Unsteady flow dynamics driven in an expansion tube was numerically reproduced by solving the axisym-metric compressible Navier-Stokes equations. The adaptive-mesh-refinement (AMR) technique was used to suppress a carbuncle phenomenon in the expansion tube. A numerical instability was sufficiently suppressed by utilizing a grid refined around the strong shock wave based on more than seventh level AMR. The maximum thickness of a boundary layer was estimated at approximately 16.5% of a radius of the expansion tube in a viscous flow. However, a speed of the shock wave obtained in the simulation was higher than measurements. The cause of the discrepancy was suspected for the high-temperature real-gas effect in the experiments.