AbstractA finite difference scheme based on flux difference splitting is presented for the solution of the two‐dimensional Euler equations of gas dynamics in a generalized co‐ordinate system. The scheme is based on numerical characteristic decomposition and solves locally linearized Riemann problems using upwind differencing. The decomposition is for a generalized co‐ordinate system and a convex equation of state. This ensures good shock‐capturing properties when incorporated with operator splitting and the advantage of using body‐fitted co‐ordinates. The resulting scheme is applied to supersonic flow of real air' past a circular cylinder.