The size of computational domain has been a major factor in the numerical solution of fluid flows. In this paper a characteristic based model for the solution of external, inviscid compressible flows is presented. In this model, the asymptotic expansions of Riemann variables along with enhanced characteristic method have been used. Applying this .model enabled us to obtain accurate results for the flow over an airfoil. The numerical solutions are compared to that of other investigators, in which a good agreement would exist. The main importance of the far-field model is the computational domain reduction, while conserving the solution accuracy. Consequently, the number of grid points is reduced considerably, leading to a reduction in competing time –and memory specially in implicit schemes.