Abstract: Gas free jet with varies underexpanded pressure ratio was simulated numerically using second order positive schemes,which was developed to solve the axisymmetric Euler equations based on two dimensional conservation laws.Computational results indicate that the method can capture the wave structures of jet flow fields including shock cell structure,slip streams,jet boundary and the triple point well.Agreement between the numerical results and experimental data or third order discontinuous Galerkin finite element method is fairly satisfactory.For the Mach disk locations,excellent agreement is obtained between numerical results and experimental measurements.It indicates that the method have high capability in capturing shocks.A new method for this flow numerical study is presented.