Abstract: The influence of main/side jet and plume exists in a wide area around the intercepting maneuvering aircraft, and the traditional Navier-Stokes (N-S) equation cannot simulate the flow near the outlet of the engine nozzle expansion well, so a new method is needed to deal with the whole flow regime flow problem. In order to solve this problem, the Boltzmann model equation governing the flow in an axisymmetric nozzle under the rarefied environment of different Knudsen numbers is mathematically derived, and the numerical scheme and gas kinetic unified algorithm for the model equation are established. Numerical results for steady/unsteady rotating flow between two coaxial cylinders, as well as flow in an axisymmetric nozzle, both agree with existing studies, which verifies the reliability of the present algorithm in the whole flow regime. By comparing with the low-density wind tunnel experiment, the plume structure in the core area of the nozzle outlet and the pressure profile along the plume axis from the simulation show good agreement with the experiment, which suggests that the proposed algorithm can effectively solve the problem of mixing in the multi-flow regime from the nozzle compression section to the expansion section, especially in the low-pressure vacuum environment near the outlet.