This work deals with the numerical solution of internal transonic flow problems. Currently we expect 1D and 2D inviscid flow of perfect gas modelled by the Euler equations. We use finite volume characteristic flux scheme, called VFFC scheme, which can be viewed as a generalization of Roe scheme. The dissipation matrix is computed analytically or numerically. We present numerical results for 1D shock tube problem computed by the second order method, where the spatial accuracy is due to linear reconstruction with the minmod limiter and temporal discretization is done using explicit three stage Runge-Kutta method. Further numerical results for 2D transonic flow in GAMM channel have been achieved by the first order method on structured quadrilateral as well as unstructured triangular meshes.