This paper describes the numerical simulation of unsteady flows due to incoming wakes and/or varying back pressure. The solution method is based upon the one-step finite-volume TVD Lax-Wendroff scheme. Dual time-step approach and multigrid algorithm are adopted to improve the computational efficiency of the baseline scheme. Numerical results for the transonic unsteady flow in a channel bump and the unsteady flow in a flat plate cascade and the VKI cascade are presented. This paper describes the numerical simulation of unsteady flows due to incoming wakes and / or varying back pressure. The solution method is based upon the one-step finite-volume TVD Lax-Wendroff scheme. Dual time-step approach and multigrid algorithm are adopted to improve the computational efficiency of the baseline scheme. Numerical results for the transonic unsteady flow in a channel bump and the unsteady flow in a flat plate cascade and the VKI cascade are presented.