The RANS equations coupled with modified S-A model in a rotating reference frame are solved using the high-order discontinuous Galerkin method (DGM). In order to obtain more accurate wall boundaries on relatively coarse grids, a multilevel high-order curved mesh method is employed. An implicit dual time stepping method is adopted for the unsteady simulation, while generalized minimal residual method (GMRES) is deployed to solve the large linear system generated in each time step. The lift and moment hysteresis curves of rotating cylinder flow and classical airfoil oscillation are calculated. The correctness and validity of the proposed method are verified by comparing with the experimental results and previous calculation results.