer code.

Some existing finite difference methods for the numerical solution of convection dominated diffusion equations are compared. Two semi‐implicit methods, Lagrangian based and applied on an Eulerian grid system, are then derived and discussed. The new methods are demonstrated to be transportive and unconditionally stable. Moreover, the artificial diffusion and the spurious oscillations of these methods are also analysed and compared. Extensions to n‐space variables and to non‐linear equations are indicated, along with various applications.