Abstract: An investigation is given on the theory of implicit approximate factorized finite difference firstly. The results show that the viscous Right-hand-side vector is a simple linear function of its basic variable vector. which is of great use for further application. A complicated turbulent flow field in a diffuser with typical geometric shape for aeroengine inlet design was calculated by the use of the implicit AF method. Studies show that the computational results are in agreement with the experimental data, which will provide the basis for the further study on three dimensional unsteady turbulent flows.

Key words: numerical analysis, viscous flow, two dimensional flow, diffusers