One dimensional gas dynamic analyses are widely used to predict the wave action phenomena in engine manifolds, and the flow velocity at the intake inlet or exhaust outlet may also be used to estimate the noise radiated by these systems. The accurate numerical methodology is required to capture the shocks and contact discontinuities in pipes, and to impose appropriate boundary conditions at the pipe junctions in engine simulation codes. The present study adopt the high order numerical scheme, shock capturingENO(Essentially Non-Oscillatory) upwind scheme with ACM(Artificial Compression Method), for pipe calculations. In comparison with a previous iterative method, a non-iterative procedure is devised that can also archive high-order accuracy in space with introducing Thompson's characteristic approach for the boundary coindition calculations. The key subjects are presented that include the numerical schemes for pipe flow and the non-iterative procedure for boundary condition as a first phase report.