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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.

A finite volume, semi‐implicit scheme, is proposed and discussed, which solves the two‐dimensional Euler equations for the hypersonic flow of a mixture of chemically reactive specie. The present scheme can be applied on a general, unstructured grid. The first order version guarantees non negativity of the densities and of the vibrational energies for arbitrarily large time steps. The semi‐implicit time discretization of advective terms and the fully implicit discretization of the highly nonlinear terms yield a simple and efficient computer algorithm. Numerical tests show that shocks are well captured and the correct profiles for the chemical specie are reproduced at low computational cost.