Abstract: A one step two order accuracy Implicit Flux Vector Splitting(IFVS)scheme is provided to solve the time average N S equations.Compared with conventional methods of implicit schemes,the present method is a Jacobian spectral radius scheme and a non approximate factorization scheme.Numerical calculations demonstrate clearly that it has obvious superiority in aspects of accuracy,robustness,calculation time and convergence.In the cases of two dimensional transonic cascade flows and diffusers,shock wave and separation are exactly captured,which shows good agreement with experimental data.

Key words: numerical analysis, transonic flow, shock wave, separation